Complementarity of Different Approaches for Assessing Vertical Turbulent Exchange Intensity in Natural Stratified Basins

A.S. Samodurov

Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation

e-mail: anatol_samodurov@mail.ru

Abstract

The comparison of previously proposed theoretical and semi-empirical approaches for assessing dependence of vertical turbulent exchange on stratification in the natural basins is carried out. The following models are compared: the semi-empirical model based on vertical probing data for revealing dependence of the required parameters on the stratification; the theoretical “spectral” model indicating qualitative differences in the exchange parameters in the “strongly” and “weakly” stratified layers of the main pycnocline in natural basins; the 1.5D model of the Black Sea vertical exchange developed within the framework of the inverse problem. The models, being analyzed in the course of calculating dependence of the energy dissipation rate ε and the diffusion coefficient K upon the buoyancy frequency N, show that they do not contradict each other and, if necessary, can complement each other. In addition, it is found that the greatest physical completeness among the considered models contains the “spectral” model that takes into account a variety of possible distributions in the upper “strongly” stratified layer. However, there are certain difficulties with assessment of the relevant coefficients in, dependencies. The latter problem can be solved within the framework of this approach via proper measurements in the investigated area using the semi-empirical approach relationships. A correspondence between the pair of “spectral” model and semi-empirical model and the 1.5D model for the Black Sea, which will be used in the future, should be also noted.

Keywords

internal wave shear instability, energy dissipation, vertical turbulent diffusion, vertical exchange models

For citation

Samodurov, A.S., 2016. Complementarity of Different Approaches for Assessing Vertical Turbulent Exchange Intensity in Natural Stratified Basins. Physical Oceanography, (6), pp. 32-42. doi:10.22449/1573-160X-2016-6-32-42

DOI

10.22449/1573-160X-2016-6-32-42

References

  1. Wunsch, C., Ferrari, R., 2004, “Vertical mixing, energy, and the general circulation of the ocean”, Ann. Rev. Fluid Mech., vol. 36, pp. 281-314.
  2. McComas, C.H., Muller, P., 1981, “The dynamic balance of internal waves”, J. Phys. Oceanogr., vol. 11, pp. 970-986.
  3. Henyey, F.S., Wright, J. & Flatte, S.M., 1986, “Energy and action flow through the internal wave field: An eikonal approach”, J. Geoph. Res., vol. 91, pp. 8487-8495.
  4. Winters, K.B., D’Asaro, E.A., 1998, “Direct simulation of internal wave energy transfer”, J. Phys. Oceanogr., vol. 27, pp. 1937-1945.
  5. Munk, W., 1981, “Internal waves and small-scale processes”, Evolution of Physical Oceanography. The MIT Press, pp. 264-291.
  6. Gargett, A.E., Holloway, G., 1984, “Dissipation and diffusion by internal wave breaking”, J. Mar. Res., vol. 42, no. 1, pp. 15-27.
  7. Gargett, A.E., 1984, “Vertical eddy diffusivity in the ocean interior”, J. Mar. Res., pp. 359-393.
  8. Samodurov, A.S., Globina, L.V., 2011, “Dissipatsiya energii i vertikal'nyy obmen v stratifitsirovannykh basseynakh za schet sdvigovoy neustoychivosti v pole kvaziinertsionnykh vnutrennikh voln [Energy dissipation and vertical exchange in the stratified basins through the shear instability in the field of quasi-inertial internal waves]”, Morskoy gidrofizicheskiy zhurnal, no. 6, pp. 16-27 (in Russian).
  9. Samodurov, A.S., Globina, L.V., 2012, “Zavisimost' skorosti dissipatsii turbulentnoy energii i vertikal'nogo obmena ot stratifikatsii po obobshchennym eksperimental'nym dannym (sravnenie s sushchestvuyushchimi modelyami) [Dependence of turbulent energy and vertical exchange dissipation rate on stratification according to experimental data (comparison with the existing models)]”, Morskoy gidrofizicheskiy zhurnal, no. 6, pp. 17-34 (in Russian).
  10. Samodurov, A.S., Lyubitskiy, A.A. & Panteleev, N.A., 1994, “Vklad oprokidyvayushchikhsya vnutrennikh voln v strukturoobrazovanie, dissipatsiyu energii i vertikal'nuyu diffuziyu v okeane [Breaking wave contribution to the structuring, energy dissipation and vertical diffusion in the ocean]”, Morskoy gidrofizicheskiy zhurnal, no. 3, pp. 14-27 (in Russian).
  11. Samodurov, A.S., Ivanov, L.I., 2003, “Mixing and energy dissipation rate in Mediterranean seas: an intercomparison of existing models”, Oceanography of the Eastern Mediterranean and Black Sea, Similarities and differences in two interconnected basins, Ankara, Tübitak Publishers, pp. 369-375.
  12. Gregg, M.C., 1977, “Variations in the intensity of small-scale mixing in the main thermocline”, J. Phys. Oceanogr., vol. 7, no. 3, pp. 436-454.
  13. Thorpe, S.A., 1973, “Experiments of instability and turbulence in a stratified shear flow”, J. Fluid Mech., vol. 6, pp. 731-751.
  14. McEwen, A.D., 1983, “The kinematics of stratified mixing through internal wave breaking”, J. Fluid Mech., vol. 128, pp. 47-57.
  15. McEwen, A.D., 1983, “Internal mixing in stratified fluids”, J. Fluid Mech., p. 59-80.
  16. Osborn, T.R., 1980, “Estimations of local rate of vertical diffusion from dissipation measurements”, J. Phys. Oceanogr., vol. 10, no. 1, pp. 83-89.
  17. Samodurov, A.S., Chukharev, A.M. & Kul'sha, O.E., 2002, “Rezhimy vertikal'nogo turbulentnogo obmena v verkhnem stratifitsirovannom sloe Chernogo morya v rayone Gerakleyskogo poluostrova [Regimes of vertical turbulent exchange in the Black Sea upper stratified layer near Heracleian Peninsula]”, Protsessy v geosredakh, no. 3, pp. 63-69 (in Russian).
  18. Fernando, H.J.S., 1989, “Oceanographic implications of laboratory experiments on diffusive interfaces”, J. Phys. Oceanogr., vol. 19, pp. 1707-1715.
  19. Gregg, M.C., “Scaling turbulent dissipation in the thermocline”, J. Geophys. Res., vol. 94, no. C7, pp. 9686-9698.
  20. Ivanov, L.I., Samodurov, A.S., 2001, “The role of lateral fluxes in ventilation of the Black Sea”, J. Mar. Syst., vol. 31/1-3, pp. 159-174.
  21. Samodurov, A.S., Ivanov, L.I., 2002, “Balansovaya model' dlya rascheta srednikh vertikal'nykh potokov zhidkosti, tepla, soli i rastvorennykh khimicheskikh veshchestv v termokhalokline Chernogo morya [Balance model for calculation of average vertical liquid fluxes, heat, salt and dissolved chemical substances in the Black Sea thermo-halocline]”, Morskoy gidrofizicheskiy zhurnal, no. 1, pp.7-24 (in Russian).
  22. Samodurov, A.S., Ivanov, V.A. & Belokopytov, V.N. [et al.], 2016, “Model' srednegodovogo vertikal'nogo obmena v kholodnom promezhutochnom sloe Chernogo morya [Model of annual average vertical exchange in Cold Intermediate Layer of the Black Sea]”, Protsessy v geosredakh, no. 2(6), pp. 141-147 (in Russian).
  23. Monin, A.S., Neyman, V.G. & Filyushkin, B.N., 1970, “O stratifikatsii plotnosti v okeane [On density stratification in the ocean]”, DAN SSSR, vol. 191, no. 6, pp. 1277-1279 (in Russian).

Download the article (PDF)