Ice and Fluid Dynamics

Abstract:

Convection from a buoyancy source distributed over a vertical wall has diverse applications, from the natural ventilation of buildings to the melting of marine terminating glaciers which impact on future sea level. A key challenge involves determining how the rate and mechanisms of turbulent heat transfer should be extrapolated across a range of scales. Ke et al (J. Fluid Mech., vol. 964, 2023, A24) explore transitions in the turbulent flow dynamics using direct numerical simulation of a convective boundary layer at a heated vertical wall. A classical regime of heat transfer, consistent with previous laboratory experiments, gives way with increasing accumulation of buoyancy to an ultimate regime with enhanced heat transfer. The key to this transition lies in a near-wall sublayer, with a switch from laminar buoyancy-driven dynamics to a sublayer dominated by turbulence and shear instability from the mean flow.

Abstract:

<jats:p>Motivated by the mushy zones of sea ice, volcanoes and icy moons of the outer solar system, we perform a theoretical and numerical study of boundary-layer convection along a vertical heated wall in a bounded ideal mushy region. The mush is comprised of a porous and reactive binary alloy with a mixture of saline liquid in a solid matrix, and is studied in the near-eutectic approximation. Here, we demonstrate the existence of four regions and study their behaviour asymptotically. Starting from the bottom of the wall, the four regions are (i) an isotropic corner region; (ii) a buoyancy dominated vertical boundary layer; (iii) an isotropic connection region; and (iv) a horizontal boundary layer at the top boundary with strong gradients of pressure and buoyancy. Scalings from numerical simulations are consistent with the theoretical predictions. Close to the heated wall, the convection in the mushy layer is similar to a rising buoyant plume abruptly stopped at the top, leading to increased pressure and temperature in the upper region, whose impact is discussed as an efficient melting mechanism.</jats:p>