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  • Numerical Modeling of Simple Laboratory Experiments of Rotating Flows  Open access

     Lopez Alonso, Jose Manuel
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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    A pesar de que se han llevado a cabo numerosos estudios en el ámbito de los fluidos turbulentos, su dinámicaasí como las causas que originan la turbulencia continúan planteando multiples interrogantes. Los experimentos sobre transición a la turbulencia se realizan generalmente en instalaciones con geometrías sencillas que permiten aislar los mecanismos físicos responsables de los cambios dinámicos en el sistema. Sin embargo, el problema es muy complejo y, a pesar de la simplicidad de los experimentos, es muy dificil alcanzar conclusiones definitivas sobre muchos de los fenómenos que se observan. Desde hace unas décadas las simulaciones numéricas complementan el trabajo de laboratorio, lo que ha acelerado notablemente el progreso de las investigaciones y también mejorado su calidad. Para comparar de una manera eficaz los resultados numéricos y experimentales es esencial llevar a cabo un proceso de calibración, en el cual las posibles discrepancias se identifican y se realizan ajustes (normalmente modificaciones en la formulación del problema) para minimizarlas al máximo.Los resultados de esta tesis pretenden servir de ayuda en el proceso de calibración para el caso de fluidos en rotación y sometidos a un gradiente de temperatura, los cuales son de gran interés en aplicaciones industriales, geofísicas y astrofísicas. Se han realizado simulaciones numéricas del flujo contenido en cavidades cilíndricas y anulares, sometidos a gradientes térmicos tanto verticales como horizontales (convección de Rayleigh--Bénard rotativa y flujos de Taylor--Couette con calentamiento lateral). Entre las técnicas de ánalisis numérico que se han empleado para la realización de la tesisse encuentran la simulación directa de las ecuaciones, análisis de estabilidad lineal, métodos de continuación o análisis de series temporales.Se han investigado tres fuentes de discrepancias entre resultados numéricos y experimentales. En primer lugar mostramos un detallado estudio sobre como una rotura de simetría debida a imperfecciones en un experimento físico modifica la dinámica de los sistemas idealizados que se emplean en simulaciones numéricas. Un ejemplo en el caso de convección de Rayleigh--Bénard rotativa es ilustrado en el cual las simulaciones capturan el comportamiento experimentalcuando la rotura de simetría se introduce en la formulación del problema a través de las condiciones de contorno. En segundo lugar, consideramos la influencia de los efectos centrífugos, generalmente despreciados en el estudio de fluidos en rotación. Esto puede ocasionar importantes diferencias con los resultados experimentales en aquellos casosdónde las fuerzas centrífugas desempeñen un papel relevante. Por este motivo proporcionamos una sencilla aproximación de tipo Boussinesq que permite considerar los efectos centrífugos en un sistema de referencia inercial, incluyendo efectos secundarios debidos a la rotación diferencial o una fuerte vorticidad interna, los cuales no habían sido considerados en ninguna formulación anterior. Tercero, discutimos la influencia de las tapaderas en la dinámica de modelos simples para el estudio de flujos baroclínicos. El objetivo es identificar el grado en que simulaciones axialmente periódicas, con un menor coste computacional, pueden ser usadas para reproducir resultados experimentales. En este problema se observa que las capas límite producen un fuerte efecto estabilizador, que aumenta a medida que se incrementa el gradiente térmico, y provoca grandes discrepancias con respecto al origen de inestabilidad en el caso periódico. Finalmente, se ha realizado un estudio numérico de un escenario de bifurcación que ha sido reportado recientemente en experimentos sobre flujos de Taylor--Couette isotérmicos. La particularidad de este problema es la aparición de estados globales caracterizadospor oscilaciones de gran amplitud localizadas en algunos de sus vortices. Los resultados experimentales y numéricos concuerdan.

    Despite the large amount of research which has been conducted on turbulent flows, a full understanding of their dynamics as well as the mechanisms involved in the onset of turbulence is still missing. Experimental studies of transition to turbulence are generally carried out in setups with simple geometries which allow isolating the physical mechanisms underlying the dynamics. However, in spite of the simplicity of the models, the problem is extremely complex and it is difficult to reach definitive conclusions on many of the observed dynamical features. Since a few decades ago numerical simulations complement laboratory experiments, significantly accelerating the scientific progress and improving the quality of investigations. In order to compare experimental and numerical results, it is essential to carry out a calibration process in which the possible discrepancies are identified and adjustments (typically modifications in the numerical formulation of the problem) are made in order to minimize them as far as possible. The results of this thesis are primarily intended as an aid in the calibration process of rotating flows in presence of a temperature gradient, which are of great interest in multiple industrial, geophysical and astrophysical applications. Numerical simulations of the flow enclosed in rotating cylindrical and annular cavities subjected to either a vertical or horizontal temperature gradient (rotating Rayleigh--Bénard convection and laterally heated Taylor--Couette flows) have been performed. Several techniques of numerical analysis such as direct simulation of the governing equations, linear stability analysis, continuation methods or time--series analysis have been used for the completion of the thesis. Three sources of discrepancies between experimental and numerical results have been investigated. First,we show a detailed study of how symmetry-breaking due to experimental imperfections may modify the dynamics of the idealized systems used in numerical simulations. An example in rotating Rayleigh-Bénard convection is illustrated in which simulations only capture the experimental behavior when this symmetry-breaking is introduced in the formulation of the problem, i.e. through the boundary conditions. Second, we consider the influence of centrifugal effects which are often neglected in theoretical and numerical studies of rotating flows. This may result in substantial differences with experimental results in those ranges of parameters in which centrifugal buoyancy plays a significant dynamical role. To this extent, we provide a straightforward Boussinesq-type approximation which allows for considering centrifugal effects in an inertial reference frame, including secondary effects stemming from differential rotation or strong internal vorticity, which had not been previously considered in any other formulation. Third, the influence of axial end walls in the dynamics of simple models for the study of baroclinic flows is discussed. The objective of this study is to identify the degree to which simulations in axially periodic systems, with a lower computational cost, can be used to reproduce experimental results. A strong stabilizing effect, which increases significantly at high temperature differences between the cylinders, results from the boundary layers and cause large discrepancies with the onset of instability in the case of axially periodic boundary conditions. Finally, a numerical study of a recently reported experimental bifurcation scenario in isothermal Taylor-Couette flow is also presented. We focus on the dynamics of flow patterns characterized by large amplitude oscillations that are localized only in some vortex-pairs. In this case, experimental and numerical results are in full agreement.

    A pesar de que se han llevado a cabo numerosos estudios en el ámbito de los fluidos turbulentos, su dinámica así como las causas que originan la turbulencia continúan planteando multiples interrogantes. Los experimentos sobre transición a la turbulencia se realizan generalmente en instalaciones con geometrías sencillas que permiten aislar los mecanismos físicos responsables de los cambios dinámicos en el sistema. Sin embargo, el problema es muy complejo y, a pesar de la simplicidad de los experimentos, es muy dificil alcanzar conclusiones definitivas sobre muchos de los fenómenos que se observan. Desde hace unas décadas las simulaciones numéricas complementan el trabajo de laboratorio, lo que ha acelerado notablemente el progreso de las investigaciones y también mejorado su calidad. Para comparar de una manera eficaz los resultados numéricos y experimentales es esencial llevar a cabo un proceso de calibración, en el cual las posibles discrepancias se identifican y se realizan ajustes (normalmente modificaciones en la formulación del problema) para minimizarlas al máximo. Los resultados de esta tesis pretenden servir de ayuda en el proceso de calibración para el caso de fluidos en rotación y sometidos a un gradiente de temperatura, los cuales son de gran interés en aplicaciones industriales, geofísicas y astrofí­sicas. Se han realizado simulaciones numéricas del flujo contenido en cavidades cilíndricas y anulares, sometidos a gradientes térmicos tanto verticales como horizontales (convección de Rayleigh--Bénard rotativa y flujos de Taylor--Couette con calentamiento lateral). Entre las técnicas de ánalisis numérico que se han empleado para la realización de la tesis se encuentran la simulación directa de las ecuaciones, análisis de estabilidad lineal, métodos de continuación o análisis de series temporales. Se han investigado tres fuentes de discrepancias entre resultados numéricos y experimentales. En primer lugar mostramos un detallado estudio sobre como una rotura de simetrí­a debida a imperfecciones en un experimento fí­sico modifica la dinámica de los sistemas idealizados que se emplean en simulaciones numéricas. Un ejemplo en el caso de convección de Rayleigh--Bénard rotativa es ilustrado en el cual las simulaciones capturan el comportamiento experimental cuando la rotura de simetría se introduce en la formulación del problema a través de las condiciones de contorno. En segundo lugar, consideramos la influencia de los efectos centrífugos, generalmente despreciados en el estudio de fluidos en rotación. Esto puede ocasionar importantes diferencias con los resultados experimentales en aquellos casos dónde las fuerzas centrí­fugas desempeñen un papel relevante. Por este motivo proporcionamos una sencilla aproximación de tipo Boussinesq que permite considerar los efectos centrí­fugos en un sistema de referencia inercial, incluyendo efectos secundarios debidos a la rotación diferencial o una fuerte vorticidad interna, los cuales no habí­an sido considerados en ninguna formulación anterior. Tercero, discutimos la influencia de las tapaderas en la dinámica de modelos simples para el estudio de flujos baroclí­nicos. El objetivo es identificar el grado en que simulaciones axialmente periódicas, con un menor coste computacional, pueden ser usadas para reproducir resultados experimentales. En este problema se observa que las capas lí­mite producen un fuerte efecto estabilizador, que aumenta a medida que se incrementa el gradiente térmico, y provoca grandes discrepancias con respecto al origen de inestabilidad en el caso periódico. Finalmente, se ha realizado un estudio numérico de un escenario de bifurcación que ha sido reportado recientemente en experimentos sobre flujos de Taylor--Couette isotérmicos. La particularidad de este problema es la aparición de estados globales caracterizados por oscilaciones de gran amplitud localizadas en algunos de sus vortices. Los resultados experimentales y numéricos concuerdan.

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    Three-dimensional instabilities in a discretely heated annular flow: onset of spatio-temporal complexity via defect dynamics  Open access

     Marques Truyol, Francisco; Lopez, Juan M
    Physics of fluids
    Vol. 26, num. 6, p. 1-17
    DOI: 10.1063/1.4881435
    Date of publication: 2014-06-10
    Journal article

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    The transition to three-dimensional and unsteady flow in an annulus with a discrete heat source on the inner cylinder is studied numerically. For large applied heat flux through the heater (large Grashof number Gr), there is a strong wall plume originating at the heater that reaches the top and forms a large scale axisymmetric wavy structure along the top. For Gr approximate to 6 x 109, this wavy structure becomes unstable to three-dimensional instabilities with high azimuthal wavenumbers m similar to 30, influenced by mode competition within an Eckhaus band of wavenumbers. Coexisting with some of these steady three-dimensional states, solution branches with localized defects break parity and result in spatio-temporal dynamics. We have identified two such time dependent states. One is a limit cycle that while breaking spatial parity, retains spatio-temporal parity. The other branch corresponds to quasi-periodic states that have globally broken parity. (C) 2014 AIP Publishing LLC.

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    Rapidly rotating cylinder flow with an oscillating sidewall  Open access

     López Moscat, Juan Manuel; Marques Truyol, Francisco
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 89, num. 1, p. 1-14
    DOI: 10.1103/PhysRevE.89.013013
    Date of publication: 2014-02-17
    Journal article

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    We present numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing via axial oscillations of the sidewall. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. For very fast rotations, these waves approach the form of the characteristics predicted from the linearized inviscid problem first studied by Lord Kelvin. The driving mechanism for the inertial waves is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom end walls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves but beyond that does not interfere with them. We show that the system loses stability to complicated three-dimensional flow when the sidewall oscillation displacement amplitude is very large (of the order of the cylinder radius), but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. This is in contrast to many other physical realizations of inertial waves where the driving mechanisms tend to lead to instabilities and complicate the study of the waves. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques.

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    Confined rotating convection with large Prandtl number: Centrifugal effects on wall modes  Open access

     Curbelo Hernández, Jezabel; López Moscat, Juan Manuel; Mancho Sánchez, Ana María; Marques Truyol, Francisco
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 89, num. 1, p. 1-8
    DOI: 10.1103/PhysRevE.89.013019
    Date of publication: 2014-01-23
    Journal article

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    Thermal convection in a rotating cylinder with a radius-to-height aspect ratio of Gamma = 4 for fluids with large Prandtl number is studied numerically. Centrifugal buoyancy effects are investigated in a regime where the Coriolis force is relatively large and the onset of thermal convection is in the so-called wall modes regime, where pairs of hot and cold thermal plumes ascend and descend in the cylinder sidewall boundary layer, forming an essentially one-dimensional pattern characterized by the number of hot and cold plume pairs. In our numerical study, we use the physical parameters corresponding to aqueous mixtures of glycerine with mass concentration in the range of 60%-90% glycerine and a Rayleigh number range that extends from the threshold for wall modes up to values where the bulk fluid region is also convecting. The study shows that for the range of Rayleigh numbers considered, the local variations in viscosity due to temperature variation in the flow are negligible. However, the mean viscosity, which varies faster than exponentially with variations in the percentage of glycerine, leads to a faster than exponential increase in the Froude number for a fixed Coriolis force, and hence an enhancement of the centrifugal buoyancy effects with significant dynamical consequences, which are detailed.

    Thermal convection in a rotating cylinder with a radius-to-height aspect ratio of G=4 for fluids with large Prandtl number is studied numerically. Centrifugal buoyancy effects are investigated in a regime where the Coriolis force is relatively large and the onset of thermal convection is in the so-called wall modes regime, where pairs of hot and cold thermal plumes ascend and descend in the cylinder sidewall boundary layer, forming an essentially one-dimensional pattern characterized by the number of hot and cold plume pairs. In our numerical study, we use the physical parameters corresponding to aqueous mixtures of glycerine with mass concentration in the range of 60%-90% glycerine and a Rayleigh number range that extends from the threshold for wall modes up to values where the bulk fluid region is also convecting. The study shows that for the range of Rayleigh numbers considered, the local variations in viscosity due to temperature variation in the flow are negligible. However, the mean viscosity, which varies faster than exponentially with variations in the percentage of glycerine, leads to a faster than exponential increase in the Froude number for a fixed Coriolis force, and hence an enhancement of the centrifugal buoyancy effects with significant dynamical consequences, which are detailed. © 2014 American Physical Society.

  • Complejidad y Génesis de la Turbulencia en Flujos Fundamentales

     Meseguer Serrano, Alvaro; Alonso Maleta, Maria Aranzazu; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Mellibovsky Elstein, Fernando; Lopez, Juan M; Avila Cañellas, Marc; Marques Truyol, Francisco
    Competitive project

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    Instability of plumes driven by localized heating  Open access

     López Moscat, Juan Manuel; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 736, p. 616-640
    DOI: 10.1017/jfm.2013.537
    Date of publication: 2013-12
    Journal article

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    Plumes due to localized buoyancy sources are of wide interest owing to their prevalence in many situations. This study investigates the transition from laminar to turbulent dynamics. Several experiments have reported that this transition is sensitive to external perturbations. As such, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose walls are all maintained at a fixed uniform temperature, except for the localized heat source. At moderate Rayleigh numbers R a, the flow consists of a steady, axisymmetric purely poloidal plume. On increasing R a, the flow undergoes a supercritical Hopf bifurcation to an axisymmetric 'puffing' plume, where a vortex ring is periodically emitted from the localized heater. At higher R a, this state becomes unstable to a sequence of symmetry-breaking bifurcations, going through a quasi-periodic 'fluttering' stage where the axisymmetric rings are tilted, and other states in which the sequence of tilted rings interact with each other. The sequence of symmetry-breaking bifurcations in the transition to turbulence culminates in a torus breakup event in which all the spatial and spatio-temporal symmetries of the system are broken.

    Plumes due to localized buoyancy sources are of wide interest owing to their prevalence in many situations. This study investigates the transition from laminar to turbulent dynamics. Several experiments have reported that this transition is sensitive to external perturbations. As such, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose walls are all maintained at a fixed uniform temperature, except for the localized heat source. At moderate Rayleigh numbers Ra, the flow consists of a steady, axisymmetric purely poloidal plume. On increasing Ra, the flow undergoes a supercritical Hopf bifurcation to an axisymmetric ‘puffing’ plume, where a vortex ring is periodically emitted from the localized heater. At higher Ra, this state becomes unstable to a sequence of symmetry-breaking bifurcations, going through a quasi-periodic ‘fluttering’ stage where the axisymmetric rings are tilted, and other states in which the sequence of tilted rings interact with each other. The sequence of symmetry-breaking bifurcations in the transition to turbulence culminates in a torus breakup event in which all the spatial and spatio-temporal symmetries of the system are broken.

  • The Boussinesq approximation in rapidly rotating ows

     Lopez Alonso, Jose Manuel; Marques Truyol, Francisco; Avila Cañellas, Marc
    Journal of fluid mechanics
    Vol. 737, p. 56-77
    DOI: 10.1017/jfm.2013.558
    Date of publication: 2013-12
    Journal article

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    In commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. Here we provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. Its application to the accretion-disc problem is discussed. We numerically compare the new approach to the typical one in fluid flows confined between two differentially heated and rotating cylinders. The results justify the need of using the proposed approximation in rapidly rotating flows

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    Fold-pitchfork bifurcation for maps with Z(2) symmetry in pipe flow  Open access

     Marques Truyol, Francisco; Mellibovsky Elstein, Fernando; Meseguer Serrano, Alvaro
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 88, num. 1, p. 1-12
    DOI: 10.1103/PhysRevE.88.013006
    Date of publication: 2013-07-11
    Journal article

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    This study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow. This particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle-node bifurcations within a two-dimensional parameter space characterized by the length of the pipe and the Reynolds number. The present work precisely provides a detailed analysis of a codimension-two saddle-node bifurcation arising in discrete dynamical systems (maps) with Z(2) symmetry. Normal form standard techniques are applied in order to obtain the reduced map up to cubic order. All possible bifurcation scenarios exhibited by this normal form are analyzed in detail. Finally, a qualitative comparison of these scenarios with the ones observed in the aforementioned hydrodynamic problem is provided.

    This study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow. This particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle-node bifurcations within a two-dimensional parameter space characterized by the length of the pipe and the Reynolds number. The present work precisely provides a detailed analysis of a codimension-two saddle-node bifurcation arising in discrete dynamical systems (maps) with Z2 symmetry. Normal form standard techniques are applied in order to obtain the reduced map up to cubic order. All possible bifurcation scenarios exhibited by this normal form are analyzed in detail. Finally, a qualitative comparison of these scenarios with the ones observed in the aforementioned hydrodynamic problem is provided.

  • Non-Linear Fluid Dynamics in Oscillatory Cylindrical Cavities  Open access

     Panades Guinart, Carles
    Department of Applied Physics, Universitat Politècnica de Catalunya
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    Encara que la transició a la turbulència s'ha estat estudiant durant més d'un segle, la comprensió completa d'aquesta, encara roman poc clara ,fins i tot en els fluxos més senzills, i contínua sent un repte d'enormes proporcions per a la comunitat científica. La complexitat d'aquest problema planteja una sèrie de dificultats que deixen poc marge de maniobra i, per tant,s'han de cercar altres mètodes per atacar aquesta qüestió. Una opció molt raonable és l'anàlisi dels fenòmens d'inestabilitats en altres sistemes amb el mateix grup de simetries. Malgrat ser molt diferents, un exemple d'aquest tipus de flux seria el que es genera en una cavitat cilíndrica sotmesa a un esforç de cisalla oscil·latori.L'objectiu de la present tesi ha estat proporcionar un coneixement més profund dels mecanismes responsables en la transició en cavitats cilíndriques. Deixant de banda les possibles implicacions d'estudiar aquests sistemes pel que fa a les transicions dels fluxos en les esteles, el sistema que s'està considerant pot resultar útil en qualsevol investigació que involucri un forçament periòdic. En un intent d'arribar a bon port des de diferents punts de vista, càlculs espectrals precisos de les equacions de Navier-Stokes s'han combinat amb la teoria de formes normals. La utilització f'aquestes tècniques ha produït resultats positius en aquest camp. L'anàlisi d'estabilitat lineal ha revelat tres tipus diferents de bifurcacions, les quals s'esperaven a causa de la teoria de formes normals i resultats anteriors. L'evolució temporal d'aquests modes que bifurquen han proporcionar estats saturats no-lineals, els quals poden ser síncrons amb el forçament o poden adquirir una freqüència addicional (quasiperiòdic). A més a més, l'exploració de les regions on dos modessíncrons esdevenen inestables a la vegada, ha proporcionat una gran varietat de nous estats que no han de ser necessàriament síncrons. La descripció d'aquest fenomen per mitjà de la teoria de bifurcacions i les tècniques de sistemes dinàmics, es troben en acord amb les simulacions numèriques, malgrat que no hi ha una concordància absoluta entre ells.La recerca focalitzada en l'estudi de fluids viscoelàstics en cavitats cilíndriques forçades perioòdicament, és una extensió natural de la temàtica principal d'aquesta tesi. Tot i que aquesta part ha de ser considerada com un estudi preliminar, hi ha algunes evidències que suggereixen que el sistema és sempre linealment estable i l'única manera de desestabilitzar l'estat bàsic és per mitjà d'una bifurcació subcrítica d'amplitud finita. La transició ens recorda en gran mesura el cas de les inestabilitats en el Couette pla i el Poiseuille cilíndric de fluids Newtonian, obtenint així un escenari per la transició molt més difícil dels que ens esperàvem.

    Even though the transition to turbulence has been studied for over a century, its complete comprehension still remains unclear even for the simplest flows and continues to be a daunting challenge for the scientific community. Among these, there is the transition from the von K\'arm\'an vortex street to turbulent wakes. The complexity of this problem poses a series of difficulties that leaves little room for manoeuvre, so other ways to tackle this question have to be sought. A reasonable option is the analysis of the instability phenomena that other flows with the same symmetry group undergo. Despite being really different, an example of such flow is the one generated in a cylindrical cavity subjected to an oscillatory shear. The purpose of the present thesis has been to provide a deeper understanding of the mechanisms that are responsible for the transition in oscillatory cylindrical cavities. Besides the potential implications of studying such systems for the transitions in wake flows, the system under consideration might be useful for any investigation involving a periodic forcing. Accurate spectral computations of the incompressible Navier-Stokes equations have been combined with equivariant bifurcation and normal form theories in an attempt to achieve our goal from different, yet complementary, perspectives. The utilisation of these techniques has produced positive results in the field under consideration. The linear stability analysis has resulted in three types of different bifurcations expected by normal form theory and previous results. The evolution in time of these bifurcating modes yield the non-linear saturated states, which can be synchronous with the forcing or acquire an additional frequency (quasiperiodic). Furthermore, the exploration of regions where two synchronous modes become unstable at the same time, has provided a wide variety of novel states that are not necessarily synchronous. The description of these phenomena via bifurcation theory and dynamical systems techniques is in accordance with the numerical simulations, despite not having an absolute quantitative agreement between them. The research focused on the study of viscoelastic fluids in periodically driven cylindrical cavities is a natural extension of the main topic of this thesis. Although this part has to be considered in a preliminary stage, there are some evidences suggesting that the system is always linearly stable and the only possibility to break the basic state is via a subcritical finite-amplitude bifurcation. The transition recalls in a great deal the instabilities in Newtonian plane Couette and pipe Poiseuille, thus resulting in a much more difficult instability scenario that the one that was initially expected.

    Encara que la transició a la turbulència s'ha estat estudiant durant més d'un segle, la comprensió completa d'aquesta, encara roman poc clara ,fins i tot en els fluxos més senzills, i contínua sent un repte d'enormes proporcions per a la comunitat científica. La complexitat d'aquest problema planteja una sèrie de dificultats que deixen poc marge de maniobra i, per tant, s'han de cercar altres mètodes per atacar aquesta qüestió. Una opció molt raonable és l'anàlisi dels fenòmens d'inestabilitats en altres sistemes amb el mateix grup de simetries. Malgrat ser molt diferents, un exemple d'aquest tipus de flux seria el que es genera en una cavitat cilíndrica sotmesa a un esforç de cisalla oscil·latori. L'objectiu de la present tesi ha estat proporcionar un coneixement més profund dels mecanismes responsables en la transició en cavitats cilíndriques. Deixant de banda les possibles implicacions d'estudiar aquests sistemes pel que fa a les transicions dels fluxos en les esteles, el sistema que s'està considerant pot resultar útil en qualsevol investigació que involucri un forçament periòdic. En un intent d'arribar a bon port des de diferents punts de vista, càlculs espectrals precisos de les equacions de Navier-Stokes s'han combinat amb la teoria de formes normals. La utilització f'aquestes tècniques ha produït resultats positius en aquest camp. L'anàlisi d'estabilitat lineal ha revelat tres tipus diferents de bifurcacions, les quals s'esperaven a causa de la teoria de formes normals i resultats anteriors. L'evolució temporal d'aquests modes que bifurquen han proporcionar estats saturats no-lineals, els quals poden ser síncrons amb el forçament o poden adquirir una freqüència addicional (quasiperiòdic). A més a més, l'exploració de les regions on dos modes síncrons esdevenen inestables a la vegada, ha proporcionat una gran varietat de nous estats que no han de ser necessàriament síncrons. La descripció d'aquest fenomen per mitjà de la teoria de bifurcacions i les tècniques de sistemes dinàmics, es troben en acord amb les simulacions numèriques, malgrat que no hi ha una concordància absoluta entre ells. La recerca focalitzada en l'estudi de fluids viscoelàstics en cavitats cilíndriques forçades perioòdicament, és una extensió natural de la temàtica principal d'aquesta tesi. Tot i que aquesta part ha de ser considerada com un estudi preliminar, hi ha algunes evidències que suggereixen que el sistema és sempre linealment estable i l'única manera de desestabilitzar l'estat bàsic és per mitjà d'una bifurcació subcrítica d'amplitud finita. La transició ens recorda en gran mesura el cas de les inestabilitats en el Couette pla i el Poiseuille cilíndric de fluids Newtonian, obtenint així un escenari per la transició molt més difícil dels que ens esperàvem.

  • Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

     Marques Truyol, Francisco; Meseguer Serrano, Alvaro; López Moscat, Juan Manuel; Pacheco, Jose Rafael; Lopez Alonso, Jose Manuel
    Proceedings of the Royal Society A. Mathematical physical and engineering sciences
    Vol. 469, num. 2152, p. 1-18
    DOI: 10.1098/rspa.2012.0348
    Date of publication: 2013-04-08
    Journal article

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    Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyse the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width and partial breaking of SO(2) to Zm are also considered. Previous as well as new experimental and numerical studies of pinned rotating waves are reviewed in the light of the new theoretical results.

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    Mode competition in cylindrical flows driven by sidewall oscillations  Open access

     Panades Guinart, Carles; Marques Truyol, Francisco; Meseguer Serrano, Alvaro
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 87, num. 4, p. 1-17
    DOI: 10.1103/PhysRevE.87.043001
    Date of publication: 2013-04
    Journal article

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    The transition from a two-dimensional to three-dimensional flow in systems with spatial O(2) symmetry and spatiotemporal Z2 symmetry happens in many fluid systems, like wakes or periodically forced flows. In most of these systems, the dynamics after the first bifurcation is very complex and involves cascades of bifurcations in a very narrow parameter range. A numerical study of a flow in an enclosed cylindrical cavity driven by axial oscillations of the sidewall, which allows a detailed study of the secondary bifurcations and the corresponding mode interactions, is presented. The study focuses on a codimension-2 point that acts as the organizing center of the dynamics for moderate values of the forcing frequency. The unraveled dynamics is very rich, including slow-fast dynamics and hysteresis, and may help understand the bifurcation cascades in more complex systems.

  • Symmetry-breaking Hopf bifurcations to 1-, 2-, and 3-tori in small-aspect-ratio counterrotating Taylor-Couette flow

     Altmeyer, S.; Do, Y.; Marques Truyol, Francisco; López Moscat, Juan Manuel
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 86, num. 4, p. 046316-1-046316-17
    DOI: 10.1103/PhysRevE.86.046316
    Date of publication: 2012-10
    Journal article

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    The nonlinear dynamics of Taylor-Couette flow in a small-aspect-ratio wide-gap annulus in the counterrotating regime is investigated by solving the full three-dimensional Navier-Stokes equations. The system is invariant under arbitrary rotations about the axis, reflection about the annulus midplane, and time translations. A systematic investigation is presented both in terms of the flow physics elucidated from the numerical simulations and from a dynamical system perspective provided by equivariant normal form theory. The dynamics are primarily associated with the behavior of the jet of angular momentum that emerges from the inner cylinder boundary layer at about the midplane. The sequence of bifurcations as the differential rotation is increased consists of an axisymmetric Hopf bifurcation breaking the reflection symmetry of the basic state leading to an axisymmetric limit cycle with a half-period-flip spatiotemporal symmetry. This undergoes a Hopf bifurcation breaking axisymmetry, leading to quasiperiodic solutions evolving on a 2-torus that is setwise symmetric. These undergo a further Hopf bifurcation, introducing a third incommensurate frequency leading to a 3-torus that is also setwise symmetric. On the 3-torus, as the differential rotation is further increased, a saddle-node-invariant-circle bifurcation takes place, destroying the 3-torus and leaving a pair of symmetrically related 2-tori states on which all symmetries of the system have been broken.

  • Introductory remarks from the editors

     Knobloch ., Edgar; Meseguer Serrano, Alvaro; Marques Truyol, Francisco
    Fluid dynamics research
    Vol. 44, num. 3, p. 2
    DOI: 10.1088/1873-7005/44/3/031001
    Date of publication: 2012
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  • Instabilities and inertial waves generated in a librating cylinder

     López, J.M.; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 687, p. 171-193
    DOI: 10.1017/jfm.2011.378
    Date of publication: 2011-11-25
    Journal article

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    A librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particular is susceptible to instabilities which can introduce additional forcing on the interior flow with time scales different from the modulation period. These instabilities may also drive and/or modify the inertial waves. In this paper, we explore such flows numerically using a spectral-collocation code solving the Navier–Stokes equations in order to capture the dynamics involved in the interactions between the inertial waves and the viscous boundary layer flows.

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    Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall  Open access

     Panades Guinart, Carles; Marques Truyol, Francisco; López Moscat, Juan Manuel
    Journal of fluid mechanics
    Vol. 681, p. 515-536
    DOI: 10.1017/jfm.2011.215
    Date of publication: 2011-08
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    The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry related to the oscillating sidewall, is Z2xO(2). Previous studies in flows with the same symmetries, such as symmetric bluff-body wakes and periodically forced rectangular cavities, were unable to obtain the theoretically predicted bifurcation to modulated travelling waves. In the simpler cylindrical geometry, where the azimuthal direction is physically periodic, we have found these predicted modulated travelling waves as stable fully saturated nonlinear solutions for the first time. A careful analysis of the base states and their linear stability identifies different parameter regimes where three-dimensional states are either synchronous with the forcing or quasi-periodic, corresponding to different symmetry-breaking processes. These results are in good agreement with theoretical predictions and previous results in similar flows. These different regimes are separated by three codimension-two bifurcation points that are yet to be fully analysed theoretically. Finally, the saturated nonlinear states and their properties in different parameter regimes are analysed.

  • Bifurcations to three-dimensional flows in a periodically driven cylindrical cavity

     Panades Guinart, Carles; Marques Truyol, Francisco
    International Couette-Taylor Workshop
    p. 1-3
    Presentation's date: 2011-07-26
    Presentation of work at congresses

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  • Boundary layer instabilities in rapidly rotating flows

     Marques Truyol, Francisco; López, J.M.
    International Couette-Taylor Workshop
    p. 67-69
    Presentation's date: 2011-07-26
    Presentation of work at congresses

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  • Instabilities and inertial waves generated in a librating cylinder

     López Moscat, Juan Manuel; Marques Truyol, Francisco
    International Symposium Bifurcations and Instabilities in Fluid Dynamics
    p. 21
    Presentation's date: 2011-07-20
    Presentation of work at congresses

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  • Numerical simulations of non-Newtonian fluids in a periodically forced enclosed cylinder

     Panades Guinart, Carles; Marques Truyol, Francisco
    International Symposium Bifurcations and Instabilities in Fluid Dynamics
    p. 14
    Presentation's date: 2011-07-18
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  • Pinning of rotating waves in systems with imperfect SO(2) symmetry

     Marques Truyol, Francisco
    Simposio Internacional Física de los sistemas fuera de equilibrio
    p. 8
    Presentation's date: 2011-02-17
    Presentation of work at congresses

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    Pinning of rotating waves to defects in finite Taylor-Couette flow  Open access

     Pacheco, J. R.; López, J. M.; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 666, p. 254-272
    DOI: 10.1017/S0022112010004131
    Date of publication: 2011-01-10
    Journal article

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    Experiments in small aspect-ratio Taylor–Couette flows have reported the presence of a band in parameter space where rotating waves become steady non-axisymmetric solutions (a pinning effect) via infinite-period bifurcations. Previous numerical simulations were unable to reproduce these observations. Recent additional experiments suggest that the pinning effect is not intrinsic to the dynamics of the problem, but rather is an extrinsic response induced by the presence of imperfections. Here we present numerical simulations that include a small tilt of one of the endwalls, simulating the effects of imperfections that break the SO(2) axisymmetry of the problem, and indeed are able to reproduce the experimentally observed pinning of the rotating waves. Dynamical systems considerations suggest that any imperfection breaking the SO(2) axisymmetry of the problem must result in the formation of a pinning region of finite width. We have also found that the particulars of the pinning process, in particular the width of the pinning region, are extremely sensitive to the type of imperfection in the system. Almost identical flows respond in completely different ways to the same imperfection, depending on subtle differences in the weak secondary characteristics of the flow. The numerical simulations of the Navier–Stokes equations for the problem with an imposed tilt of an endwall together with normal-form analysis of a Hopf bifurcation subjected to imposed symmetry-breaking help shed some light on previous experiments that reported a variety of different dynamical behaviour for which a clear explanation was lacking.

  • Sidewall boundary layer instabilities in a rapidly rotating cylinder driven by a differentially corotating lid

     López Moscat, Juan Manuel; Marques Truyol, Francisco
    Physics of fluids
    Vol. 22, num. 11
    DOI: 10.1063/1.3517292
    Date of publication: 2010-11-03
    Journal article

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    Optimal harmonic response in a confined Bödewadt boundary layer flow  Open access

     Younghae, Do; López Moscat, Juan Manuel; Marques Truyol, Francisco
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 82, p. 036301-1-036301-08
    DOI: 10.1103/PhysRevE.82.036301
    Date of publication: 2010-09-01
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    The Bödewadt boundary layer flow on the stationary bottom end wall of a finite rotating cylinder is very sensitive to perturbations and noise. Axisymmetric radial waves propagating inward have been observed experimentally and numerically before the appearance of spiral three-dimensional instabilities. In this study, the sensitivity and response of the finite Bödewadt flow to a harmonic modulation of the rotation rate are analyzed. A comprehensive exploration of response to variations in the amplitude and frequency of the forcing has been carried out. There are sharply delineated linear- and nonlinear-response regimes, with a sharp transition between them at moderate amplitudes. The periodic forcing leads to a steady-streaming flow, even in the linear-response regime, and to a period-doubling bifurcation in the nonlinear regime. Frequency response curves at different forcing amplitudes over a wide range of frequencies have been computed and used to identify the frequency band that excites the axisymmetric radial waves and the forcing frequency that elicits the strongest response. Finally, we have shown that the axisymmetric waves always decay to the steady basic state when the harmonic modulation is suppressed, and conclude that the experimentally observed persistent circular waves are not self-sustained.

  • Spiral and localised turbulence in annular shear flows

     Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Marques Truyol, Francisco; Avila Cañellas, Marc
    Joint SIAM/RSME-SCM-SEMA Meeting Emerging Topics in Dynamical Systems and Partial Differential Equations
    p. 74
    Presentation's date: 2010-06-03
    Presentation of work at congresses

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  • Crossflow instability of finite Bödewadt flows: transients and spiral waves

     Marques Truyol, Francisco; López Moscat, Juan Manuel; Avila Cañellas, Marc; Rubio, Antonio
    Emerging Topics in Dynamical Systems and Partial Differential Equations
    p. 61
    Presentation's date: 2010-06-01
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  • Onset of Kuppers-Lortz-like dynamics in finite rotating thermal convection

     Lopez, J. M.; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 644, p. 337-357
    DOI: 10.1017/S0022112009992400
    Date of publication: 2010-02-10
    Journal article

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  • ESTRUCTURAS COHERENTES Y TURBULENCIA EN DOMINIOS SIMPLES

     Mercader Calvo, Maria Isabel; Avila Cañellas, Marc; Batiste Boleda, Oriol; Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Panades Guinart, Carles; Alonso Maleta, Maria Aranzazu; López Moscat, Juan Manuel; Marques Truyol, Francisco
    Competitive project

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    Crossflow instability of finite Bödewadt flows: transients and spiral waves  Open access

     López, Juan A.; Marques Truyol, Francisco; Rubio, Antonio M.; Avila Cañellas, Marc
    The physics of fluids
    Vol. 21, num. 11, p. 114107-1-114107-9
    DOI: 10.1063/1.3262817
    Date of publication: 2009-11
    Journal article

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    The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primarily present in the boundary layers on the rotating top and sidewalls and the stationary bottom wall, with a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows on the top and bottom. The top end wall boundary layer has a profile that very closely matches the von Kármán solution for a rotating disk boundary layer; it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer on the stationary bottom end wall has a profile that agrees with the Bödewadt solution for a stationary disk with an ambient flow in solid-body rotation. This boundary layer is not robust, suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most inflectional. In the absence of any external forcing, the circular waves are transitory, but low amplitude forcing can sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing.

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    Instability mechanisms and transition scenarios of spiral turbulence in Taylor-Couette flow  Open access

     Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Avila Cañellas, Marc; Marques Truyol, Francisco
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 80, num. 4, p. 1-4
    DOI: 10.1103/PhysRevE.80.046315
    Date of publication: 2009-10
    Journal article

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    Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified for the first time. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localised turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified.

    Postprint (author’s final draft)

  • Shear instabilities in Taylor-Couette flow

     Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Marques Truyol, Francisco; Avila Cañellas, Marc
    European Turbulence Conference
    p. 115-118
    DOI: 10.1007/978-3-642-03085-7_27
    Presentation's date: 2009-09-09
    Presentation of work at congresses

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    Subcritical instabilities in small gap Taylor-Couette (TCF) problem are studied numerically when both cylinders rotate in opposite directions. The computations are carried out for a radius ratio A first exploration is focused on the study of spiral flows originated from subcritical Hopf bifurcations of the basic circular Couette solution. The second exploration addresses the transition from laminar flow to the usually termed as spiral turbulence regime characterized by alternating laminar and turbulent spiral bands which coexist even in regions of the parameter space where the circular Couette flow is linearly stable.

  • Laminar and turbulent spirals in counter-rotating Taylor-Couette flow

     Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Marques Truyol, Francisco; Avila Cañellas, Marc
    Bifurcations and Instabilities in Fluid Dynamics
    p. 10
    Presentation's date: 2009-08-11
    Presentation of work at congresses

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  • Rotating convection: transition from wall modes to quasi-geostrophic turbulence

     Marques Truyol, Francisco; Rubio, Antonio; López Moscat, Juan Manuel
    Bifurcations and Instabilities in Fluid Dynamics
    p. 25-26
    Presentation's date: 2009-08-10
    Presentation of work at congresses

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  • Centrifugal effects in rotating convection: nonlinear dynamics

     Lopez, Jm; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 628, num. -, p. 269-297
    Date of publication: 2009-06
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  • Interacting oscillatory boundary layers and wall modes in modulated rotating convection

     Lopez, Jm; Marques Truyol, Francisco
    Journal of fluid mechanics
    Vol. 625, p. 75-96
    Date of publication: 2009-04
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  • Families of subcritical spirals in highly counter-rotating Taylor-Couette flow

     Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Avila Cañellas, Marc; Marques Truyol, Francisco
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 79, num. 3, p. 036309-
    DOI: 10.1103/PhysRevE.79.036309
    Date of publication: 2009-03
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  • Dinàmica de fluids; formació d'estructures i aplicacions geofísiques

     Marques Truyol, Francisco; Falques Serra, Alberto; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Calvete Manrique, Daniel; Garnier, Roland Charles; Mellibovsky Elstein, Fernando; Mercader Calvo, Maria Isabel; Meseguer Serrano, Alvaro; Pino Gonzalez, David; Ribas Prats, Francesca; van en Berg, Niels; Panades Guinart, Carles
    Competitive project

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  • Harmonically forced enclosed swirling flow

     Cui, Yd; Lopez, Jm; Lim, Tt; Marques Truyol, Francisco
    Physics of fluids
    Vol. 21, num. 3, p. 1
    DOI: 10.1063/1.3093236
    Date of publication: 2009-01
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  • Interacting Stokes layers and wall modes in modulated rotating convection

     Marques Truyol, Francisco
    61th Annual Meeting of the APS Division of Fluid Dynamics
    Presentation's date: 2008-11-23
    Presentation of work at congresses

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  • Centrifugal effects in rotating convection: nonlinear dynamics

     Marques Truyol, Francisco
    61th Annual Meeting of the APS Division of Fluid Dynamics
    Presentation's date: 2008-11-23
    Presentation of work at congresses

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  • Harmonically forced enclosed swirling flow

     Marques Truyol, Francisco
    61th Annual Meeting of the APS Division of Fluid Dynamics
    Presentation's date: 2008-11-23
    Presentation of work at congresses

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  • Global endwall effects on centrifugally stable flows

     Avila Cañellas, Marc; Grimes, Matt; LOPEZ, J M; Marques Truyol, Francisco
    Physics of fluids
    Vol. 20, num. 104104, p. 1-7
    Date of publication: 2008-10
    Journal article

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  • Bursting dynamics due to a homoclinic cascade in Taylor-Couette flow

     Abshagen, Jan; LOPEZ, J M; Marques Truyol, Francisco; Pfister, Gerd
    Journal of fluid mechanics
    Vol. 613, p. 357-384
    Date of publication: 2008-10
    Journal article

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  • Subcritical transition in shear flows

     Mellibovsky Elstein, Fernando
    Castelldefels School of Telecommunications and Aerospace Engineering (EETAC), Universitat Politècnica de Catalunya
    Theses

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  • Modulated Rotating Convection: Radially Traveling Concentric Rolls

     Marques Truyol, Francisco
    NoLineal 2008
    Presentation's date: 2008-06-16
    Presentation of work at congresses

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  • Convección con Rotación en Cilindros: Transición de los Modos de Pared a Caos Espacio-temporal

     Marques Truyol, Francisco
    NoLineal 2008
    Presentation's date: 2008-06-16
    Presentation of work at congresses

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  • Control de Oscilaciones en la Rotura de Vórtices

     Marques Truyol, Francisco
    NoLineal 2008
    Presentation's date: 2008-06-16
    Presentation of work at congresses

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  • Competencia de Modos en Fluidos: Experimentos y Simulaciones

     Marques Truyol, Francisco
    NoLineal 2008
    Presentation's date: 2008-06-16
    Presentation of work at congresses

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  • Nonlinear dynamics of mode competition in annular flows

     Avila Cañellas, Marc
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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  • Contributiones a la sexta edicion del congreso Nolineal 2008

     Marques Truyol, Francisco; Delshams i Valdes, Amadeu
    Date of publication: 2008-06
    Book

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  • Quenching of unsteady vortex breakdown via harmonic modulation

     LOPEZ, J M; Cui, Y D; Marques Truyol, Francisco; Lim, T T
    Journal of fluid mechanics
    Vol. 599, p. 441-464
    Date of publication: 2008-05
    Journal article

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