Ice and Fluid Dynamics

Abstract:

The physics of planetary climate features a variety of complex systems that are challenging to model as they feature turbulent flows. A key example is the heat flux from the upper ocean to the underside of sea ice which provides a key contribution to the evolution of the Arctic sea ice cover. Here, we develop a model of the turbulent ice-ocean heat flux using coupled ordinary stochastic differential equations to model fluctuations in the vertical velocity and temperature in the Arctic mixed layer. All the parameters in the model are determined from observational data. A detailed comparison between the model results and measurements made during the Surface Heat Budget of the Arctic Ocean (SHEBA) project reveals that the model is able to capture the probability density functions (PDFs) of velocity, temperature and heat flux fluctuations. Furthermore, we show that the temperature in the upper layer of the Arctic ocean can be treated as a passive scalar during the whole year of SHEBA measurements. The stochastic model developed here provides a computationally inexpensive way to compute an observationally consistent PDF of this heat flux, and has implications for its parametrization in regional and global climate models.

Abstract:

We study a simplified model of ice-ocean interaction beneath a floating ice shelf, and investigate the possibility for channels to form in the ice shelf base due to spatial variations in conditions at the grounding line. The model combines an extensional thin-film description of viscous ice flow in the shelf, with melting at its base driven by a turbulent ocean plume. Small transverse perturbations to the one-dimensional steady state are considered, driven either by ice thickness or subglacial discharge variations across the grounding line. Either forcing leads to the growth of channels downstream, with melting driven by locally enhanced ocean velocities, and thus heat transfer. Narrow channels are smoothed out due to turbulent mixing in the ocean plume, leading to a preferred wavelength for channel growth. In the absence of perturbations at the grounding line, linear stability analysis suggests that the one dimensional state is stable to initial perturbations, chiefly due to the background ice advection.

Abstract:

We take a numerical approach to analyze the mechanisms controlling the spacing of chimneys -- channels devoid of solid -- in two-dimensional mushy layers formed by solidifying a binary alloy. Chimneys are the principal conduits through which buoyancy effects transport material out of the mushy layer and into the liquid from which it formed. Experiments show a coarsening of chimney spacing and we pursue the hypothesis that this observation is a consequence of a variational principle: the chimney spacing adjusts to optimize material transport and hence maximize the rate of removal of potential energy stored in the mushy layer. The optimal solute flux increases approximately linearly with the mushy layer Rayleigh number. However, for spacings below a critical value the chimneys collapse and solute fluxes cease, revealing a hysteresis between chimney convection and no flow.