Convection in a mushy layer along a vertical heated wall

Journal of Fluid Mechanics Cambridge University Press (CUP) 926 (2021) A33


S Boury, Cr Meyer, Gm Vasil, Aj Wells


<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>

The role of grain-environment heterogeneity in normal grain growth: A stochastic approach

ACTA MATERIALIA 209 (2021) ARTN 116699


Thomas Breithaupt, Lars N Hansen, Srikanth Toppaladoddi, Richard F Katz

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

Journal of Fluid Mechanics 919 (2021)


Well-resolved numerical simulations are used to study Rayleigh-Bénard-Poiseuille flow over an evolving phase boundary for moderate values of Péclet and Rayleigh numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number:, where is the Prandtl number. For, we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction and, for, the flow properties and heat transport closely correspond to the purely convective case. We also find that for certain and, such that, there is a pattern competition for convection cells with a preferred aspect ratio. Furthermore, we find travelling waves at the solid-liquid interface when, 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).

Thermal convection over fractal surfaces

Journal of Fluid Mechanics Cambridge University Press 907 (2020) A12


Srikanth Toppaladoddi, Andrew J Wells, Charles R Doering, John S Wettlaufer


We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-B´enard convection in cells with a fractal boundary in two dimensions for P r = 1 and Ra ∈ [10^7 , 10^10]. The fractal boundaries are functions characterized by power spectral densities S(k) that decay with wavenumber, k, as S(k) ∼ k^p (p < 0). The degree of roughness is quantified by the exponent p with p < −3 for smooth (differentiable) surfaces and −3 ≤ p < −1 for rough surfaces with Hausdorff dimension D_f =1/2 (p + 5). By computing the exponent β in power law fits Nu ∼ Ra^β, where Nu and Ra are the Nusselt and the Rayleigh numbers for Ra ∈ [10^8, 10^10], we observe that heat transport scaling increases with roughness over the top two decades of Ra ∈ [10^8, 10^10]. For p = −3.0, −2.0 and −1.5 we find β = 0.288 ± 0.005, 0.329 ± 0.006 and 0.352 ± 0.011, respectively. We also observe that the Reynolds number, Re, scales as Re ∼ Ra^ξ , where ξ ≈ 0.57 over Ra ∈ [10^7, 10^10], for all p used in the study. For a given value of p, the averaged Nu and Re are insensitive to the specific realization of the roughness.

Modeling sea ice

Notices of the American Mathematical Society American Mathematical Society 67:10 (2020) 1535-1555


Kenneth Golden, Luke Bennetts, Elena Cherkaev, Ian Eisenman, Daniel Feltham, Christopher Horvat, Elizabeth Hunke, Christopher Jones, Donald Perovich, Pedro Ponte-Castaneda, Courtenay Strong, Deborah Sulsky, Andrew Wells