Wave generation in a circular Couette flow in thermoelectric radial buoyancy

International audienceThermal convection in a centripetal gravity field is of primary importance in geo-and astrophysics , as it is responsible for global-scale heat and mass transport in a planet. Application of a radial electric field to a non isothermal Taylor-Couette system of a dielectric fluid provides a simple analogical system to simulate such convection [1]. Indeed, an electrohydrodynamic force exerted by the electric field can be regarded as thermal buoyancy due to the following radial effective gravity g e : g e = − eΦ 2 0 ρα (log η) 2 F (r, η, e∆T) e r , (ρ: the fluid density, : the fluid electric permittivity, α: the coefficient of thermal expansion, e: the coefficient of thermal variation, Φ 0 : the applied electric tension, ∆T : the temperature difference). The correcting factor F depends on the radial position r, the radius ratio of the inner to outer cylinders η = R 1 /R 2 and the dimensionless parameter e∆T that characterizes the thermal stratification of the fluid permittivity. Under the action of this thermoelectric buoyancy, a temperature difference in the fluid can give rise to the convection [2]. The electric gravity has also potential applications in aerospace engineering, as it can enhance heat transfer by inducing thermal convection under microgravity conditions. We performed a linear perturbation analysis to investigate the development of convective flows in the circular Couette flow under the action of the radial acceleration field g e. The analysis focused to the situation of vanishing Grashof number, i.e., under microgravity conditions , in order to highlight the effects of the electric gravity. The critical parameters, at which the flow lost stability, were determined with varying the Taylor number T a or the Rayleigh number L = α∆T g e (R 2 − R 1) 3 /νκ. Wide ranges of the Prandtl number P r = ν/κ and of the radius ratio η were considered. The different energy transfer processes from the basic to perturbation flows were examined in detail to get insight into instability mechanism