Ice and Fluid Dynamics

Abstract:

The growth of frazil or granular ice is an important mode of ice formation in the cryosphere. Recent advances have improved our understanding of the microphysical processes that control the rate of ice-crystal growth when water is cooled beneath its freezing temperature. These advances suggest that crystals grow much faster than previously thought. In this paper, we consider models of a population of ice crystals with different sizes to provide insight into the treatment of frazil ice in large-scale models. We consider the role of crystal growth alongside the other physical processes that determine the dynamics of frazil ice. We apply our model to a simple mixed layer (such as at the surface of the ocean) and to a buoyant plume under a floating ice shelf. We provide numerical calculations and scaling arguments to predict the occurrence of frazilice explosions, which we show are controlled by crystal growth, nucleation and, gravitational removal. Faster crystal growth, higher secondary nucleation and slower gravitational removal make frazil-ice explosions more likely. We identify steady-state crystal size distributions, which are largely insensitive to crystal growth rate but are affected by the relative importance of secondary nucleation to gravitational removal. Finally, we show that the fate of plumes underneath ice shelves is dramatically affected by frazil-ice dynamics. Differences in the parameterization of crystal growth and nucleation give rise to radically different predictions of basal accretion and plume dynamics; and can even impact whether a plume reaches the end of the ice shelf or intrudes at depth.

Abstract:

The growth of frazil or granular ice is an important mode of ice formation in the cryosphere. Recent advances have improved our understanding of the microphysical processes that control the rate of ice-crystal growth when water is cooled beneath its freezing temperature. These advances suggest that crystals grow much faster than previously thought. In this paper, we consider models of a population of ice crystals with different sizes to provide insight into the treatment of frazil ice in large-scale models. We consider the role of crystal growth alongside the other physical processes that determine the dynamics of frazil ice. We apply our model to a simple mixed layer (such as at the surface of the ocean) and to a buoyant plume under a floating ice shelf. We provide numerical calculations and scaling arguments to predict the occurrence of frazil-ice explosions, which we show are controlled by crystal growth, nucleation and, gravitational removal. Faster crystal growth, higher secondary nucleation and slower gravitational removal make frazil-ice explosions more likely. We identify steady-state crystal size distributions, which are largely insensitive to crystal growth rate but are affected by the relative importance of secondary nucleation to gravitational removal. Finally, we show that the fate of plumes underneath ice shelves is dramatically affected by frazil-ice dynamics. Differences in the parameterization of crystal growth and nucleation give rise to radically different predictions of basal accretion and plume dynamics; and can even impact whether a plume reaches the end of the ice shelf or intrudes at depth.

Abstract:

We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr=1 and Ra=[4×10^{6},3×10^{9}]. By varying the wavelength λ at a fixed amplitude, we find an optimal wavelength λ_{opt} for which the Nusselt-Rayleigh scaling relation is (Nu-1∝Ra^{0.483}), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)JFLSA70022-112010.1017/jfm.2016.528] who prove that Nu can grow no faster than O(Ra^{1/2}) as Ra→∞, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When λ≪λ_{opt} and λ≫λ_{opt}, the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all λ, thus optimizing over all λ, to find Nu_{opt}-1=0.01×Ra^{0.444}.

Abstract:

The melting of submerged faces of marine-terminating glaciers is a key contributor to the glacial mass budget via direct thermodynamic ablation and the impact of ablation on calving. This study considers the behavior of turbulent plumes of buoyant meltwater in a stratified ocean, generated by melting of either near-vertical calving faces or sloping ice shelves. We build insight by applying a turbulent plume model to describe melting of a locally planar region of ice face in a linearly stratified ocean, in a regime where subglacial discharge is insignificant. The plumes rise until becoming neutrally buoyant, before intruding into the ocean background. For strong stratifications, we obtain leading-order scaling laws for the flow including the height reached by the plume before intrusion, and the melt rate, expressed in terms of the background ocean temperature and salinity stratifications. These scaling laws provide a new perspective for parameterizing glacial melting in response to a piecewise-linear discretization of the ocean stratification.