Nonlinear interactions between an unstably stratified shear flow and a phase boundary

S. Toppaladoddi

doi:10.1017/jfm.2021.396

paper

Nonlinear interactions between an unstably stratified shear flow and a phase boundary

arXiv:2008.10043 · doi:10.1017/jfm.2021.396

Abstract

Well-resolved numerical simulations are used to study Rayleigh-Bénard-Poiseuille flow over an evolving phase boundary for moderate values of Péclet ( $P e \in [0, 50]$ ) and Rayleigh ( $R a \in [2.15 \times 1 0^{3}, 1 0^{6}]$ ) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: $R i_{b} = R a \cdot P r / P e^{2} \in [8.6 \times 1 0^{- 1}, 1 0^{4}]$ , where $P r$ is the Prandtl number. For $R i_{b} = O (1)$ , we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction; and, for $R i_{b} ≫ 1$ the flow properties and heat transport closely correspond to the purely convective case. We also find that for certain $R a$ and $P e$ , such that $R i_{b} \in [15, 95]$ , there is a pattern competition for convection cells with a preferred aspect ratio. Furthermore, we find travelling waves at the solid-liquid interface when $P e \neq = 0$ , in qualitative agreement with other sheared convective flows in the experiments of Gilpin \emph{et al.} (\emph{J. Fluid Mech} {\bf 99}(3), pp. 619-640, 1980) and the linear stability analysis of Toppaladoddi and Wettlaufer (\emph{J. Fluid Mech.} {\bf 868}, pp. 648-665, 2019).

14 pages, 25 figures

Nonlinear interactions between an unstably stratified shear flow and a phase boundary

Abstract

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