The effects of salinity and inclination on the morphology of melting ice

Abstract

The salinity of water and the slope of ice significantly influence the melt rate and surface morphology of ice, both highly relevant in the context of glacier and iceberg melting in oceanic environments. In this study, we conducted experiments on vertical and sloped ice blocks melting in quiescent saline water. Through the use of fringe projection profilometry, we measured the morphology of the ice's front face. In particular, we combine the spatio-temporal phase shifting and orthogonal sampling moire methods. The far field salinity in the experiments ranged from 0 g/kg to 35 g/kg, and angles were between -18° and 50°. The ice block sizes were 32 cm $\times$ 23 cm $\times$ 12 cm high, wide, and long respectively, leading to Ra = $\mathcal{O}(10^7)$. We identified and classify five surface morphologies and regimes arising from the flow regimes imposed by salinity and inclination, namely scalloped, channelized, top-melting, bottom-melting, and incurved. The channelized morphology consists of vertical channels carved along the ice surface, whose development originates from a Rayleigh--Bénard type instability, and which are enhanced by bubbles released from the melting ice and rising along the interface. The scalloped regime is characterize by a rough dimpled pattern commonly referred to as scallops. We observe that increasing the salinity leads to scallops that are smaller, shallower, and more uniform in size. Additionally, a salinity dependence of the melt rate is found, showing a non-monotonic behavior, while the inclination angle shows little influence on the overall melt rate.

Figures (12)

• Figure 1: Top $a)$ and side $b)$ views of the experimental setup. A rectangular ice block of dimensions $H\times W\times L$ is placed in the center of the glass tank. A projector and camera, with parallel optical axes, are at a distance $D$ from the ice block, while being a distance $d$ from each other. The ice block is inclined with an angle $\theta$, where the arrow denotes positive angles.
• Figure 2: Side view sketch of the boundary layers for the three different regimes. The boundary layer thicknesses are not shown to scale. $a)$ In the temperature-driven regime ($R_\rho < 1$) the thermal boundary layer is denser than the ambient water, therefore it flows down. $b)$ A inner solutal boundary layer forms in the competing regime ($R_\rho \approx 2$). This layer is less dense than the outer thermal boundary layer, creating a bidirectional flow. $c)$ In the salinity driven regime ($R_\rho \gg 1$) the driving of the solutal boundary layer is much stronger than the thermal boundary layer, except near the leading edge at the bottom where the solutal boundary layer is forming.
• Figure 3: $R_\rho - \theta$ parameter space of the performed experiments, including the observed morphology at the end of each experiment. Background colors indicate the morphology at the nearest experimental data point (Voronoï construction), providing a visual guide to the distribution of morphologies in phase space. For the Voronoï construction, both axes are normalized by their respective ranges so that distances in the parameter space are treated equally. 3D renders of the different surface morphologies are shown on the bottom, see the supplemental material at [URL will be inserted by publisher] for a movie of the renders. For reference, the bounding box height is 28 cm. Figures \ref{['fig:profile_salinity']} and \ref{['fig:profile_inclined']} show quantitative profiles for the experiments marked with filled triangles and disks, respectively.
• Figure 4: Vertical ice faces: height profiles at 30 minutes of starting the experiment for three different flow regimes: $a)$$S=0.0$ g/kg, $T_w = 21.0$ °C, $\theta = -2.0$°, Ra $= 4.1 \times 10^6$, and $R_\rho=0.0$; $b)$$S=14.8$ g/kg, $T_w = 20.0$ °C, $\theta = -0.3$°, Ra $= 2.1 \times 10^7$, and $R_\rho=4.6$; $c)$$S=27.4$ g/kg, $T_w = 17.8$ °C, $\theta = 1.1$°, Ra $= 8.5 \times 10^7$, and $R_\rho=8.5$.
• Figure 5: Tilted ice faces: height profiles at 30 minutes for two different flow regimes and three different morphologies: $a)$$S=0.0$ g/kg, $T_w = 19.0$ °C, $\theta = 34.5$°, Ra $= 2.6 \times 10^6$, and $R_\rho=0.0$; $b)$$S=7.0$ g/kg, $T_w = 20.3$ °C, $\theta = 29.3$°, Ra $= 7.0 \times 10^6$, and $R_\rho=2.6$; $c)$$S=13.3$ g/kg, $T_w = 19.4$ °C, $\theta = 28.8$°, Ra $= 1.7 \times 10^7$, and $R_\rho=4.6$.