Abstract
Ice-covered waterbodies are far from being quiescent systems. In this paper, we investigate ice-covered freshwater basins heated by solar radiation that penetrates across waters with temperatures below or near the temperature of maximum density. In this scenario, solar radiation sets a radiative buoyancy flux, $\unicode[STIX]{x1D6F7}_{r}$, that forces increments of temperature/density in the upper fluid volume, which can become gravitationally unstable and drive convection. The goal of this study is twofold. We first focus on formulating the mechanical energy budget, putting emphasis on the conversion of $\unicode[STIX]{x1D6F7}_{r}$ to available potential energy, $E_{a}$. We find that $E_{a}$ results from a competition among $\unicode[STIX]{x1D6F7}_{r}$ and the irreversible mixing controlled by the diapycnal and the laminar mixing rates, respectively. Secondly, and based on the above result, we introduce an integral formulation of the mixing efficiency to quantify the rate of mixing over the relevant time scale $\unicode[STIX]{x1D70F}$, $\unicode[STIX]{x1D702}_{c}\equiv \unicode[STIX]{x0394}E_{b,\unicode[STIX]{x1D70F}}/E_{r,\unicode[STIX]{x1D70F}}$, where $\unicode[STIX]{x0394}E_{b,\unicode[STIX]{x1D70F}}$ and $E_{r,\unicode[STIX]{x1D70F}}$ are the change of background potential energy and the time-integrated $\unicode[STIX]{x1D6F7}_{r}$ over $\unicode[STIX]{x1D70F}$. The above definition is applied to estimate $\unicode[STIX]{x1D702}_{c}$ for the first time, finding an approximate value of $\unicode[STIX]{x1D702}_{c}\approx 0.65$. This result suggests that radiatively heated ice-covered waterbodies might be subject to high mixing rates. Overall, the present work provides a framework to examine energetics and mixing in ice-covered waters.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
27 articles.
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