Abstract
This work continues a series of studies by the authors, where a comparative analysis of the influence of topography, β-effect, and gradient variability of a background flow on the propagation of barotropic topographic Rossby waves is carried out. The novelty of this study lies in the fact that here we consider a non-zonal shear flow and also non-zonal topographic changes. We establish that the non-zonal shear flow enhances the β-effect from the north side of the main flow and reduces from the south side. Contrary, the influence of the joint effect of the Earth rotation and bottom topography enhances the β-effect in the study area and the joint effect of the shear flow and topography reduces it slightly. We exclude the effect of stratification based on the results already obtained that short waves are not observed practically, and also the effect of stratification for Rossby long waves is insignificant. The transverse variability of the shear plane-parallel flow in the WKB approximation is studied. This allows us to obtain a dispersion relation for the flat barotropic topographic Rossby waves with taking into account the above conditions. The estimates of the dispersion equation terms are obtained for the Kuroshio Extension area, where a flow branch turns to the northeast and makes an angle of 55° with latitude. Applied the exponential approximation for bottom topography we obtain that the First approximation by Rhines for the Rossby waves is true for the study area because the parameter of the relief transverse change l0 equals 780 km (exceeds typical Rossby wavelengths). It allows simplifying the corresponding dispersion relation.
Similar content being viewed by others
REFERENCES
Belonenko, T.V., Kubrjakov, A.A., and Stanichny, S.V., Izv. Atmos. Ocean. Phys., 2016, vol. 52, no. 9, pp. 920–928. https://doi.org/10.1134/S0001433816090073
Chelton, D. and Schlax, M., Global observations of oceanic Rossby waves, Sci., 1996, vol. 272, no. 5259, pp. 234–238.
Chelton, D.B., de Szoeke, R.A., Schlax, M.G., El Naggar, K., and Siwertz, N., Geographical variability of the first-baroclinic Rossby radius of deformation, J. Phys. Oceanogr., 1998, vol. 28, pp. 433–460.
Chelton, D.B., Schlax, M.G., and Samelson, R.M., Global observations of nonlinear mesoscale eddies, Prog. Oceanogr., 2011, vol. 91, pp. 167–216.
Gill, A.E., Atmosphere–Ocean Dynamics, Academic Press, 1982.
Gnevyshev, V.G. and Belonenko, T.V., The Rossby paradox and its solution, Gidrometeorologiya i Ekologiya, Hydrometeorol. Ecol. (Proc. Russian State Hydrometeorol. Univ.), 2020, vol. 61, pp. 480–493. https://doi.org/10.33933/2074-2762-2020-61-480-493
Gnevyshev, V.G., Frolova, A.V., Koldunov, A.V., and Belonenko, T.V., Topographic Effect for Rossby Waves on a Zonal Shear Flow, Fundament. Prikl. Gidrofiz., 2021, vol. 14, no. 1, pp. 4–14. https://doi.org/10.7868/S2073667321010019
Gnevyshev, V.G. and Shrira, V.I., On the evaluation of barotropic–baroclinic instability parameters of zonal flows on a beta-plane, J. Fluid Mech., 1990, vol. 221, pp. 161–181. https://doi.org/10.1017/S0022112090003524
Gnevyshev, V.G., Frolova, A.V., Kubryakov, A.A., Sobko, Yu.V., and Belonenko, T.V., Interaction of Rossby waves with a jet stream: basic equations and their verification for the Antarctic circumpolar current, Izv., Atmos. Ocean. Phys., 2019, vol. 55, no. 5, pp. 412–422. https://doi.org/10.1134/S0001433819050074
Gnevyshev, V.G., Badulin, S.I., Koldunov, A.V., and Belonenko, T.V., Rossby waves on non-zonal flows: Vertical focusing and effect of the current stratification, Pure Appl. Geophys., 2021. https://doi.org/10.1007/s00024-021-02799-8
Kamenkovich, I.V. and Pedlosky, J., Radiating instability of nonzonal ocean currents, J. Phys. Oceanogr., 1996, vol. 26, no. 4, pp. 622–643. https://doi.org/10.1175/1520-0485(1996)026<0622:rionoc>2
Killworth, P.D., Chelton, D.B., and de Szoeke, R.A. The speed of observed and theoretical long extra-tropical planetary waves, J. Phys. Oceanogr., 1997, vol. 27, pp. 1946–1966.
La Casce, J.H., The prevalence of oceanic surface modes, Geophys. Res. Lett., 2017, vol. 44, pp. 11097–11105. https://doi.org/10.1002/2017GL075430
Le Blond, P.H. and Mysak, L.A., Waves in the Ocean, Elsevier Scientific Publishing Company, 1978.
Miles, J.M., Baroclinic instability of the zonal wind, Rev. Geophys., 19642, pp. 155–176.
Mizuno, K. and White, W.B., Annual and interannual variability in the Kuroshio Current System, J. Phys. Oceanogr., 1983, vol. 13, pp. 1847–1867.
Nezlin, M.V., Rossby solitons (Experimental investigations and laboratory model of natural vortices of the Jovian Great Red Spot type), Phys.-Usp., 1986, vol. 29, no. 9, pp. 807–842.
Pedlosky, J., Geophysical Fluid Dynamics, N. Y.: Springer-Verlag, 1987.
Pedlosky, J., The stability of currents in the atmosphere and the ocean, J. Atmos. Sci., 1964, vol. 21, pp. 201–219.
Rhines, P.B., Edge-, bottom-, and Rossby waves in a rotating stratified fluid, Geophys. Fluid Dyn., 1970, vol. 1, pp. 273–302.
Funding
The research was funded by RFBR, project no. 20-05-00066. V.G. Gnevyshev was supported in the framework of the Shirshov Institute of Oceanology RAS state assignment no. 0128-2021-0003.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Gnevyshev, V.V., Frolova, A.V. & Belonenko, T.V. Topographic Effect for Rossby Waves on Non-Zonal Shear Flow. Water Resour 49, 240–248 (2022). https://doi.org/10.1134/S0097807822020063
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0097807822020063