Rotating Rayleigh-Benard Convection

Many flows in nature and technology are driven by buoyant convection and subsequently modulated by rotation. One of the classical convection systems is the Rayleigh-Bénard setup: a fluid in a container heated from below and cooled from above. An interesting variation of Rayleigh-Bénard convection is the case where the sample is rotated about the vertical axis. This system is relevant to numerous astro- and geophysical phenomena, including convection in the Arctic Ocean, in the earth's outer core, in the interior of gaseous giant planets, and the outer layer of the Sun. Thus the problem is of interest in a wide range of sciences, including geology, oceanography, climatology, and astrophysics. Furthermore, the knowledge can be used in industrial applications like metal production. We investigate turbulent rotating convection with experiment and numerical simulation.

Experiments

Local in situ velocity measurements are performed using stereoscopic particle image velocimetry (SPIV) in a cylindrical convection cell, placed on top of a rotating table. SPIV is a nonintrusive method that measures the three components of velocity at many positions in a two-dimensional cross-section of the fluid. Experiments at various rotation rates showed that the organisation of the flow into coherent structures is strongly dependent on rotation. For small rotation rates the domain-filling large-scale circulation, well-known from non-rotating convection, is the dominant feature. At larger rotation rates an irregular, unsteady array of vortical plumes is found. The turbulence intensity is reduced by rotation, and the vertical inhomogeneity increases.

Numerical simulations

Numerical simulations of turbulent rotating convection in a cylinder are carried out to compare with and expand on the experimental results. The Navier–Stokes and heat equations are written in cylindrical coordinates and discretised using second-order accurate finite-difference approximations for the derivatives. The simulations confirm the findings from the experiments. Additionally, it is found that, despite the reduction of turbulence intensity, the convective heat transfer through the fluid layer is enhanced in a certain range of rotation rates. The vortical plumes are responsible for nearly all vertical transport of fluid and heat. They possess an efficient means for entraining boundary-layer fluid and transporting it towards the vertically opposite side: Ekman pumping. Ekman pumping enhances the heat transfer. At the highest rotation rates, however, the inhibition of velocity by rotation dominates and the heat flux decreases abruptly.

Questions

The control parameters are the fluid properties, the container geometry, and the strength of the temperature gradient, or, in dimensionless form, the Prandtl-number Pr, the Rayleigh number Ra, and the aspect ratio. The response of the system can be expressed as the dimensionless heat flux (Nusselt number denoted by Nu) and the dimensionless strength of the turbulence (Reynolds number Re). The rotation speed of the system is defined by the Rossby number (Ro), which is the inverse rotation rate. One of the key question to be addressed is how do Nusselt and Reynolds depend on Ra, Pr, Ro, and the aspect ratio of the vessel ?

Large-scale circulation

In the turbulent regime, the flow is characterized by a large-scale circulation (LSC) near boundaries of the container. The figure above shows an schematic overview of flow structure in non-rotating Rayleigh- Bénard convection. When rotation is applied the heat transfer (Nusselt number) in the system can increase up to 30% as shown below. This is accompanied by a change in the flow structure, i.e. vortex structures are formed when rotation when rotation is applied.

Questions we address are: (1) Influence of rotation on the Nusselt number, (2) Influence of rotation on the LSC.