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Mechanical energy budget and mixing efficiency for a radiatively heated ice-covered waterbody

Published online by Cambridge University Press:  03 August 2018

Hugo N. Ulloa Open the ORCID record for Hugo N. Ulloa [Opens in a new window] ,
Alfred Wüest  and
Damien Bouffard
Hugo N. Ulloa*
Affiliation:
Physics of Aquatic Systems Laboratory (APHYS) – Margaretha Kamprad Chair, École Polytechnique Fédérale de Lausanne, CH-1014 Lausanne, Switzerland
Alfred Wüest
Affiliation:
Physics of Aquatic Systems Laboratory (APHYS) – Margaretha Kamprad Chair, École Polytechnique Fédérale de Lausanne, CH-1014 Lausanne, Switzerland Eawag, Swiss Federal Institute of Aquatic Science and Technology, Aquatic Physics Group, Department of Surface Waters – Research and Management, Seestrasse 79, CH-6047 Kastanienbaum, Switzerland
Damien Bouffard
Affiliation:
Eawag, Swiss Federal Institute of Aquatic Science and Technology, Aquatic Physics Group, Department of Surface Waters – Research and Management, Seestrasse 79, CH-6047 Kastanienbaum, Switzerland
*
†Email address for correspondence: hugo.ulloa@epfl.ch
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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.

JFM classification

Convection: Convection in cavities Geophysical and Geological Flows: Ice sheets Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , R1
Copyright
© 2018 Cambridge University Press 

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