Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 48758 10.2205/2021ES000780 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Convectively mixed layer in a boreal lake during the period of spring under-ice heating: Spatial structure and hydrodynamic parameters Convectively mixed layer in a boreal lake during the period of spring under-ice heating: Spatial structure and hydrodynamic parameters Bogdanov S. R. Bogdanov S. R. Zdorovennov R. E. Zdorovennov R. E. Palshin N. I. Palshin N. I. Zdorovennova G. E. Zdorovennova G. E. Volkov S. Yu. Volkov S. Yu. Efremova T. V. Efremova T. V. Gavrilenko G. G. Gavrilenko G. G. Terzhevik A. Yu. Terzhevik A. Yu. 04 02 2022 04 02 2022 21 6 1 11 05 10 2021 28 10 2021 https://rjes.ru/en/nauka/article/48758/view

The paper presents the quantitative assessment of the hydrodynamic parameters of the convectively mixed layer (CML) arising in ice-covered boreal lakes as a result of non- homogeneous heating of the water column. The study is focused on revealing the features of CML spatial structure and calculating all six elements of the turbulent stress matrix. The main feature of the experimental technique is application of two rigidly coupled acoustic current profilers (ADCP) installed on ice and operating in the asynchronous measurement mode. In the case of down-looking axes of both devices, their positions relative to each other were chosen so that one or two pairs of beams intersected at a certain depth. Due to this configuration, it was possible to perform a rigorous calculation of all turbulent stresses based on the data obtained from all six beams. The intensities of pulsations were estimated along all three axes, complete with error analysis. A high degree of anisotropy of the pulsations and a periodic nature of its change over time were detected. An analysis of the dynamics of average velocities carried out for depths of up to 2.87 m with discreteness of 2.5 cm (for CML thickness of 3–6 m) revealed the presence of quasi-deterministic convective cells. In the horizontal plane, a systematic “drift” was found, due to the presence of large-scale geostrophic circulation. The presence of such a drift made it possible, as a first approximation, to convert the experimentally obtained Eulerian characteristics into Lagrangian ones and, accordingly, draw conclusions about the spatial structure of the cells. In particular, based on the analysis of progressive vector diagrams in vertical planes, the depth ranges were determined at which the zones of up- or downwelling prevailed. The distribution of these zones is of great importance in studying the spatial dynamics of plankton. KEYWORDS: Boreal lakes; under-ice radiation; convectively mixed layer; acoustic Doppler current profilers; quasi-deterministic structures; progressive vector diagrams; up- and downwelling zones; turbulent stresses.

The paper presents the quantitative assessment of the hydrodynamic parameters of the convectively mixed layer (CML) arising in ice-covered boreal lakes as a result of non- homogeneous heating of the water column. The study is focused on revealing the features of CML spatial structure and calculating all six elements of the turbulent stress matrix. The main feature of the experimental technique is application of two rigidly coupled acoustic current profilers (ADCP) installed on ice and operating in the asynchronous measurement mode. In the case of down-looking axes of both devices, their positions relative to each other were chosen so that one or two pairs of beams intersected at a certain depth. Due to this configuration, it was possible to perform a rigorous calculation of all turbulent stresses based on the data obtained from all six beams. The intensities of pulsations were estimated along all three axes, complete with error analysis. A high degree of anisotropy of the pulsations and a periodic nature of its change over time were detected. An analysis of the dynamics of average velocities carried out for depths of up to 2.87 m with discreteness of 2.5 cm (for CML thickness of 3–6 m) revealed the presence of quasi-deterministic convective cells. In the horizontal plane, a systematic “drift” was found, due to the presence of large-scale geostrophic circulation. The presence of such a drift made it possible, as a first approximation, to convert the experimentally obtained Eulerian characteristics into Lagrangian ones and, accordingly, draw conclusions about the spatial structure of the cells. In particular, based on the analysis of progressive vector diagrams in vertical planes, the depth ranges were determined at which the zones of up- or downwelling prevailed. The distribution of these zones is of great importance in studying the spatial dynamics of plankton. KEYWORDS: Boreal lakes; under-ice radiation; convectively mixed layer; acoustic Doppler current profilers; quasi-deterministic structures; progressive vector diagrams; up- and downwelling zones; turbulent stresses.

 Boreal lakes; under-ice radiation; convectively mixed layer; acoustic Doppler current profilers; quasi-deterministic structures; progressive vector diagrams; up- and downwelling zones; turbulent stresses. Boreal lakes; under-ice radiation; convectively mixed layer; acoustic Doppler current profilers; quasi-deterministic structures; progressive vector diagrams; up- and downwelling zones; turbulent stresses. The work was carried out under state assignment to the Northern Water Problems Insti- tute (Karelian Research Centre of the Russian Academy of Sciences). Field studies were carried out with fi- nancial support from Russian Foundation for Basic Re- search (Project No. 18-05-60261). The work was carried out under state assignment to the Northern Water Problems Insti- tute (Karelian Research Centre of the Russian Academy of Sciences). Field studies were carried out with fi- nancial support from Russian Foundation for Basic Re- search (Project No. 18-05-60261).

Austin, J. A. (2019), Observations of radiatively driven convection in a deep lake, Limnol. Oceanogr., 64, 2152-2160, Crossref Austin, J. A. (2019), Observations of radiatively driven convection in a deep lake, Limnol. Oceanogr., 64, 2152-2160, Crossref Bogdanov, S., et al. (2019), Structure and dynamics of convective mixing in Lake Onego under ice covered conditions, Inland Waters, 9, No. 2, 177-192, Crossref Bogdanov, S., et al. (2019), Structure and dynamics of convective mixing in Lake Onego under ice covered conditions, Inland Waters, 9, No. 2, 177-192, Crossref Bogdanov, S., et al. (2021), Deriving of turbulent stresses in a convectively mixed layer in a shallow lake under ice by coupling two ADCPs, Fundamentalnaya i Prikladnaya Gidrofizica, 14,No. 2, 17-28, Crossref Bogdanov, S., et al. (2021), Deriving of turbulent stresses in a convectively mixed layer in a shallow lake under ice by coupling two ADCPs, Fundamentalnaya i Prikladnaya Gidrofizica, 14,No. 2, 17-28, Crossref Bouffard, D., A. W ̈uest (2018), Convection inlakes, Annu. Rev. Fluid Mech., 51, 189-215, Crossref Bouffard, D., A. W ̈uest (2018), Convection inlakes, Annu. Rev. Fluid Mech., 51, 189-215, Crossref Bouffard, D., et al. (2019), Under ice convection dynamics in a boreal lake, Inland Waters, 9, No. 2, 142-161, Crossref Bouffard, D., et al. (2019), Under ice convection dynamics in a boreal lake, Inland Waters, 9, No. 2, 142-161, Crossref Bouillaut, V., S. Lepot, et al. (2019), Transition to the ultimate regime in a radiatively driven convection experiment, Journal of Fluid Mechanics, 861, R5, Crossref Bouillaut, V., S. Lepot, et al. (2019), Transition to the ultimate regime in a radiatively driven convection experiment, Journal of Fluid Mechanics, 861, R5, Crossref Farmer, D. M. (1975), Penetrative convection in the absence of mean shear, Q. J. R. Meteorol.Soc., 101, 869-891, Crossref Farmer, D. M. (1975), Penetrative convection in the absence of mean shear, Q. J. R. Meteorol.Soc., 101, 869-891, Crossref Forrest, A., B. E. Laval, et al. (2008), Convectively driven transport in temperate lakes, Limnology and Oceanography, 53, 2321-2332, Crossref Forrest, A., B. E. Laval, et al. (2008), Convectively driven transport in temperate lakes, Limnology and Oceanography, 53, 2321-2332, Crossref Howarth, M. J., A. J. Souza (2005), Reynolds stress observations in continental shelf seas, Deep Sea Res. II, 52, 1075-1086, Crossref Howarth, M. J., A. J. Souza (2005), Reynolds stress observations in continental shelf seas, Deep Sea Res. II, 52, 1075-1086, Crossref Jewson, D., N. Granin, et al. (2009), Effect of snow depth on under ice irradiance and growth of Aulacoseira baicalensis in Lake Baikal, Aquatic Ecology, 43, 673-679, Crossref Jewson, D., N. Granin, et al. (2009), Effect of snow depth on under ice irradiance and growth of Aulacoseira baicalensis in Lake Baikal, Aquatic Ecology, 43, 673-679, Crossref Jonas, T., A. Terzhevik, et al. (2003), Radiatively driven convection in an ice covered lake investigated by using temperature microstructure technique, J. Geophys. Res., 108, No. C6,3183, Crossref Jonas, T., A. Terzhevik, et al. (2003), Radiatively driven convection in an ice covered lake investigated by using temperature microstructure technique, J. Geophys. Res., 108, No. C6,3183, Crossref Kelley, D. (1997), Convection in ice covered lakes: effects on algal suspension, Journal of Plankton Research, 19, 1859-1880, Crossref Kelley, D. (1997), Convection in ice covered lakes: effects on algal suspension, Journal of Plankton Research, 19, 1859-1880, Crossref Lepot, S., S. Auma^ıtre, B. Gallet (2018), Radiative heating achieves the ultimate regime of thermal convection, Proc. Nat. Acad. Sci. USA,115, 8937-8941, Crossref Lepot, S., S. Auma^ıtre, B. Gallet (2018), Radiative heating achieves the ultimate regime of thermal convection, Proc. Nat. Acad. Sci. USA,115, 8937-8941, Crossref Maffioli, A., G. Brethouwer, E. Lindborg (2016),Mixing efficiency in stratified turbulence, Journal of Fluid Mechanics, 794, R3, Crossref Maffioli, A., G. Brethouwer, E. Lindborg (2016),Mixing efficiency in stratified turbulence, Journal of Fluid Mechanics, 794, R3, Crossref Mironov, D., S. Danilov, D. Olbers (2001), Large eddy simulation of radiatively driven convection in ice covered lakes, X. Casamitjana (ed.),Proc. Sixth Workshop on Physical Processes in Natural Waters, 27-29 June, 2001, Girona, Catalonia, Spain p. 71-75, Univ. of Girona, Spain. Mironov, D., S. Danilov, D. Olbers (2001), Large eddy simulation of radiatively driven convection in ice covered lakes, X. Casamitjana (ed.),Proc. Sixth Workshop on Physical Processes in Natural Waters, 27-29 June, 2001, Girona, Catalonia, Spain p. 71-75, Univ. of Girona, Spain. Mironov, D., A. Terzhevik, et al. (2002),Radiatively driven convection in ice covered lakes: observations, scaling and a mixed layer model, J. Geophys. Res., 107, C4, Crossref Mironov, D., A. Terzhevik, et al. (2002),Radiatively driven convection in ice covered lakes: observations, scaling and a mixed layer model, J. Geophys. Res., 107, C4, Crossref McNeill, A. R. (1990), Size, Speed and Buoyancy Adaptations in Aquatic Animals, American Zoologist, 30, No. 1, 189-196, Crossref McNeill, A. R. (1990), Size, Speed and Buoyancy Adaptations in Aquatic Animals, American Zoologist, 30, No. 1, 189-196, Crossref Nystrom, E. A., C. R. Rehmann, K. A. Oberg(2007), Evaluation of mean velocity and turbulence measurements with ADCPs, J. Hydraul. Eng., 133, 1310-1318, Crossref Nystrom, E. A., C. R. Rehmann, K. A. Oberg(2007), Evaluation of mean velocity and turbulence measurements with ADCPs, J. Hydraul. Eng., 133, 1310-1318, Crossref Pernica, P., R. L. North, H. M. Baulch (2017),In the cold light of day: the potential importance of underice convective mixed layers to primary producers, Inland Waters, 7, No. 2, 138-150,Crossref Pernica, P., R. L. North, H. M. Baulch (2017),In the cold light of day: the potential importance of underice convective mixed layers to primary producers, Inland Waters, 7, No. 2, 138-150,Crossref Palshin, N., et al. (2017), Geostrophic currents in the small ice covered lake, Advances in Current Natural Sciences, 11, 89-94. (URL, In Russian) Palshin, N., et al. (2017), Geostrophic currents in the small ice covered lake, Advances in Current Natural Sciences, 11, 89-94. (URL, In Russian) Palshin, N., et al.(2019), Effect of Under Ice Light Intensity and Convective Mixing on Chlorophylla Distribution in a Small Mesotrophic Lake, Water Resources, 46, 384-394, Crossref Palshin, N., et al.(2019), Effect of Under Ice Light Intensity and Convective Mixing on Chlorophylla Distribution in a Small Mesotrophic Lake, Water Resources, 46, 384-394, Crossref Stacey, M. T., S. G. Monismith, J. R. Burau(1999), Measurements of Reynolds stress profiles in unstratified tidal flow, J. Geophys. Res.,104, 10,933-10,949, Crossref Stacey, M. T., S. G. Monismith, J. R. Burau(1999), Measurements of Reynolds stress profiles in unstratified tidal flow, J. Geophys. Res.,104, 10,933-10,949, Crossref Ulloa, H. N., A. W ̈uest, D. Bouffard (2018), Mechanical energy budget and mixing efficiency for a radiatively heated ice covered waterbody, Journal of Fluid Mechanics, 852, R1, Crossref Ulloa, H. N., A. W ̈uest, D. Bouffard (2018), Mechanical energy budget and mixing efficiency for a radiatively heated ice covered waterbody, Journal of Fluid Mechanics, 852, R1, Crossref Vermeulen, B., A. J. F. Hoitink, M. G. Sassi(2011), Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows, Geophys. Res. Lett., 38, L06406, Crossref Vermeulen, B., A. J. F. Hoitink, M. G. Sassi(2011), Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows, Geophys. Res. Lett., 38, L06406, Crossref Volkov, S., et al. (2019), Large scale structure of convectively mixed layer in a shallow ice covered lake, Fundamentalnaya i Prikladnaya Gidrofizica, 12, No. 1, 30-39, (In Russian) Crossref Volkov, S., et al. (2019), Large scale structure of convectively mixed layer in a shallow ice covered lake, Fundamentalnaya i Prikladnaya Gidrofizica, 12, No. 1, 30-39, (In Russian) Crossref Williams, E., J. H. Simpson (2004), Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method, J. Atmos. Oceanic Technol., 21,347-357, Crossref Williams, E., J. H. Simpson (2004), Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method, J. Atmos. Oceanic Technol., 21,347-357, Crossref Woodcock, A. H. (1965), Melt patterns in ice over shallow waters, Limnology and Oceanography, 10, R290-R297, Crossref Woodcock, A. H. (1965), Melt patterns in ice over shallow waters, Limnology and Oceanography, 10, R290-R297, Crossref Woodward, J. R., J. W. Pitchford, M. A. Bees(2019), Physical flow effects can dictate plankton population dynamics, J. R. Soc. Interface,20190247, Crossref Woodward, J. R., J. W. Pitchford, M. A. Bees(2019), Physical flow effects can dictate plankton population dynamics, J. R. Soc. Interface,20190247, Crossref Yang, B., J. Young, et al. (2017), High Frequency Observations of Temperature and Dissolved Oxygen Reveal Under Ice Convection in a Large Lake, Geophys. Res. Lett., 44, No. 24,12,218-12,226, Yang, B., J. Young, et al. (2017), High Frequency Observations of Temperature and Dissolved Oxygen Reveal Under Ice Convection in a Large Lake, Geophys. Res. Lett., 44, No. 24,12,218-12,226,