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Double diffusion flows with shear: space-time complexity.

Total activity: 1
Type of activity
Competitive project
Acronym
DODISH
Funding entity
AGENCIA ESTATAL DE INVESTIGACION
Funding entity code
FIS2017-85794-P
Amount
54.450,00 €
Start date
2018-01-01
End date
2020-12-31
Keywords
Complejidad, Complexity, Navier-Stokes equations, bifurcaciones, bifurcations, doble difusión, double diffusion, dynamical systems, ecuaciones de Navier-Stokes, estados localizados, flujos de cizalla, hydrodynamic instabilities, inestabilidades hidrodinámicas, localized states, métodos espectrales, numerical simulation, shear flows, simulación numérica, sistemas dinámicos, spectral methods
Abstract
Double diffusion in fluids appears when the fluid density depends on to scalars with different diffusivities, as temperature and
concentration. It is a common phenomenon in a variety of geophysical problems (such as the interaction of salinity and temperature in the
ocean, or between pollutants and temperature gradients in the atmosphere), and industrial processes (such as the mixing and separation
techniques), among others. In these phenomena, it is common the presence of shear, induced typically by large scale flows (both in the
ocean, the atmosphere and industry). Both mechanisms, double diffusion and shear, have been the subject of many studies separately,
and the research team has ample experience in both of them.
Theoretical and experimental studies considering both processes simultaneously have recently appeared. The present project joins this
new challenging research line. The main goal is to study the interaction between double diffusion and shear in a few fundamental problems
in simple geometries; analyze the changes in the dynamics already known in double diffusion and shear treated separatedly, and the
emergence of new phenomena due to their interaction. We will analyze in detail the transition from laminarity to complex spatio-temporal
flows that takes place when the thermal and shear gradients are increased. For this analysis we will use advanced numerical methods and
dynamical systems theory.
The study that we propose involves a number of challenges. One of them is to capture the dynamics when the time-scales of the problem
differ by several orders of magnitude when realistic values of the parameters are used, so that direct comparison with experiments is
feasible. Another challenge is to be capable of accurately computing localized states whose dynamics, typically chaotic, concetrates within
isolated small regions within the fluid.
One aspect of the project to be studied is binary convection in enclosed flows, with shear induced by the presence of a large scale
circulation. These large scale currents can be induced by tilting the container, the gravity component orthogonal to the temperature
gradient providing the current driving. Alternatively, the circulation can be generated by rotating the container, the centrifugal force being
the driving mechanism in this case. Preliminary results in the tilted problem suggest that even very small inclinations produce substantial
changes in the flow structure, resulting in new phenomena. The centrifugal large scale flow has been extensively studied by the research
team in pure fluid rotating convection.
The second aspect of the project consists of the study of classical shear open flows, with the shear induced by moving walls (like in
Couette flow) or induced by pressure gradients (like channel or pipe flow). In these problems the dynamics abruptly changes from laminar
to very complex, with localized states with chaotic spatio-temporal dynamics, that eventually fill the whole domain. In this project, binary
convection will be added to the classical shear open flows, and the new dynamics that will emerge will be studied.

Participants

Scientific and technological production

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