Non-Stationary Turbulence Model for the Upper Boundary Layer of the Sea

A. M. Chukharev

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

e-mail: alexchukh@mail.ru

Abstract

Purpose. The purpose of the study is to develop the physical concepts of dynamic interaction of two media on small and submesoscales, as well as to create an objective model for describing the turbulent regime of the sea near-surface layer.

Methods and Results. Significant scales of turbulence energy supply are established, and a non-stationary numerical model of turbulent exchange in the near-surface layer of the sea is proposed based on the large arrays of experimental data on marine turbulence intensity under different hydrometeorological conditions. Four basic generation mechanisms are considered as the sources of turbulence, namely drift current velocity shear, surface waves and their breakings, and submesoscale eddy structures. The influence of the latter is assessed through the structural function calculated using the synchronous measurements of current velocity in two points. The numerical solutions for velocity profiles, turbulence energy, and dissipation rate are compared to the experimental data, at that the necessary model constants are selected. Verification of the calculations has shown their good agreement with the measurements in a fairly wide range of wind speeds including the weak winds for which the other models yield the significantly lower results as compared to the experimental data.

Conclusions. A non-stationary model is proposed for calculating the turbulence characteristics in the upper mixed layer of the sea. The application of structural function in the turbulent energy balance equation improves the agreement between model calculations and experimental data. The developed model quite reliably describes the turbulent structure of the layer under study and permits to calculate the intensity of vertical turbulent exchange in different hydrometeorological conditions.

Keywords

sea turbulence, near-surface layer, turbulence generation mechanisms, structural function, non-stationary model of turbulence, dissipation rate, experimental data

Acknowledgements

Experimental studies and data preprocessing were carried out within the framework of theme of state assignment of FSBSI FRC MHI FNNN-2021-0004 “Oceanological processes”. Data analysis, and model development and verification were performed with financial support of RSF grant 22-17-00150.

Original russian text

Original Russian Text © A. M. Chukharev, 2025, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 41, Iss. 1, pp. (2025)

For citation

Chukharev, A.M., 2025. Non-Stationary Turbulence Model for the Upper Boundary Layer of the Sea. Physical Oceanography, 32(1), pp. 116-132.

References

  1. Belcher, S.E., Grant, A.L., Hanley, K.E., Fox-Kemper, B., Van Roekel, L., Sullivan, P.P., Large, W.G., Brown, A., Hines, A. [еt al.], 2012. A Global Perspective on Langmuir Turbulence in the Ocean Surface Boundary Layer. Geophysical Research Letters, 39(18), L18605. https://doi.org/10.1029/2012GL052932
  2. Sullivan, P.P. and McWilliams, J.C., 2010. Dynamics of Winds and Currents Coupled to Surface Waves. Annual Review of Fluid Mechanics, 42, pp. 19-42. https://doi.org/10.1146/annurev-fluid-121108-145541
  3. Csanady, G.T., 1984. The Free Surface Turbulent Shear Layer. Journal of Physical Oceanography, 14(2), pp. 402-411. https://doi.org/10.1175/1520-0485(1984)014%3C0402:TFSTSL%3E2.0.CO;2
  4. Benilov, A.Yu. and Ly, L.N., 2002. Modelling of Surface Waves Breaking Effects in the Ocean Upper Layer. Mathematical and Computer Modelling, 35(1-2), pp. 191-213. https://doi.org/10.1016/S0895-7177(01)00159-5
  5. Craig, P.D. and Banner, M.L., 1994. Modelling of Wave-Enhanced Turbulence in the Ocean Surface Layer. Journal of Physical Oceanography, 24(12), pp. 2546-2559. https://doi.org/10.1175/1520-0485(1994)024%3C2546:MWETIT%3E2.0.CO;2
  6. Kudryavtsev, V., Shrira, V., Dulov, V. and Malinovsky, V., 2008. On the Vertical Structure of Wind-Driven Sea Currents. Journal of Physical Oceanography, 38(10), pp. 2121-2144. https://doi.org/10.1175/2008JPO3883.1
  7. Chukharev, A.M., 2013. Multitime Scale Model of Turbulence in the Sea Surface Layer. Izvestiya, Atmospheric and Oceanic Physics, 49(4), pp. 439-449. https://doi.org/10.1134/S0001433813040026
  8. Pearson, B.C., Grant, A.L.M., Polton, J.A. and Belcher, S.E., 2015. Langmuir Turbulence and Surface Heating in the Ocean Surface Boundary Layer. Journal of Physical Oceanography, 45(12), pp. 2897-2911. https://doi.org/10.1175/JPO-D-15-0018.1
  9. Pearson, J., Fox-Kemper, B., Pearson, B., Chang, H., Haus, B.K., Horstmann, J., Huntley, H.S., Kirwan, A.D., Lund, B. [et al.], 2020. Biases in Structure Functions from Observations of Submesoscale Flows. Journal of Geophysical Research: Oceans, 125(6), e2019JC015769. https://doi.org/10.1029/2019JC015769
  10. Samodurov, A.S., Dykman, V.Z., Barabash, V.A., Efremov, O.I., Zubov, A.G., Pavlenko, O.I. and Chukharev, A.M., 2005. “Sigma-1” Measuring Complex for the Investigation of Small-Scale Characteristics of Hydrophysical Fields in the Upper Layer of the Sea. Physical Oceanography, 15(5), pp. 311-322. https://doi.org/10.1007/s11110-006-0005-1
  11. Astaf’eva, N.M., 1996. Wavelet Analysis: Basic Theory and Some Applications. Advances in Physical Sciences, 39(11), pp. 1085-1108. https://doi.org/10.1070/PU1996v039n11ABEH000177
  12. Kolmogorov, A.N., 1968. Local Structure of the Turbulence in an Incompressible Viscous Fluid at Very High Reynolds Numbers. Soviet Physics Uspekhi, 10(6), pp. 734-736. https://doi.org/10.1070/PU1968v010n06ABEH003710
  13. Nosov, V.V., Kovadlo, P.G., Lukin, V.P. and Torgaev, A.V., 2012. Atmospheric Coherent Turbulence. Atmospheric and Oceanic Optics, 26(3), pp. 201-206. https://doi.org/10.1134/S1024856013030123
  14. Chukharev, A.M. and Pavlov, M.I., 2024. Turbulent Exchange in Unsteady Air–Sea Interaction at Small and Submesoscales. Izvestiya, Atmospheric and Oceanic Physics, 60(1), pp. 87-94. https://doi.org/10.1134/S0001433824700105
  15. Lukin, V.P., Nosov, E.V., Nosov, V.V. and Torgaev, A.V., 2016. Causes of Non-Kolmogorov Turbulence Manifestation in the Atmosphere. Applied Optics, 55(12), pp. B163-B168. https://doi.org/10.1364/AO.55.00B163
  16. Hussain, A.K.M.F., 1986. Coherent Structures and Turbulence. Journal of Fluid Mechanics, 173, pp. 303-356. https://doi.org/10.1017/S0022112086001192
  17. Zatsepin, A.G., Piotukh, V.B., Korzh, A.O., Kukleva, O.N. and Soloviev, D.M., 2012. Variability of Currents in the Coastal Zone of the Black Sea from Long-Term Measurements with a Bottom Mounted ADCP. Oceanology, 52(5), pp. 579-592. https://doi.org/10.1134/S0001437012050177
  18. Agrawal, Y.C., Terray, E.A., Donelan, M.A., Hwang, P.A., Williams III, A.J., Drennan, W.M., Kahma, K.K. and Kitaigorodskii, S.A., 1992. Enhanced Dissipation of Kinetic Energy beneath Surface Waves. Nature, 359, pp. 219-220. https://doi.org/10.1038/359219a0
  19. Cheung, T.K. and Street, R.L., 1988. The Turbulent Layer in Water at an Air-Water Interface. Journal of Fluid Mechanics, 194, pp. 133-151. https://doi.org/10.1017/S0022112088002927
  20. Terray, E.A., Donelan, M.A., Agrawal, Y.C., Drennan, W.M., Kahma, K.K., Williams III, A.J., Hwang, P.A. and Kitaigorodskii, S.A., 1996. Estimates of Kinetic Energy Dissipation under Breaking Waves. Journal of Physical Oceanography, 26(5), pp. 792-807. https://doi.org/10.1175/1520-0485(1996)026%3C0792:EOKEDU%3E2.0.CO;2

Download the article (PDF)