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

Well-resolved numerical simulations are used to study Rayleigh-Benard-Poiseuille flow over an evolving phase boundary for moderate values of Peclet (Pe is an element of[0, 50]) and Rayleigh (Ra is an element of [2.15 x 10(3), 10(6])) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: Ri(b) = Pr/Pe(2) is an element of[8.6 x 10(-1), 10(4)], where is the Prandtl number. For Ri(b) = 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) >> 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) is an element of[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 Pe not equal 0, in qualitative agreement with other sheared convective flows in the experiments of Gilpin et al. (J. Fluid Mech., vol. 99(3), 1980, pp. 619-640) and the linear stability analysis of Toppaladoddi & Wettlaufer (J. Fluid Mech., vol. 868, 2019, pp. 648-665).

Automated summary

The study investigates the Rayleigh-Benard-Poiseuille flow over an evolving phase boundary using numerical simulations. The results show that Poiseuille flow inhibits convective motion, leading to heat transport primarily through conduction, while for Ri(b) >> 1, flow properties and heat transport closely resemble the purely convective case. In certain conditions, there is pattern competition for convection cells with a preferred aspect ratio. Additionally, traveling waves at the solid-liquid interface are observed when Pe is not equal to 0, in agreement with experimental findings and linear stability analysis.