Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.

Adviser: John S. Wettlaufer.

Arctic sea ice occupies a central place in the Earth's climate system because of (a) its role in driving the global thermohaline circulation, which, in addition to transporting dense waters to the midlatitudes, transports nutrients and dissolved gases around the globe, and (b) its albedo, which causes a large fraction of the incoming short-wave radiation to be reflected back to space, thus influencing Earth's radiation budget. The key quantity of interest in climate studies is the sea-ice volume. Although the areal extent of sea ice is routinely measured using satellites, measuring its thickness still remains technically challenging.

Using concepts from non-equilibrium statistical physics, we develop a mathematical theory for the evolution of the sea-ice thickness. The evolution of the thickness field is sought in terms of a probability distribution function (PDF) that evolves due to (a) the motion of ice floes, which is forced by wind and ocean currents, (b) thermal growth, and (c) mechanical interactions between the ice floes. The principal difficulty in developing a closed theory for the evolution of the PDF has been the intransigency of the mechanical-interaction term, whose mathematical form could not be deduced from observations. We overcome this difficulty by interpreting the term as a collision integral, thereby deriving a Fokker-Planck equation for the PDF. The functional form of the steady solution of this equation is shown to be in agreement with recent satellite measurements. Moreover, by solving the corresponding Langevin equation we show that the thickness field is ergodic, which implies that its basin-wide measurement at any given time and its measurement from a fixed location over a long period of time would result in the same PDF.

We further demonstrate the utility of our approach by coupling the Fokker-Planck equation to an observationally consistent one-dimensional thermodynamic model for sea-ice growth to study the climatological evolution of the PDF. We find the seasonal changes in the PDF from our theory to be in qualitative agreement with recent satellite measurements; and also that the ice cover survives large greenhouse-gas forcing because of mechanics.

Another aspect that has considerable influence on the sea-ice growth rate, and hence on the PDF, is the turbulent oceanic heat flux. It is known from solely thermodynamic models that the thickness is sensitive to this flux, but a systematic study has not been attempted because it involves turbulent flow of ocean over a moving ice-ocean interface, which is observed to be a fractal. Using the Lattice Boltzmann Method, which is derived from Boltzmann kinetic theory, for simulation of turbulent thermal convection over regular rough walls; we show that the heat flux is maximized at a certain wavelength of roughness.

Finally, to understand the coupling between a layer of ice and fluid flow over it, we study penetrative convection of a fluid with a density maximum at a certain temperature and the effects of shear and buoyancy on the stability of a solid-liquid interface. Using analytical and numerical tools, we show that the overlying stable layer has a considerable influence on the flow structure and heat transport in penetrative convection. We also demonstrate the importance of convection, together with shear, in creating an instability of the solid-liquid interface, which is important in the generation of underice topography and its coupling to the flow of ocean.

Taken together, the confluence of phenomena that control the climatological fate of the ice cover and hence global scale climate change, are understood within the framework of non-equilibrium statistical mechanics.