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A Method for Estimation of Turbulence Fine-Scale Anisotropy Parameters from ADCP Data

https://doi.org/10.7868/S2073667321010093

Abstract

Acoustic Doppler Current Profilers (ADCP) are widely used for deriving velocity vertical profiles. In recent years these devices were also actively explored for estimations of the energy dissipation rate ε by studying longitudinal velocity structure functions (SF). However, these estimates remain questionable because the correspondent SF method is based on the assumption of the fine-scale isotropy and explores the canonical values for Kolmogorov constants. The last ones, as recent direct measurements and numerical computations prove, are highly variable, thus triggering the errors of ε estimations, which may exceed 50 %. This paper presents an approach to derive the retained information, hidden in the raw along-beam velocities data, which can shed a light on the anisotropy parameters. For this, we developed the inter-beam correlations method, based on the analysis of generalized (fourpoint) SF. The explicit expression for transverse SF was derived, which made it possible to check the “4/3 law” directly. The method was tested by processing velocity data, obtained from the convective mixing layer in ice-covered lakes Onega and Vendyurskoe.

About the Authors

S. Volkov
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



S. Bogdanov
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences; Petrozavodsk State University
Russian Federation

Petrozavodsk



G. Zdorovennova
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



A. Terzhevik
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



R. Zdorovennov
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



N. Palshin
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



T. Efremova
Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences
Russian Federation

Petrozavodsk



G. Kirillin
Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB)
Germany

12587, Müggelseedamm 310, Berlin



References

1. Greene A.D., Hendricks P.J., Gregg M.C. Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters. J. Atmos. Oceanic Technol. 2015, 32(2), 318–333. doi: 10.1175/JTECH-D-13–00207.1

2. Kirillin G.B., Forrest A.L., Graves K.E., Fischer A., Engelhardt C., Laval B.E. Axisymmetric circulation driven by marginal heating in ice-covered lakes. Geophys. Res. Lett. 2015, 42(8), 2893–2900. doi: 10.1002/2014GL062180

3. Bouffard D., Wüest A. Convection in lakes. Annu. Rev. Fluid Mech. 2019, 51, 189–215. doi: 10.1146/annurev-fluid-010518–040506

4. Flood B., Wells M., Dunlop E., Young J. Internal waves pump waters in and out of a deep coastal embayment of a large lake. Limnol. Oceanogr. 2020, 65(2), 205–223. doi: 10.1002/lno.11292

5. Wiles P.J., Rippeth T.P., Simpson J.H., Hendricks P.J. A novel technique for measuring the rate of turbulent dissipation in the marine environment. Geophys. Res. Lett. 2006, 33(21), L21608. doi: 10.1029/2006GL027050

6. Lucas N.S., Simpson J.H., Rippeth T.P., Old C.P. Measuring Turbulent Dissipation Using a Tethered ADCP. J. Atmos. Oceanic Technol. 2014, 31, 1826–1837. doi: 10.1175/JTECH-D-13–00198.1

7. Volkov S., Bogdanov S., Zdorovennov R., Zdorovennova G., Terzhevik A., Palshin N., Bouffard D., Kirillin G. 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

8. Lorke A., Wüest A. Application of coherent ADCP for turbulence measurements in the bottom boundary layer. J. Atmos. Oceanic Technol. 2005, 22, 1821–1828. doi: 10.1175/JTECH1813.1

9. Howarth M.J., Souza A.J. Reynolds stress observations in continental shelf seas. Deep Sea Res II. 2005, 52, 9, 1075–1086. doi: 10.1016/j.dsr2.2005.01.003

10. Whipple A.C., Luettich R.A. Jr., Seim H.E. Measurements of Reynolds stress in a wind-driven lagoonal estuary. Ocean Dyn. 2006, 56, 169–185. doi: 10.1007/s10236–005–0038-x

11. Rosman J.H., Hench J.L., Koseff J.R., Monismith S.G. Extracting Reynolds Stresses from Acoustic Doppler Current Profiler Measurements in Wave-Dominated Environments. J. Atmos. Oceanic Technol. 2008, 25, 286–306. doi: 10.1175/2007JTECHO525.1

12. Whipple A.C., Luettich R.A. A comparison of acoustic turbulence profiling techniques in the presence of waves. Ocean Dynamics. 2009, 59, 719. doi: 10.1007/s10236–009–0208–3

13. 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: 10.1007/s10236–009–0208–3

14. Guerra M., Thomson J. Turbulence measurements from five-beam acoustic doppler current profilers. J. Atmos. Oceanic Technol. 2017, 34, 1267–1284. doi: 10.1175/JTECH-D-16–0148.1

15. Jabbari A., Boegman L., Piomelli U. Evaluation of the inertial dissipation method within boundary layers using numerical simulations. Geophys. Res. Lett. 2015, 42, 5, 1504–1511. doi: 10.1002/2015GL063147

16. Jabbari A., Rouhi A., Boegman L. Evaluation of the structure function method to compute turbulent dissipation within boundary layers using numerical simulations. J. Geophys. Res. Oceans. 2016, 121, 8. doi: 10.1002/2015JC011608

17. Peltier W.R., Caulfield C.P. Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 2003, 35 (1), 135–167. doi: 10.1146/annurev.fluid.35.101101.161144

18. Biferale L. Shell models of energy cascade in turbulence. Annu. Rev. Fluid Mech. 2003, 35(1), 441–468. doi: 10.1146/annurev.fluid.35.101101.161122

19. Kassinos S., Reynolds W., Rogers M. One-point turbulence structure tensors. J. Fluid Mech. 2001, 428, 213–248. doi: 10.1017/S0022112000002615

20. Cambon C. Strongly Anisotropic Turbulence, Statistical Theory and DNS. Turbulence and Interactions. Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Eds. Deville M., Lê TH., Sagaut P. Springer, Berlin, Heidelberg. 2009, 105. doi: 10.1007/978–3–642–00262–5_1

21. Lilly D.K. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 1983, 40, 749–761. doi: 10.1175/1520–0469(1983)040<0749:STATMV>2.0.CO;2

22. Lindborg E. The energy cascade in a strongly stratified fluid. J. Fluid. Mech. 2006, 550, 207–242. doi: 10.1017/S0022112005008128

23. Bogdanov S., Zdorovennova G., Volkov S., Zdorovennov R., Palshin N., Efremova T., Terzhevik A., Bouffard D. Structure and dynamics of convective mixing in Lake Onego under ice-covered conditions. Inland Waters. 2019, 9(2), 177–192. doi: 10.1080/20442041.2018.1551655

24. Casciola C.M., Gualtieri P., Jacob B., Piva R. Scaling Properties in the Production Range of Shear Dominated Flows. Phys. Rev. Lett. 2005, 95, 024503. doi: 10.1103/PhysRevLett.95.024503

25. Lohse D., Xia K.-Q. Small-Scale Properties of Turbulent Rayleigh-Bénard Convection. Annu. Rev. Fluid Mech. 2010, 42, 1, 335–364. doi: 10.1146/annurev.fluid.010908.165152

26. Kimura Y., Herring J.R. Energy spectra of stably stratified turbulence. J. Fluid. Mech. 2012, 698, 19–50. doi:10.1017/jfm.2011.546

27. Gilcoto M., Jones E., Fariña-Busto L. Robust Estimations of Current Velocities with Four-Beam Broadband ADCPs. J. Atmos. Oceanic Technol. 2009, 26, 2642–2654.

28. Monin A.S., Yaglom A.M. Statistical fluid mechanics, M.I.T. Press, Cambridge, Mass., 1971.

29. Chandrasekhar S. The theory of axisymmetric turbulence. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1950, 242, 557–577. doi: 10.1098/rsta.1950.0010

30. Jonas T., Terzhevik A.Y., Mironov D.V., Wüest A. Radiatively driven convection in an ice-covered lake investigated by using temperature microstructure technique. J. Geophys. Res. 2003, 108, C6, 3183. doi: 10.1029/2002JC001316

31. Bogdanov S.R. Kolmogorov constants in the spectra of anisotropic turbulence. J. Appl. Mech. Tech. Phys. 1990, 31, 802. doi: 10.1007/BF00852459


Review

For citations:


Volkov S., Bogdanov S., Zdorovennova G., Terzhevik A., Zdorovennov R., Palshin N., Efremova T., Kirillin G. A Method for Estimation of Turbulence Fine-Scale Anisotropy Parameters from ADCP Data. Fundamental and Applied Hydrophysics. 2021;14(1):86-96. https://doi.org/10.7868/S2073667321010093

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ISSN 2073-6673 (Print)
ISSN 2782-5221 (Online)