Turbulent heat exchange between water and ice at an evolving ice-water interface

Experimental results are presented on the time evolution of ice subject to a turbulent shear flow in a layer of water of uniform depth. Our study is motivated by observations in the ocean cavity beneath Antarctic ice shelves, where shoaling of Circumpolar Deep Water into the cavity has been implicated in the accelerated melting of the ice shelf base. Measurements of inflow and outflow at the ice shelf front have shown that not all of the heat entering the cavity is delivered to the ice shelf, suggesting that turbulent transfer to the ice represents an important bottleneck. Given that a range of turbulent transfer coefficients has been used in models it is important to better constrain this parameter. We measure as a function of time in our experiments the thickness of the ice, temperatures in the ice and water, and fluid velocity in the shear flow, starting from an initial condition in which the water is at rest and the ice has grown by conduction above a cold plate. The strength of the applied turbulent shear flow is represented in terms of a Reynolds number Re, which is varied over the range 3.5 × 103 ≤ Re ≤ 1.9 × 104. Transient partial melting of the ice occurs at the lower end of this range of Re and complete transient melting of the ice occurs at the higher end of the range. Following these melting transients, the ice reforms at a rate that is independent of Re. We fit to our experimental measurements of ice thickness and temperature a one-dimensional model for the evolution of the ice thickness in which the turbulent heat transfer is parameterized in terms of the friction velocity of the shear flow. Comparison with the Pine Island Glacier Ice Shelf yields qualitative agreement between the transient ice melting rates predicted by our model and the shelf melting rate inferred from the field observations.