Direct Numerical Simulations of Ice-Ocean Boundary Turbulence

Abstract

Turbulent heat and freshwater transport at ice-ocean interfaces controls glacier and iceberg melt rates, yet the underlying physics remains poorly constrained. Parameterizations that assume shear boundary layer scaling are commonly used, which neglects meltwater buoyancy-driven convective processes. Using Direct Numerical Simulations with realistic salt diffusivity, which is critical for representing the thin solutal boundary layer (deltaS ~ 0.4 mm) and resulting convective instabilities, we investigate ice-ocean boundary layer turbulence across varying temperature, salinity, stratification, external velocity, and interfacial slope angles. Our simulations agree with laboratory measurements of melt rate and interfacial temperature. In the absence of external flows, we find no transition from buoyancy-controlled to shear-controlled regimes and convection is important even at near-horizontal slopes. External shear becomes significant only when it is strong enough to thin the thermal and solutal boundary layers, which starts influence melting substantially above background flow speeds of 5 cm/s. Understanding how shear and convection compete to determine the ice-ocean diffusive boundary layer enables accurate melt rate predictions across the parameter space relevant to ice shelves and marine-terminating glaciers.

Figures (8)

• Figure 1: Side view (x is normal to ice) of (a) w (vertical velocity), (b) $\zeta_y$ vorticity in y-plane (c) T (in situ temperature), (d) S (salinity) (e) temperature at yz-plane 1 mm away from the ice wall, (f) salinity at yz plane at 1 mm away from the ice wall, and (g) melt rate on the yz plane (um/s). All fields show the instantaneous variable at time t=600 seconds for reference case.
• Figure 2: Instantaneous fields at $t=600$ s for the reference case in the $xz$-plane: ($a$) vorticity in $y$-plane, ($b$) temperature $T$, ($c$) salinity $S$. Panels ($d$)--($f$) show the same fields as ($a$)--($c$) zoomed to the millimeter scale near the ice interface. Panels ($g$)--($h$) show three-dimensional vortex tube visualizations using isosurfaces of the $Q$-criterion ($Q = 0.03$ s$^{-2}$), colored by vorticity magnitude.
• Figure 3: Wall-normal ($x$) profiles of (a,b) temperature, (c,d) salinity, and (e,f) vertical velocity from simulations with varying Schmidt number and melt boundary conditions. Left column (a,c,e) shows linear scaling, while right column (b,d,f) shows logarithmic scaling to resolve near-interface structure. Three cases are compared: $Sc = 100$ (red), $Sc = 2500$ with a stationary boundary (green), and $Sc = 2500$ with retreating melt boundary (blue). Shading represents the root-mean square deviation of each parameter and these profiles are time- and vertically averaged.
• Figure 4: Temperature-Salinity diagram illustrating turbulent mixing and closure behavior near the ice-ocean interface. The diagram shows the evolution of water properties in T-S space, with salinity (psu) on the vertical axis and temperature ($^\circ$C) on the horizontal axis. The solid blue line represents the model output trajectory, with shaded regions indicating temporal variability. The dotted blue line denotes the inner closure approximation using Eq. \ref{['Eq33']}. The red dashed line indicates the meltwater mixing line, connecting the ambient ocean properties to the interface conditions. The solid black line represents the full closure solution. Three distinct mixing regimes are identified in the panels above: (left) $\hat{\kappa}_T = \kappa_T$, $\hat{\kappa}_S = \kappa_S$, representing independent thermal and haline diffusion; (center) $\kappa_S = \kappa_e$, $\kappa_T = \kappa_T$, indicating enhanced salt transport; and (right) $\hat{\kappa}_T = \hat{\kappa}_S = \kappa_e$, representing uniform turbulent diffusion. The characteristic boundary layer thicknesses $\delta_T$ and $\delta_S$ are marked with vertical and horizontal bars, respectively, illustrating the different diffusively-dominated regions for heat and salt.
• Figure 5: Vertically and time-averaged budget terms for (a) temperature, (b) salinity, and (c) vertical momentum. Vertical dashed lines indicate the characteristic boundary layer thicknesses $\delta_T$, $\delta_S$, and $\delta_u$. Red lines denote the molecular diffusion terms for temperature and salinity ($\kappa_T \partial_{xx} T$, $\kappa_S \partial_{xx} S$) and the buoyancy term, $b = g(\alpha T - \beta S)$. Yellow and purple curves denote the horizontal and vertical advection terms in the scalar budgets and yellow denotes the Reynolds stress term in the momentum budget. $\overline{\cdot}$ denotes a time average.