Transition from buoyancy-driven to shear-driven melting in a buoyant plume at a vertical ice face

Melting of a vertical ice face in otherwise quiescent saline water generates a buoyant plume that rises along the ice. Heat and salt transfer through the thin near-wall boundary layers controls the melt rate and must be parameterized in models that do not resolve these layers. In plume models, the three-equation framework of Holland \& Jenkins (1999) is commonly coupled to transfer laws based on plume-induced shear. Under weak-shear conditions, however, laboratory experiments and simulations show that melting is controlled by buoyancy-driven convection and is approximately independent of plume velocity. Here, we develop a boundary-layer theory that unifies these two transfer regimes. The melt rate is set by the boundary-layer thicknesses, which in turn is governed by two competing length scales: a viscous length and a buoyancy viscous length scale. The resulting flux laws recover existing shear-driven and buoyancy-driven models as limits, retain the algebraic structure of the three-equation model, and predict a regime transition when the two length scales become comparable, corresponding to a plume velocity of roughly 6-8 cm/s for typical fjord conditions. We test the theory using large-eddy simulations that resolve the diffusive sublayers adjacent to a melting vertical ice face. In these simulations a melt-driven plume starts in the buoyancy-driven regime and transitions into the shear-driven regime. The melt rates across the transition are well described by the unified theory.