Turbulent convection in subglacial lakes

Subglacial lakes are isolated, low-temperature and high-pressure water environments hidden under ice sheets. Here, we use two-dimensional direct numerical simulations in order to investigate the characteristic temperature fluctuations and velocities in freshwater subglacial lakes as functions of the ice overburden pressure, pi, the water depth, h, and the geothermal flux, F. Geothermal heating is the unique forcing mechanism as we consider a flat ice–water interface. Subglacial lakes are fully convective when pi is larger than the critical pressure p∗≈2848 dbar, but self-organize into a lower convective bulk and an upper stably stratified layer when pi<p∗, because of the existence at low pressure of a density maximum at temperature Td greater than the freezing temperature Tf. For both high and low pi, we demonstrate that the Nusselt number, Nu, and Reynolds number, Re, satisfy classical scaling laws provided that an effective Rayleigh number Raeff is considered. We show that the convective and stably stratified layers at low pressure are dynamically decoupled at leading order because plume penetration is weak and induces limited entrainment of the stable fluid. From the empirical equation for Nu with Raeff, we derive two sets of closed-form expressions for several variables of interest, including the unknown bottom temperature, in terms of the problem parameters pi, h and F. The two predictions correspond to two limiting regimes obtained when the effective thermal expansion coefficient is either approximately constant or linearly proportional to the temperature difference driving the convection.

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