Fine scale structure of convective mixed layer in ice-covered lake

Abstract

Nonstationary convection forced by distributed buoyancy sources is a fundamental environmental fluid mechanics process, particularly in ice-covered freshwater waterbodies. In this paper, we present novel field-based results that characterise the diurnal evolution of the main energetics of radiatively-driven convection in ice-covered lakes that is the radiatively-induced buoyancy flux, B, and the kinetic energy dissipation rate, $\varepsilon$. To estimate the spatiotemporal distribution of $\varepsilon$, we applied scale similarity of the velocity structure functions to identify the fine turbulence scales from high-frequency velocity measurements. The field study was carried out at Lake Vendyurskoe, Russia, in April 2016. Small-scale velocity fluctuations were measured using acoustic Doppler current profiler in a 2 m layer beneath the ice cover. The method was proven to be valid for low-energy convection without mean shear. The inertial subrange, covering order of magnitude in the spatial domain, was identified by fitting the $^2/_3$ scaling power law to the structure function method, thus confirming the regime of fully developed turbulence. The calculated rate of dissipation of turbulent kinetic energy $\varepsilon$ reaches values up to $3 \times 10^{-9} \hbox { m}^{2}\hbox {s}^{-3}$. Although a strong correlation between $\varepsilon$ and B was observed, $\varepsilon$ picks up about 1 h later after the onset of the heating-phase. This delay roughly corresponds to the turnover time of the energy containing eddies. We finally observed a decay of $\varepsilon$ at night, during the relaxation-phase, but, interestingly, the level remained above the statistical error.