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.]]>

Journal of fluid mechanics

Vol. 580, p. 303-318

DOI: 10.1017/S0022112007005447

Date of publication: 2007-06

Abstract:

Rotating convection is analysed numerically in a cylinder of aspect ratio one, for Prandtl number about 7. Traditionally, the problem has been studied within the Boussinesq approximation with density variation only incorporated in the gravitational buoyancy term and not in the centrifugal buoyancy term. In that limit, the governing equations admit a trivial conduction solution. However, the centrifugal buoyancy changes the problem in a fundamental manner, driving a large-scale circulation in which cool denser fluid is centrifuged radially outward and warm less-dense fluid is centrifuged radially inward, and so there is no trivial conduction state. For small Froude numbers, the transition to three-dimensional flow occurs for Rayleigh number R ˜ 7.5 × 103. For Froude numbers larger than 0.4, the centrifugal buoyancy stabilizes the axisymmetric large-scale circulation flow in the parameter range explored (up to R = 3.5 × 104). At intermediate Froude numbers, the transition to three-dimensional flow is via four different Hopf bifurcations, resulting in different coexisting branches of three-dimensional solutions. How the centrifugal and the gravitational buoyancies interact and compete, and the manner in which the flow becomes three-dimensional is different along each branch. The centrifugal buoyancy, even for relatively small Froude numbers, leads to quantitative and qualitative changes in the flow dynamics.]]>

Nolineal 2007 : Nuevos retos y perspectivas de la dinámica no lineal y sus aplicaciones

p. 34

Annual Meeting of The American Physical Society - Division of Fluid Dynamics

p. 2004

Annual Meeting of The American Physical Society - Division of Fluid Dynamics

p. 68