Dissolution of a vertical solid surface by turbulent compositional convection

Abstract

We examine the dissolution of a vertical solid surface in the case where the heat and mass transfer is driven by turbulent compositional convection. A theoretical model of the turbulent dissolution of a vertical wall is developed, which builds on the scaling analysis presented by Kerr (J. Fluid Mech., vol. 280, 1994, pp. 287–302) for the turbulent dissolution of a horizontal floor or roof. The model has no free parameters and no dependence on height. The analysis is tested by comparing it with laboratory measurements of the ablation of a vertical ice wall in contact with salty water. The model is found to accurately predict the dissolution velocity for water temperatures up to approximately 5–$6\,^{\circ }\text{C}$, where there is a transition from turbulent dissolution to turbulent melting. We quantify the turbulent convective dissolution of vertical ice bodies in the polar oceans, and compare our results with some field observations.

The effect of a salinity gradient on the dissolution of a vertical ice face

“…Figure 3 shows the measured interface temperature as a function of the BruntVäisälä frequency, N = (−(g/ρ 0 )(dρ/dz)) 1/2 , where ρ 0 is the density at mid-depth. The theory of Kerr & McConnochie (2015) suggests that, for a far-field temperature of T f = 3.5 • C and a homogeneous far-field salinity of C f = 3.5 wt% NaCl, the interface temperature should be −0.52 • C. This agrees with the low-stratification experiments shown in figure 3.…”

“…Table 1 shows the experimental parameters and results for the stratified ambient experiments where an interface temperature was measured. Like the homogeneous ambient experiments of Kerr & McConnochie (2015), we observed no height dependence on interface temperature. Figure 3 shows the measured interface temperature as a function of the BruntVäisälä frequency, N = (−(g/ρ 0 )(dρ/dz)) 1/2 , where ρ 0 is the density at mid-depth.…”

“…However, when ice dissolves the interface temperature will be below the freezing point of the solid and the interface concentration will be non-zero. Kerr & McConnochie (2015) observed the dissolution of ice for similar experiments in a homogeneous ambient fluid.…”

“…During filling the ice was protected from the salty water by an acrylic barrier. The experimental apparatus and method are more fully described in Kerr & McConnochie (2015).…”

“…It was estimated that the ablation velocity is reduced by up to an order of magnitude when compared with the homogeneous case, but no more detail was provided (Huppert & Josberger 1980). Kerr & McConnochie (2015) showed that when ice dissolves into cold homogeneous salty water the ablation velocity, V, is given by…”