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Effects of Friction and Buoyancy Diffusion on the Dynamics of Geostrophic Oceanic Currents with a Linear Vertical Velocity Profile

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Abstract

A spectral problem of the Orr–Sommerfeld type is considered to describe unstable disturbances of oceanic geostrophic currents with a linear vertical velocity profile by taking into account the vertical diffusion of buoyancy and friction. Numerical solutions are obtained for different values of the dimensionless parameters of the problem. Calculations of the spectra of eigenvalues and growth rates are compared with those of a similar problem for an ideal fluid. It is shown that (a) dissipation expands the range of wave numbers of unstable disturbances, (b) dissipation can increase the growth rates of baroclinic disturbances, (c) disturbances driven by the instability of the critical layer can grow faster than baroclinic disturbances, and (d) currents with a width equal to or less than the Rossby radius can be unstable; nearly circular (axisymmetric) unstable disturbances (submesoscale eddies) can develop in narrow currents or frontal zones.

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REFERENCES

  1. Kuzmina, N.P., “On the hypothesis on the formation of large-scale intrusions in the Arctic basin,” Fundam. Prikl. Gidrofiz., 2016, vol. 9, no. 2, pp. 15–26.

    Google Scholar 

  2. Kuzmina, N.P., “Generation of large-scale intrusions at baroclinic fronts: An analytical consideration with a reference to the Arctic Ocean,” Ocean Sci., 2016, vol. 12, pp. 1269–1277. .https://doi.org/10.5194/os-12-1269-2016

    Article  Google Scholar 

  3. Kuzmina, N.P., Skorokhodov, S.L., Zhurbas, N.V., and Lyzhkov, D.A., “On instability of geostrophic current with linear vertical shear at length scales of interleaving,” Izv., Atmos. Oceanic Phys., 2018, vol. 54, pp. 47–55.

    Article  Google Scholar 

  4. Zhurbas, N.V., “On spectra of the eigenvalues in a model problem for describing the formation of large-scale intrusions in the Arctic basin,” Fundam. Prikl. Gidrofiz., 2018, vol. 11, no. 1, pp. 40–45.

    Google Scholar 

  5. Kuzmina, N.P., Skorokhodov, S.L., Zhurbas, N.V., and Lyzhkov, D.A., “Description of the perturbations of oceanic geostrophic currents with linear vertical velocity shear taking into account friction and diffusion of density,” Izv., Atmos. Oceanic Phys., 2019, vol. 55, pp. 207–217 (2019).

  6. McIntyre, M.E., “Diffusive destabilization of the baroclinic circular vortex,” Geophys. Fluid Dyn., 1970, vol. 1, nos. 1-2, pp. 19–57.

    Article  Google Scholar 

  7. Kuzmina, N.P. and Rodionov, V.B., “On baroclinicity effect on the formation of thermohaline intrusion in oceanic frontal zones,” Izv. Akad. Nauk: Fiz. Atmos. Okeana, 1992, vol. 28, nos. 10–11, pp. 1077–1086.

    Google Scholar 

  8. May, B.D. and Kelley, D.E., “Effect of baroclinicity on double-diffusive interleaving,” J. Phys. Oceanogr., 1997, vol. 27, 1997–2008.

    Article  Google Scholar 

  9. Kuzmina, N.P. and Zhurbas, V.M., “Effects of double diffusion and turbulence on interleaving at baroclinic oceanic front,” J. Phys. Oceanogr., 2000, vol. 30, pp. 3025–3038.

    Article  Google Scholar 

  10. Kuzmina, N.P., “On the parameterization of interleaving and turbulent mixing using CTD data from the Azores Frontal Zone,” J. Mar. Syst., 2000, vol. 23, pp. 285–302.

    Article  Google Scholar 

  11. Merryfield, W.J., “Intrusions in double-diffusively stable Arctic waters: Evidence for differential mixing?” J. Phys. Oceanogr., 2002, vol. 32, pp. 1452–1439.

    Article  Google Scholar 

  12. Kuzmina, N.P., Zhurbas, N.V., Emelianov, M.V., and Pyzhevich, M.L., “Application of interleaving models for the description of intrusive layering at the fronts of deep polar water in the Eurasian basin (Arctic),” Oceanology (Engl. Transl.), 2014, vol. 54, no. 5, pp. 557–566.

  13. Kuzmina, N., Rudels, B., Zhurbas, V., and Stipa, T., “On the structure and dynamical features of intrusive layering in the Eurasian basin in the Arctic Ocean,” J. Geophys. Res., 2011, vol. 116, no. D11. https://doi.org/10.1029/2010JC006920

  14. Eady, E.T. “Long waves and cyclone waves,” Tellus, 1949, vol. 1, no. 3, pp. 33–52.

    Article  Google Scholar 

  15. Charney, J.G., “The dynamics of long waves in a baroclinic westerly current,” J. Meteorol., 1947, vol. 4, no. 5, pp. 135–162.

    Article  Google Scholar 

  16. Green, J.S.A., “A problem in baroclinic stability,” Q. J. R. Meteorol. Soc., 1960, vol. 86, no. 368, pp. 237–251.

    Article  Google Scholar 

  17. Miles, J.W., “Effect of diffusion on baroclinic instability of the zonal wind,” J. Atmos. Sci., 1965, vol. 22, pp. 146–151.

    Article  Google Scholar 

  18. Cushman-Roisin, B., Introduction to the Geophysical Fluid Dynamics, Englewood Cliffs, NJ: Prentice Hall, 1994.

    Google Scholar 

  19. Eady, E.T. “Long waves and cyclone waves,” Tellus, 1949, vol. 1, no. 3, pp. 33–52.

    Article  Google Scholar 

  20. Okeanologiya. Fizika okeana. Tom 2 (Oceanology. Ocean Physics. Vol. 2), Kamenkovich, V.M. and Monin, A.S., Eds., Moscow: Nauka, 1978.

    Google Scholar 

  21. Farrell, B.F., “The initial growth of disturbances in a baroclinic flow,” J. Atmos. Sci., 1982, vol. 39, pp. 1663–1686.

    Article  Google Scholar 

  22. Kalashnik, M.V., “Resonant and quasi-resonant excitation of baroclinic waves in the Eady model,” Izv., Atmos. Oceanic Phys., 2015, vol. 51, pp. 576–584.

    Article  Google Scholar 

  23. Lin, C.C., The Theory of Hydrodynamic Stability, Cambridge: Cambridge University Press, 1955.

    Google Scholar 

  24. Skorokhodov, S.L., “Numerical analysis of the spectrum of the Orr–Sommerfeld problem,” Comput. Math. Math. Phys., 2007, vol. 47, no. 10, pp. 1672–1691.

    Google Scholar 

  25. Skorokhodov, S.L., “Branching points of the eigenvalues of the Orr–Sommerfeld operator,” Dokl. Math., 2007, vol. 76, no. 2, pp. 744–749.

    Article  Google Scholar 

  26. Skorokhodov, S.L. and Kuzmina, N.P., “Analytical–numerical method for solving an Orr–Sommerfeld-type problem for analysis of instability of ocean currents,” Comput. Math. Math. Phys., 2018, vol. 58, no. 6, pp. 976–992.

    Article  Google Scholar 

  27. Skorokhodov, S.L. and Kuzmina, N.P., “Spectral analysis of model Couette flows in application to the ocean,” Comput. Math. Math. Phys., 2019, vol. 59, pp. 815–835.

    Article  Google Scholar 

  28. Kalashnik, M.V., “On the theory of symmetric and asymmetric stability of zonal geostrophic currents,” Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana, 2001, vol. 37, no. 3, pp. 418–421.

    Google Scholar 

  29. Stern, M.E., Ocean Circulation Physics, New York: Academic Press, 1975.

    Google Scholar 

  30. Smyth, W.D. “Instabilities of a baroclinic, double diffusive frontal zone,” J. Phys. Oceanogr., 2008, vol. 38, pp. 840–861.

    Article  Google Scholar 

  31. Fedorov, K.N., Fizicheskaya priroda i struktura okeanicheskikh frontov (Physical Nature and Structure of Oceanic Fronts), Leningrad: Gidrometeoizdat, 1983.

  32. Zhurbas, V.M., Kuzmina, N.P., Ozmidov, R.V., Golenko, N.N. and Paka, V.T., “On the manifestation of subduction in thermohaline fields of the vertical fine structure and horizontal mesostructure in the frontal zone of the Azores Current,” Okeanologiya, 1993, vol. 33, no. 3, pp. 321–326.

    Google Scholar 

  33. Stern, M.E., “Lateral mixing of water masses,” Deep-Sea Res., Part A, 1967, vol. 14, pp. 747–753.

    Google Scholar 

  34. Munk, W. and Armi, L., in Proc. 12th ‘Aha Huliko’a Hawaiian Winter Workshop (2001), pp. 81–86.

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ACKNOWLEDGMENTS

We thank an anonymous reviewer for helpful remarks.

Funding

This work was performed under the state assignment of Shirshov Institute of Oceanology, Russian Academy of Sciences (theme no. 0149-2019-0013).

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Authors and Affiliations

  1. Shirshov Institute of Oceanology, Russian Academy of Sciences, 117997, Moscow, Russia

    N. P. Kuzmina, N. V. Zhurbas & D. A. Lyzhkov

  2. Federal Research Center Computer Science and Control, Russian Academy of Sciences, 119333, Moscow, Russia

    S. L. Skorokhodov

Authors
  1. N. P. Kuzmina
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  2. S. L. Skorokhodov
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  3. N. V. Zhurbas
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  4. D. A. Lyzhkov
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Correspondence to N. P. Kuzmina or S. L. Skorokhodov.

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Translated by N. Tret’yakova

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Kuzmina, N.P., Skorokhodov, S.L., Zhurbas, N.V. et al. Effects of Friction and Buoyancy Diffusion on the Dynamics of Geostrophic Oceanic Currents with a Linear Vertical Velocity Profile. Izv. Atmos. Ocean. Phys. 56, 591–602 (2020). https://doi.org/10.1134/S0001433820060067

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