Destabilization of free convection by weak rotation

Abstract

This study offers an explanation of a recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by a simultaneous action of convection and rotation, it is concluded that the destabilization is observed in the cases where centrifugal force acts against main convective circulation. At relatively low Prandtl numbers this counter action can split the main vortex into two counter rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter action of the centrifugal force steepens an unstable thermal stratification, which triggers Rayleigh-B\'enard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied considering a combined convective/rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating magnetic field driven flow and melt flow in a Czochralski crystal growth model were derived

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

“…This is in full agreement with similar observations of [5,10]. The explanation for the destabilization by a slow rotation is given in a recent study [9]. Basing on the above frequency comparison one would expect experimental point to lay along the k = 0 numerical curve, however only two points out of six are close to this curve.…”

“…As a result, we are able to conrm experimentally the numerically predicted eect of destabilization of the Czochralski convective ow by a slow rotation [9,10], and to obtain certain quantitative agreement in comparison of experimentally * corresponding author; e-mail: gelfgat@tau.ac.il measured and numerically predicted frequencies of the ow oscillations.…”

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

“…1,2,28 The results showed that the flow structures and the critical condition for flow pattern transition are dependent on the rotation. Haslavsky et al 29 confirmed the destabilization effect of rotation that was reported by Gelfgat et al 14 With a high rotation rate, a good quantitative comparison between the numerical and experimental results was reached. Meanwhile, Lappa 30 investigated the hybrid thermocapillary-rotation-driven flow in both liquid bridge and annular pool when the buoyancy effect was absent.…”

“…It was found that the pool rotation destabilizes the basic steady axisymmetric thermocapillary flow. Gelfgat 14 also reported the destabilization effect of weak rotation. Recently, Shvarts 15 analytically investigated the stability of thermocapillary flow in a slowly rotating liquid layer in microgravity.…”

Primary oscillatory instability in a rotating disk–cylinder system with aspect (height/radius) ratio varying from 0.1 to 1

“…Since viscosity effects are necessarily strong near the corners and changes of the meridional velocities are steeper than that of the rotational one, neither of the two criteria is applicable there. We applied also the approach of Gelfgat (2011) in which different terms of the linear stability problem are cancelled one by one, while observing the cancellation of which leads to flow stabilization. Here, 'flow stabilization' means a change of sign of the leading eigenvalue from positive to negative.…”