Convection in a mushy layer along a vertical heated wall
Journal of Fluid Mechanics Cambridge University Press (CUP) 926 (2021) A33
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>
Thermal convection over fractal surfaces
Journal of Fluid Mechanics Cambridge University Press 907 (2020) A12
Abstract: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
A synthesis of thermodynamic ablation at ice-ocean interfaces from theory, observations and models
Ocean Modelling Elsevier 154 (2020) 101692
Abstract:Thermodynamic ablation of ice in contact with the ocean is an essential element of ice sheet and ocean interactions but is challenging to model and quantify. Building on earlier observations of sea ice ablation, a variety of recent theoretical, experimental and observational studies have considered ice ablation in contrasting geometries, from vertical to near-horizontal ice faces, and reveal different scaling behaviour for predicted ablation rates in different dynamical regimes. However, uncertainties remain about when the contrasting results should be applied, as existing model parameterisations do not capture all relevant regimes of ice–ocean ablation. To progress towards improved models of ice–ocean interaction, we synthesise current understanding into a classification of ablation types. We examine the effect of the classification on the parameterisation of turbulent fluxes from the ocean towards the ice, and identify the dominant processes next to ice interfaces of different orientation. Four ablation types are defined: melting and dissolving based on ocean temperatures, and shear-controlled and buoyancy-controlled regimes based on the dynamics of the near-ice molecular sublayer. We describe existing observational and modelling studies of sea ice, ice shelves, and glacier termini, as well as laboratory studies, to show how they fit into this classification. Two sets of observations from the Ross and Ronne Ice Shelf cavities suggest that both the buoyancy-controlled and shear-controlled regimes may be relevant under different oceanographic conditions. Overall, buoyancy-controlled dynamics are more likely when the molecular sublayer has lower Reynolds number, and shear for higher Reynolds number, although the observations suggest some variability about this trend.
The dynamics of a subglacial salt wedge
Journal of Fluid Mechanics Cambridge University Press 895 (2020) A20