Laminar uni- and bi-directional boundary-layer flow of a melting vertical ice face: experiments and direct numerical simulations

A combined experimental and direct numerical simulation (DNS) investigation is undertaken to study the laminar boundary-layer (BL) flow adjacent to a melting vertical ice face at two far-field water salinities ( $S_\infty =0$ and 34 ‰) and a range of far-field temperatures ( $T_\infty$ ). Wall-normal distributions of vertical velocity and temperature within the BL are measured by a modified molecular tagging velocimetry and thermometry technique. Experimental data match with DNS only when a nonlinear equation of state (EoS) for density is used rather than a linear EoS. For all $S_\infty =0$ , i.e. freshwater cases, the flow remains uni-directional, although the flow reverses direction at $T_\infty =4^{\,\circ} \text{C}$ . A bi-directional flow, however, exists for $S_\infty =$ 34 g kg −1 , where an inner salinity-driven upward flow of fresher water is accompanied by a downward-flowing temperature-driven outer flow. Although the contribution of temperature to density relative to salinity is small $({\approx}1/40)$ , the thermal BL region is larger owing to higher diffusivity. This results in increased total buoyancy force when the buoyancy is integrated across the BL, which combined with effects of wall shear stress on salinity BL and a freer thermal BL growth reveals that buoyancy from temperature contributes almost equally to the overall flow. Melt rates ( $V$ ) also show differing features in uni- and bi-directional flows. The uni-directional flows exhibit the standard scaling of increasing velocity magnitude and BL thickness, and decreasing $V$ with distance along the flow direction. Such scalings are not followed in the bi-directional flows. These show a more uniform $V$ with height, which is attributed to the counteracting effects of an upward-growing salinity BL and a downward-growing temperature BL, combined with the necessity of maintaining salinity and temperature flux balance at the ice–water interface.