The mixing of waterbodies and mixing efficiency estimates for different forcing mechanisms remain one of the main challenges in limnological studies, with a deep theoretical background and a wide range of practical applications. This paper examines the mixing that is triggered by surface cooling during the period of open water. The cooling often occurs at night and is largely determined by infrared radiation fluxes, in this regard, this type of forcing is usually positioned as the radiative mixing mechanism. To calculate the mixing efficiency η, an integral energy method was used, within which this parameter is defined as that portion of the external forcing that is spent on mixing itself, as opposed to viscous dissipation. Specific features of energy fluxes between different energy pools have been revealed for radiative type of forcing. For each identified mixing episode the changes of background potential energy were assessed, together with energy sink due to dissipation. Long-term temperature series for different depths at two small water bodies – a forest lake and a city pond – were used as initial data. Calculations carried out for several hundred mixing episodes showed that the mixing efficiency value, on average, significantly exceeds the canonical threshold 0.17. The correlation has also been identified between efficiency and CML thickness: vertical mixing resistance increases with CML deepening. This result introduces a new challenge to the “universality vs variability” dilemma: the efficiency may depend not only on the type and intensity of forcing, but also on the parameters of the initial temperature profile.

We address eddy generation in the middle part of Lake Baikal-a large freshwater dimictic lake in Siberia, where river discharge, wind influence and coastline shape impact horizontal water exchange. We use satellite remote sensing, historical observations and in situ data to follow the different stages of warm and cold anticyclonic eddy generation before and after vertical overturn; an aspect that has received little attention in previous works. Thermal satellite images for 1998-2022 indicate a stable repeating seasonal pattern which is classified into stage of eddy generation and development. Field observations complement satellite imagery to characterize the vertical structure of the eddies. The main source of eddy generation is the outflow from Barguzin Bay which interacts with the coastline. Subsequent eddy generation is driven by density gradients and geostrophic adjustment. In summer, this outflow is dominated by river inflow and lead to the formation of warm anticyclonic eddies. After autumnal vertical overturn, the outflow is forced by the wind bringing cold water from the bay to Middle Baikal and creating cold anticyclonic eddies. We suggest that in the autumn, when the surrounding water cools to a temperature below about 4 degrees C, these cold eddies sink and transform into intrathermocline lens-like eddies that persist under ice and can later create giant ice rings on the Baikal ice cover.

In the paper, the results of eddy-resolving numerical simulation of convection generated by inhomogeneous heating of water column by solar radiation in an ice-covered shallow lake (the factor of wind impact on the water surface is excluded). The calculations have been performed using the Implicit LES method for different values of the extinction coefficient, which defines the degree of attenuation of solar radiation in the water column. An analysis of the three-dimensional flow structure, the time evolution of temperature and velocity pulsations was carried out, and the increments of the lower boundary and the temperature of the convective mixed layer were calculated depending on the incoming heat. The results obtained shed light upon the nature of the processes occurring in the type of lakes under consideration, in particular, to identify the influence of water transparency on the convective mixing process.

Lake ice has a major impact on the functioning of lake ecosystems, the thermal and gas regimes of lakes, habitat conditions, socio-economic aspects of human life, local climate, etc. The multifaceted influence of lake ice makes it important to study its changes associated with global warming, including lake ice phenology, ice thickness, and the snow–ice fraction. This article presents a study of lake ice changes in different regions of Eurasia: the Arctic (Lake Imandra in the Murmansk region and Lake Kilpisjärvi in Finland), the temperate zone (six small and medium lakes in Karelia, Mozhaysk Reservoir in the Moscow region, and Lake Pääjärvi in Finland), the arid zone (Lake Ulansuhai in China), and the highlands (lakes Arpi and Sevan in Armenia). In the study regions, a statistically significant increase in winter air temperature has been recorded over the past few decades. The number of days with thaw (air temperature above 0 °C) has increased, while the number of days with severe frost (air temperature below −10 °C and −20 °C) has decreased. The share of liquid or mixed precipitation in winter increases most rapidly in the temperate zone. For two Finnish lakes, lakes Vendyurskoe and Vedlozero in Karelia, and Mozhaysk Reservoir, a decrease in the duration of the ice period was revealed, with later ice-on and earlier ice-off. The most dramatic change occurred in the large high-mountain Lake Sevan, where the water area has no longer been completely covered with ice every winter. In contrast, the small high-mountain Lake Arpi showed no significant changes in ice phenology over a 50-year period. Changes in the ice composition with an increase in the proportion of white ice and a decrease in the proportion of black ice have occurred in some lakes. In the temperate lakes Pääjärvi and Vendyurskoe, inverse dependences of the thickness of black ice on the number of days with thaw and frost in December–March for the first lake and on the amount of precipitation in the first month of ice for the second were observed. In the arid study region of China, due to the very little winter precipitation (usually less than 10 mm) only black ice occurs, and significant interannual variability in its thickness has been identified.

The regime of lake mixing has a considerable effect on many aspects of the functioning of aquatic ecosystems, which increases the importance of identifying changes in water mass stability under the effect of climatic factors. This study is focused on the stability of the water mass of a small Vendyurskoe Lake (southern Karelia) in the open-water season in years with various weather conditions. Water temperature measurements in 2008–2013 and 2015–2022 at an autonomous station (thermistor chain) in the central vertical of the lake were used to assess the duration of stratification and the stability of water mass according to various criteria, including the temperature difference over water column of 1 and 2°C, and by threshold values of Schmidt stability, Wedderburn number, and Lake Number. To study the role of radiation mixing in weakening the stability of the lake water mass, the seasonal and interannual variability of the temperature difference between the upper layer of the lake and the air was analyzed using ERA-5 reanalysis data. For detail analysis of this parameter, an appropriate density function was constructed for each year, and its major characteristics were calculated. It was shown that, despite the continuing regional warming and an increase in the temperature of air and the top water layer in Vendyurskoe Lake, no increase in stability was recorded in 2008–2022. Limiting factors can be an increase in convective mixing due to radiative cooling, as well as increased wind load on the water body.

The article presents the results of a study of the mixing regime of a small lake, the wind effect on the water column of which is significantly weakened by the forest cover of the adjacent coastal area. Temperature measurements using a chain of thermistors were carried out during two open seasons, in 2021 and 2023. The main attention was paid to periods of night cooling, since it is this mechanism that can be considered prevalent in the mixing of the water column and the formation of a convectively mixed surface layer. Wherein, in the summer months, despite significant nighttime heat fluxes on the surface, complete mixing does not occur. The analysis of the dynamics of the temperature profile and the calculation of the efficiency of mixing were carried out using the integral energy method, based on the identification of mixing episodes and calculations of the background potential energy and buoyancy flux. For mixing efficiency, estimates of 0.45 and 0.49 were obtained for two seasons, significantly exceeding the canonical value of 0.17. It was also revealed that the efficiency value depends on the shape of the density profile and, in particular, on the thickness of the mixed layer

The calculation of the turbulent stress matrix using acoustic Doppler current profiler (ADCP) data remains a challenging problem in the study of geophysical flows. One of the ways to overcome the problem is to use a system of two coupled ADCP with pairs of beams intersecting at a certain depth. When device configuration is symmetric in horizontal, this setting makes it possible to estimate the stresses only for a small range of depths, close to the depth of beam intersection point. To overcome this restriction, in this paper the modified setting is proposed, when both devices are symmetrically turned in the horizontal plane. The X axes of the devices are not collinear for such setting, and two pairs of beams intersect at two different depths, which depend on the distance between the emitters and devices’ rotation angle, and can be chosen in advance. At each of these depths, six beam velocity variances can be directly calculated, as well as the correlation of those velocity components, which correspond to the intersecting beams. As a result, an overdetermined system of equations is derived for unknown stresses, for both depths. The method was approbated during the processing of two series of field data obtained in lakes during open water and ice-covered periods. In most cases, calculations lead to physically consistent results; in particular, the stress matrix turns out to be positive definite. The method’s limitations and perspectives of its development are discussed.

Convectively mixed layer (CML) forms due to radiatively driven convection (RDC) in the upper part of the water column in shallow ice-covered lakes. The spatial structure of this layer has been very poorly studied. The long-standing hypothesis postulates a continuum of convective cells in this layer. The invariant analysis is used to reveal the spatial inhomogeneity of the turbulence parameters within CML and their evolution during the daily cycle of RDC based on solar radiation, water temperature and current measurements in a small shallow ice-covered lake. The values of all six components of the Reynolds-stress tensor are estimated using the method suggested by Bogdanov et al. (Fundam Prikl Gidrofiz 14:17–28, 2021). A high level of turbulence anisotropy within CML was observed throughout the entire measurement period (10 days). Anisotropy invariant maps demonstrate multiple transitions between prolate (rod-like) and oblate (disk-like) types of axisymmetry, without reference to the diurnal cycle of RDC. The dynamics of anisotropy tensor eigenvalues, in contrast to that of the stresses per se, also exhibited no connection with the diurnal cycle of RDC. Considering the presence of mean geostrophic drift in the studied lake, the revealed changes of axisymmetry types and anisotropy tensor eigenvalues are most likely associated with the spatial inhomogeneity of turbulence within the convective cells moving through the measurement zone. The absence of an explicit dependence of turbulence anisotropy on the diurnal cycle of RDC suggests that convective cells "survive" at night and, together with geostrophic drift, maintain the turbulence of the mixed layer.

The paper presents the results of studying the mixing of the water mass of a small forest dimictic lake at the stage of summer heating. The wind effect is limited by the small area of the mirror (the size of the lake is 80–110 by 400 m) and the forested shores, so in summer the convective mixing mechanism prevails when the lake surface cools at night. Evaluation of the mixing efficiency η was carried out by the integral energy method, based on the calculations of energy pumping and changes in the background potential energy according to the temperature profile transformation. For this purpose, a chain with 13 highly sensitive temperature sensors was used; the measurements were carried out in the middle of summer 2022 for 35 days with a time interval of one minute. Acoustic current profiler’s data were used to estimate turbulent velocity fluctuations and calculate the energy dissipation rate, which made it possible to make an alternative assessment of the mixing efficiency. The value of η ~0,4 was obtained, which significantly exceeds the “canonical” value of 0,17 for the case of wind mixing.

The spatio-temporal variability of the modern sedimentation process in Lake Onego, the second largest lake in Europe, was evaluated. The chemical composition of the lake water was studied. Sedimentation takes place in the oxidation conditions of low TDS water of the calcium bicarbonate type, where the ratio between terrigenous clastic material and lacustrine biochemical suspended matter in the material deposited to the bottom is close to one. We demonstrate that the sedimentation process in the lake is non-uniform. Sedimentation rates in different regions of the lake were estimated (0.1 to 2 kg per sq. m of bottom surface per year) through in situ surveys with sediment traps. Annual sediment input was estimated on the basis of the lake’s chemical balance. Analysis of the qualitative characteristics of the material deposited to the bottom shows its composition corresponds to the humus-Fe-Si type of sedimentation. The uniform texture and mineral composition and the similar multielement spectra of the sediments suggest that active water dynamics cause fine-grained suspended load to remain in the water column for prolonged time periods. Variations in the sediment chemical composition across the lake are due to natural causesand to unevenly distributed anthropogenic pressure.

The intensity of vertical heat and mass transfer remains among the challenging topics in the study of ice-covered lakes. Presumably, internal waves (IWs) make a significant contribution to the heat transfer in the water column. However, the mechanisms of mixing enhancement by generation, interaction, and breaking of IWs of different scales, especially short-wavelength ones, have not been sufficiently studied. Furthermore, the experimental data required for estimating the key parameters of IWs (wavelengths, propagation velocities) are rather fragmentary, which makes it difficult to quantify the turbulent transfer caused by IWs. This paper presents the estimates of these IW parameters based on data obtained in the winter months of 2014 and 2016 in a small boreal ice-covered lake. Having analyzed horizontally spaced thermistor chain data, we managed to detect the presence of short standing and propagating IWs, and to estimate their length (from several meters to several tens of meters) and phase and group velocities (from several mm/s to several tens of mm/s). Also, their vertical mode structure was detected. It was shown that IW generation events were characterized by a high degree of spatial localization, and the IW energy was unevenly distributed through the water column.

The article presents the results of application of Implicit Large Eddy Simulation method to numerical simulation of under-ice radiatively driven convection, developing in ice-covered water bodies in the moderate zone at the end of freeze-up period. Studies of the radiatively driven convection are of importance because of the role it plays in the temperature regime of lakes and the functioning of lake ecosystems at the end of freeze-up period. The simulation was carried out with the use of the finite-volume software code SINF/Flag-S, developed in SPbPU. The SIMPLEC algorithm with second-order accuracy was used for ad­vancing in time. The discretization of the convective terms was made with the use of QUICK scheme. The results of calculations were used to study variations in the temperature and pulsation velocity components with periodically varying intensity of external energy pumping during the daily cycle. The dissipation of the kinetic energy, background potential energy, and buoyancy flux were evaluated, and changes in these variables during a daily cycle of radiation impact were calculated. The efficiency mixing of water column was evaluated for the period of development of radiatively driven convection in a model domain simulating a small lake covered by ice.

The results of a numerical simulation of radiatively driven convection (RDC) in a small ice-covered lake with a lateral pressure gradient are shown. RDC influences aquatic ecosystems as convective flow transfers heat and dissolved and suspended matter through the water column. There is a hypothesis that a continuum of convective cells with areas of ascending and descending water flows exists in a convective mixed layer (CML). Until now, little has been known about how the structure of the CML changes in lakes with lateral transport. In this work, the evolution of the CML in the computational domain with a lateral pressure gradient over several days is reproduced using an Implicit Large Eddy Simulation. We show that after a few days of lateral pressure gradient occurrence, convective cells are replaced by rolls oriented along the lateral transport direction. The change in the CML’s turbulence patterns under a lateral pressure gradient is confirmed by Anisotropic Invariant Map analysis. The study revealed a heterogeneity of pulsations of the horizontal and vertical velocity components over the entire depth of the CML and showed that when a horizontal gradient is present, the velocity pulsations generally increase.

Information is presented on the directions and results of research at the Hydrophysics Laboratory of the Northern Water Problems Institute of the Karelian Research Center of the Russian Academy of Sciences in 1991–2022. Laboratory staff study hydrophysical processes and phenomena in various lakes of Karelia, in the largest lakes of Eurasia – Onego and Ladoga, in Lake Baikal, in the White Sea, as well as in small lakes of the Arctic zone of Russia. Brief information is provided on the applied developments and basic scientific results produced while implementing state-ordered assignments, international and domestic research projects, including those carried out jointly with Russian and foreign scientific and educational organizations. The main results include: identification of patterns in the formation of the thermal, hydrodynamic, ice, radiation and oxygen regimes of lakes through the annual cycle (with more focus on the ice-covered period); development of a thermal model of Lake Onego; development and implementation of FLake lake model in collaboration with colleagues from the Institute of Limnology of the Russian Academy of Sciences, German Weather Service, and the Institute for Freshwater Ecology and Inland Fisheries (IGB, Germany); development of a 3D model of Lake Vendyurskoe; investigation of energy and greenhouse gas transport in high-latitude lake ecosystems in collaboration with colleagues from the University of Helsinki; assessment of the adaptive properties of Arctic aquatic ecosystems (lakes of the Yamal Peninsula, deltas of the Lena River, Kola Peninsula) in a changing climate in collaboration with colleagues from the St. Petersburg State University; study of turbulence parameters in ice-covered lakes during the period of spring underice convection, numerical modeling (Implicit LES) of radiation-generated convection in collaboration with colleagues from the Physical-Mechanical Institute of the Peter the Great St. Petersburg Polytechnic University; study of hydrophysical processes and phenomena in bays and inlets of the White Sea in collaboration with colleagues from the Water Problems Institute RAS (Moscow) and the Russian State Humanitarian University (St. Petersburg); study of turbulent transport, which determines the conditions for ice build-up and melting in the subglacial boundary layer of Lake Baikal in collaboration with colleagues from the University of Toulouse, France, and the Limnological Institute in Irkutsk.

Purpose. The purpose of the study consists in identifying the characteristic features of the distribution of hydrophysical and biogeochemical parameters of marine environment depending on the tide phases in the Onezhskiy Bay (the White Sea) in September.Methods and Results. In the cruise of the R/V << Ekolog >> (September 6-11, 2019), synchronous integrated hydrological and biogeochemical studies were for the first time performed in the Onezhskiy Bay depending on the phase of a tidal cycle in September. The standard methods applied for this purpose included two sections in the White Sea, namely along the Western Solovetskaya Salma Strait and through the Onezhskiy Bay from north to south. This permitted to determine the chlorophyll a and nutrients contents, the taxonomic composition, abundance and biomass of phytoplankton including its vertical distribution within the photic zone, as well as the qualitative and quantitative composition of zooplankton. Organic forms of nitrogen (0.62-0.83 mg/l) prevailed among the nutrients in the Onezhskiy Bay, the contents of Pmin and Porg were close (on average 9 mu g/l), the concentration of phosphorus mineral forms was predominant in the water bottom layer at the deep-sea stations. In the Western Solovetskaya Salma, the phytoplankton biomass average values during high and low water were 6.75 +/- 1.18 mg C/m3 and 10.25 +/- 11.34 mg C/m3, and in the Onezhskiy Bay - 8.07 +/- 2.43 mg C/m3 and 16.61 +/- 13.54 mg C/m3, respectively. Phytoplankton was represented by diatoms, dinophytes, cryptophytes and dictyochas. In the southern part of the Onezhskiy Bay, a significant increase in the abundance of all common zooplankton species was found at night.Conclusions. In the area under study, the impact of the tidal cycle phases on spatial and temporal variability of the marine environment characteristics was manifested in a change in the thickness of the layer of temperature and salinity surface anomalies; position of the Onezhskiy frontal section shifted by 8-9 km; the changes in the nitrites, ammonium ions and chlorophyll a concentrations, and also in the phytoplankton biomass were statistically insignificant; the composition of dominant phytoplankton species did not change; the horizontal distribution of zooplankton, primarily its warm-forms, corresponded to the water temperature horizontal gradient: in the southern part of the Onezhskiy Bay, the abundance of boreal species is by orders of magnitude higher than that near the boundary with the basin.