Deriving of Turbulent Stresses in a Convectively Mixed Layer in a Shallow Lake Under Ice by Coupling Two ADCPs

This paper presents a method for deriving turbulent stresses using a pair of ADCPs with one or two points of beam intersections. A specific experiment, which includes measurements of water temperature, under-ice irradiation levels, and velocity components in the convectively mixed layer of a shallow ice-covered boreal lake, validated the method. The experimental data allows calculations of both the pulsation intensities along the three orthogonal axes and off-diagonal components of the Reynolds tensor. The specific features of spring under-ice convection processes, in particular, the anisotropy of turbulent pulsations and the correlation of turbulence energy with the turbulence energy production (as the buoyancy flux), were described using the horizontal homogeneity assumption. Finally, the paper presents a qualitative analysis of the parameters and dynamics of energy-containing structures developing in the convective layer of small ice-covered lakes in spring.

1. Howarth M.J., Souza A.J. Reynolds stress observations in continental shelf seas. Deep Sea Res II. 2005, 52(9–10), 1075–1086.

2. Guerra M., Thomson J. Turbulence measurements from five-beam acoustic doppler current profilers. J. Atmos. Oceanic Technol. 2017, 34(6), 1267–1284.

3. Kirillin G. et al. Turbulence in the stratified boundary layer under ice: observations from Lake Baikal and a new similarity model. Hydrol. Earth Syst. Sci. 2020, 24(4), 1691–1708.

4. Lohrmann A., Hackett B., Roed L. High-resolution measurements of turbulence, velocity, and stress using a pulse-topulse coherent sonar. J. Atmos. Oceanic Technol. 1990, 7(1), 19–37.

5. Lorke A., Wüest A. Application of coherent ADCP for turbulence measurements in the bottom boundary layer. J. Atmos. Oceanic Technol. 2005, 22, 1821–1828.

6. Wiles P.J. et al. A novel technique for measuring the rate of turbulent dissipation in the marine environment. Geophys. Res. Lett. 2006, 33, L21608. doi: 10.1029/2006GL027050

7. Nystrom E.A., Rehmann C.R., Oberg K.A. Evaluation of mean velocity and turbulence measurements with ADCPs. J. Hydraul. Eng. 2007, 133(12), 1310–1318.

8. Kirincich A.R., Rosman J.H. A Comparison of Methods for Estimating Reynolds Stress from ADCP Measurements in Wavy Environments. J. Atmos. Oceanic Technol. 2011, 28, 1539–1553. doi: 10.1175/JTECH-D-11–00001.1

9. Farmer D.M. Penetrative convection in the absence of mean shear. QJR Meteorol. Soc. 1975, 101, 869–891. doi: 10.1002/qj.49710143011

10. Mironov D. et al. Radiatively driven convection in ice-covered lakes: Observations, scaling, and a mixed layer model. J. Geophys. Res. 2002, 107(C4). doi: 10.1029/2001JC000892

11. Petrov M.P. et al. Motion of Water in an Ice-Covered Shallow Lake. Water Resources. 2007, 34(2), 113–122.

12. Kirillin G. et al. Physics of seasonally ice-covered lakes: a review. Aquat Sci. 2012, 74, 659–682. doi: 10.1007/s00027–012–0279-y

13. Bouffard D. et al. Ice-covered Lake Onega: effects of radiation on convection and internal waves. Hydrobiologia. 2016, 780 (1), 21–36. doi:10.1007/s10750–016–2915–3

14. Kirillin G. et al. Turbulent mixing and heat fluxes under lake ice: the role of seiche oscillations. Hydrol. Earth Syst. Sci. 2018, 22, 6493–6504. doi: 10.5194/hess-22–6493–2018

15. Bogdanov S. et al. Structure and dynamics of convective mixing in Lake Onego under ice-covered conditions. Inland Waters. 2019, 9(2), 177–192.

16. Volkov S. et al. Fine scale structure of convective mixed layer in ice-covered lake. Environ. Fluid Mech. 2019, 19, 751– 764. doi: 10.1007/s10652–018–9652–2

17. Zdorovennov R. et al. Interannual variability of ice and snow cover of a small shallow lake. Est. J. Earth Sci. 2013, 61(1), 26–32. doi: 10.3176/earth.2013.03

18. Greene A.D. et al. Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters. J. Atmos. Oceanic Technol. 2015, 32, 318–333.

19. Deardorff J.W. Preliminary results from numerical integrations of the unstable planetary boundary layer. J. Atmos. Sci. 1970, 27, 1209–1211.

20. MacIntyre S. et al. Turbulence in a small Arctic pond. Limnol. Oceanogr. 2018, 63(6), 2337–2358. doi: 10.1002/lno.10941

21. Williams E., Simpson J.H. Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method. J. Atmos. Oceanic Technol. 2004, 21, 347–357. doi: 10.1175/1520–0426(2004)021<0347:UIEORS>2.0.CO;2

22. Henderson S.M. Turbulent production in an internal wave bottom boundary layer maintained by a vertically propagating seiche. J. Geophys. Res. Oceans. 2016, 121. doi: 10.1002/2015JC011071

23. Stacey M.T., Monismith S.G., Burau J.R. Measurements of Reynolds stress profiles in unstratified tidal flow. J. Geophys. Res. 1999, 104(C5), 10933–10949, doi: 10.1029/1998JC900095

24. Forrest A.L. et al. Convectively driven transport in temperate lakes. Limnol. Oceanogr. 2008, 53(5), 2321–2332. doi: 10.4319/lo.2008.53.5_part_2.2321

25. Korotenko K.A., Sentchev A.V., Schmitt F.G. Effect of variable winds on current structure and Reynolds stresses in a tidal flow: Analysis of experimental data in the eastern English Channel. Ocean Sci. 2012, 8(6), 1025–1040. doi: 10.5194/os-8–1025–2012

26. Yang B., Wells M., Li J., Yang J. Mixing, stratification and plankton under lake-ice during winter in a large lake: implications for spring dissolved oxygen levels. EarthArXiv Preprimts. 2019, Preprint. doi: 10.31223/osf.io/5uvwc

27. DelSontro T., del Giorgio P.A., Prairie Y.T. No longer a paradox: the interaction between physical transport and biological processes explains the spatial distribution of surface water methane within and across lakes. Ecosystems. 2018, 21(6), 1073–1087.

28. McGinnis D.F. et al. Enhancing surface methane fluxes from an oligotrophic lake: exploring the microbubble hypothesis. Environ. Sci. Technol. 2015, 49(2), 873–880.

29. Austin J.A. Observations of radiatively driven convection in a deep lake. Limnol. Oceanogr. 2019, 64(5), 2152–2160. doi:10.1002/lno.11175

30. Vermeulen B., Hoitink A.J.F., Sassi M.G. Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows. Geophys. Res. Lett. 2011, 38, L06406. doi: 10.1029/2011GL046684