Turbulence in the stratified boundary layer under ice: observations from Lake Baikal and a new similarity model

Abstract

Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice-water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We present the first detailed observations on mixing under ice of Lake Baikal, obtained with the help of advanced acoustic methods. The dissipation rate of the turbulent kinetic energy (TKE) was derived from correlations (structure functions) of current velocities within the boundary layer. The range of the dissipation rate variability covered 2 orders of magnitude, demonstrating strongly turbulent conditions. Intensity of mixing was closely connected to the mean speeds of the large-scale under-ice currents. Mixing developed on the background of stable density (temperature) stratification, which affected the vertical structure of the boundary layer. To account for stratification effects, we propose a model of the turbulent energy budget based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty-Ozmidov scaling). The model agrees well with the observations and yields a scaling relationship for the ice-water heat flux as a function of the shear velocity squared. The ice-water heat fluxes in the field were the largest among all reported in lakes (up to 40 W m −2 ) and scaled well against the proposed relationship. The ultimate finding is that of a strong dependence of the water-ice heat flux on the shear velocity under ice. The result suggests large errors in the heat flux estimations when the traditional "bulk" approach is applied to stratified boundary layers. It also implies that under-ice currents may have much stronger effect on the ice melt than estimated by traditional models.

Autonomous System for Lake Ice Monitoring

“…To explain stratification effects, we proposed a model of the turbulent energy budget based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty-Ozmidov scaling). The model agrees well with the observations and yields a scaling relationship for the ice-water heat flux as a function of the shear velocity squared [40].…”

“…The next year, we carried out a special field experiment to closely estimate the effects of under-ice current intensity on the ice-water heat flux under the same meteorological conditions [40], combining high temporal and spatial resolution temperature measurements with the developed systems and fine-scale registration of current velocities under the ice base with a Doppler current velocity profiler, HR Aquadopp (Nortek AS, Norway). The data on velocity fluctuations provided information on the variability of mean currents under the ice as well as on the characteristics of turbulent mixing in the ice-water boundary layer in the form of the dissipation rate of the turbulent kinetic energy (TKE).…”

Winter Limnology: How do Hydrodynamics and Biogeochemistry Shape Ecosystems Under Ice?

“…Turbulence is expected under lake ice prior to the onset of penetrative convection in spring, but has only been measured in a few cases (Kirillin et al, 2018(Kirillin et al, , 2020. It is expected from cryoconcentration (Bluteau et al, 2017;Granin et al, 2000;Olsthoorn et al, 2020) and from the interaction of Kelvin waves with the benthic boundary layer (Kirillin et al, 2009(Kirillin et al, , 2012.…”

Mechanisms and effects of under-ice warming water in Ngoring Lake of Qinghai–Tibet Plateau

“…While the major pre-requisite for the ice cover development is a sufficiently long season with air temperature below the freezing point of water, the heat budget of ice-covered lakes varies with latitude and altitude, depending strongly on the available solar radiation, the latter being the major source of heat for under-ice lake water (Kirillin et al, 2012). During the polar night in the Arctic and temperate lakes covered by snow, the solar heating is minor, and the bottom sediment is the main heat source (Winter I according to Kirillin et al, 2012); at later stages of the ice season (Winter II), as the snow melts, solar radiation becomes the main heat source governing thermal stratification and mixing under ice and the melting process at the ice base (Kirillin et al, 2018(Kirillin et al, , 2020. Further, lakes with seasonal ice cover can be divided into cryomictic and cryostratified according to their maximum depth, surface area, and wind speed (Yang et al, 2021).…”