Under‐ice salinity transport in low‐salinity waterbodies

Abstract

In cold and temperate climates, ice typically covers the surface of waterbodies during winter. Many of these systems are also weakly saline where, unlike seawater, the temperature of maximum density, Tfalse˜md, is higher than its freezing temperature, Tfalse˜f. This feature of the equation of state results in a stable temperature stratification when surface waters cool below Tfalse˜md. Conversely, salts excluded from the growing ice can destabilize the underlying water. Previous laboratory and field experiments demonstrated that excluded salts generate localized overturning and downward transport of salt, despite the persistence of a stable temperature gradient. Those experiments were not able to determine the processes responsible for this transport. Here, we use direct numerical simulations to visualize and characterize the plumes generated when ice excludes salt into a stable temperature gradient. We restrict our analysis to times much earlier than the diffusion timescale of temperature over the domain. We define a mass flux parameter ℜ that considers the strength of the reverse‐temperature stratification relative to the rate of salt exclusion. We identify two types of plumes whose characteristics depend mainly on ℜ: double‐diffusive salt‐fingering plumes and convective plumes. The former encourages transport of salt to the bottom without significantly mixing the temperature stratification, while the latter tends to mix the water column. We apply a scaled mass flux parameter to published laboratory and field observations in low‐salinity systems. These limited observations compare favorably with our numerical analysis.

Brine rejection leads to salt-fingers in seasonally ice-covered lakes

“…We observe that w rms increases with R. For large values of R 1, w rms appears to saturate with a value of w rms /w rms,0 ≈ 2. We associate this saturation with the expected regime change around R ≈ 1 from double-diffusive fingers to salt-driven convection (Olsthoorn et al, 2020). Olsthoorn et al (2020) similarly observed a saturation in the relative heat flux and associated it with the same regime transition.…”

“…We note that both axes contain the brine rejection rate F S , and, in that sense, are not orthogonal quantities. We include the data from the two-dimensional numerical simulations from Olsthoorn et al (2020). For the numerical data, the mean salinity in the bottom 5% of the domain was used as a numerical proxy for S B .…”

“…This nonlinear temperature dependence enables lakes to reverse stratify under ice, with colder-water (reaching the freezing temperature at the ice-water interface) above warmer water below. Despite this stable temperature stratification, Bluteau et al (2017) and Olsthoorn et al (2020) showed that once enough brine is rejected, double-diffusive plumes will form that transport salty water from the ice-water interface to the lake bottom. This type of double-diffusive salt-fingering has been shown to be complicated by the nonlinear equation of state ( Özgökmen & Esenkov, 1998).…”

The Cooling Box Problem: Convection with a quadratic equation of state

“…As shown by Veronis [32], there exists a minimum Ra, below which the system is stable. For Ra close to this value, the fit (23) does not agree well with the data. Further, there is a minimum T B [T B,min ], where the system is linearly stable.…”

“…Bouffard and Wüest [5] further stressed the importance of radiatively driven convection and other under-ice processes such as thermobaric instability and bottom sediment heating. Other recent advances have included a discussion of under-ice intrusions [12], internal wave generation [6,11], and brine rejection [4,23].…”