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

TL;DR

This study uses high-resolution simulations to explore the nonlinear interactions between shear flow, buoyancy, and phase boundaries, revealing how these factors influence heat transport, flow patterns, and interface dynamics in stratified flows.

Contribution

It provides new insights into the combined effects of shear and buoyancy on phase boundary behavior and heat transfer in stratified flows, with detailed analysis across a range of parameters.

Findings

Flow inhibition at Ri_b ≈ 1 leads to conduction-dominated heat transfer.

Flow resembles pure convection at high Ri_b values.

Traveling waves observed at the solid-liquid interface for Pe ≠ 0.

Abstract

Well-resolved numerical simulations are used to study Rayleigh-B\'enard-Poiseuille flow over an evolving phase boundary for moderate values of P\'eclet ($Pe \in \left[0, 50\right]$) and Rayleigh ($Ra \in \left[2.15 \times 10^3, 10^6\right]$) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: $Ri_b = Ra \cdot Pr/Pe^2 \in [8.6 \times 10^{-1}, 10^4]$, where $Pr$ is the Prandtl number. For $Ri_b = \mathcal{O}(1)$, we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction; and, for $Ri_b \gg 1$ the flow properties and heat transport closely correspond to the purely convective case. We also find that for certain $Ra$ and $Pe$, such that $Ri_b \in \left[15,95\right]$, there is a pattern competition for convection cells with a preferred aspect ratio. Furthermore, we find travelling waves at the solid-liquid interface when $Pe \neq 0$, 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).