Symmetric instability of geostrophic currents with a finite transverse lengthscale
https://doi.org/10.7868/S2073667321040018
Abstract
A comparative analysis of unstable symmetric perturbations of the geostrophic current with a constant vertical and horizontal velocity shear in an unbounded region and a region with lateral boundaries is performed accounting for vertical diffusion of buoyancy and momentum. Calculations of the growth rate of unstable perturbations are presented as a function of the vertical wavenumber for various dimensionless parameters of the problem. It is found that in the case of the geostrophic current with lateral boundaries, the maximum-growing mode of symmetric instability arising when condition Ri · (1 + Ro) < 1 (Ri is the geostrophic Richardson number, Ro is the Rossby number) is satisfied has a finite vertical length scale, while in the case of the unbounded region, the vertical wavenumber of the maximum-growing mode is asymptotically vanishing. A combined effect of lateral boundaries and diffusion of buoyancy and momentum at Pr ≥ 1 (Pr is the Prandtl number), depending on the values of the dimensionless parameters of the problem, can significantly affect the dynamics of symmetric perturbations, namely, lead to a narrowing of the spectrum of unstable perturbations and a decrease in their growth rates, and even prevent the development of instability.
About the Authors
N. P. KuzminaRussian Federation
117997, Nahimovskiy prospekt, 36, Moscow
N. V. Zhurbas
Russian Federation
117997, Nahimovskiy prospekt, 36, Moscow
References
1. Kuzmina N.P., Rodionov V.B. Influence of baroclinicity on formation of thermohaline intrusions in oceanic frontal zones. Izv. Akad. Nauk USSR, Atmos. Oceanic Phys. 1992, 28, 804–810.
2. May B.D., Kelley D.E. Effect of baroclinicity on double-diffusive interleaving. J. Phys. Oceanogr. 2007, 27, 1997–2008.
3. Kuzmina N.P., Zhurbas V.M. Effects of double diffusion and turbulence on interleaving at baroclinic oceanic fronts. J. Phys. Oceanogr. 2000, 30, 3025–3038.
4. Kuzmina N.P., Zhurbas N.V., Emelianov M.V., 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. 2014, 54, 5, 557–566.
5. Kuzmina N.P. About one hypothesis of generation of large-scale intrusions in the Arctic Ocean. Fundam. Prikl. Gidrofiz. 2016, 9, 2, 15–26 (in Russian).
6. Kuzmina N.P. Generation of large-scale intrusions at baroclinic fronts: an analytical consideration with a reference to the Arctic Ocean. Ocean Sci. 2016, 12, 1269–1277. doi: 10.5194/OS–12–1269–2016
7. Zhurbas N.V. On the eigenvalue spectra for a model problem describing formation of the large-scale intrusions in the Arctic basin. Fundam. Prikl. Gidrofiz. 2018, 11, 1, 40–45. doi: 10.7868/S2073667318010045
8. Eady E.T. Long waves and cyclone waves. Tellus. 1949, 1, 3, 33–52.
9. Kuzmina N.P., Skorokhodov S.L., Zhurbas N.V., 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, 55, 207–217. doi: 10.1134/S0001433819020117
10. Stern M.E. Lateral mixing of water masses. Deep Sea Res. Part A. 1967, 14, 747–753.
11. Kuzmina N.P. On the parameterization of interleaving and turbulent mixing using CTD data from the Azores Frontal Zone. J. Mar. Syst. 2000, 23, 285–302.
12. Zhurbas V.M., Kuzmina N.P., Ozmidov R.V., Golenko N.N., 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, 33, 3, 321–326 (in Russian).
13. Zhurbas V.M., Paka V.T., Golenko M.N., Korzh A.O. Transformation of eastward spreading saline water at the Słupk Sill of the Baltic Sea: an estimate based on microstructure measurements. Fundam. Prikl. Gidrofiz. 2019, 12, 2, 43–49. doi: 10.7868/S2073667319020060
14. Väli G., Zhurbas V.M., Laanemets J., Lips U. Clustering of floating particles due to submesoscale dynamics: a simulation study for the Gulf of Finland, Baltic Sea. Fundam. Prikl. Gidrofiz. 2018, 11, 2, 21–35. doi: 10.7868/S2073667318020028
15. Haine T.W., Marshall J. Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr. 1998, 28(4), 634–658. doi: 10.1175/1520–0485(1998)028<0634: GSABIO>2.0.CO;2
16. Thomas L.N., Taylor J.R., D’Asaro E.A., Lee C.M., Klymak J.M., Shcherbina A. Symmetric instability, inertial oscillations, and turbulence at the Gulf Stream front. J. Phys. Oceanogr. 2016, 46, 1, 197–217. doi: 10.1175/JPO-D-15–0008.1
17. Taylor J.R., Ferrari R. On the equilibration of a symmetrically unstable front via a secondary shear instability. J. Fluid Mech. 2009, 622, 103–113. doi: 10.1017/S0022112008005272
18. Bachman S.D., Fox-Kemper B., Taylor J.R., Thomas L.N. Parameterization of frontal instabilities. I: Theory for Resolved Fronts. Ocean Model. 2017, 109, 72–95. doi: 10.1016/j.ocemod.2016.12.003
19. McIntyre E. Diffusive destabilization of the baroclinic circular vortex. Geophys. Fluid Dyn. 1970, 1, 19–57. doi: 10.1080/03091927009365767
20. Stone P.H. On non-geostrophic baroclinic stability. J. Atmos. Sci. 1966, 23, 4, 390–400.
21. Hoskins B.J. The role of potential vorticity in symmetric stability and instability. Q.J.R. Met. Soc. 1974, 100, 480–482.
22. Boccaletti G., Ferrari R., Fox-Kemper B. Mixed Layer Instabilities and Restratification. J. Phys. Oceanogr. 2007, 37, 2228–2250. doi: 10.1175/JPO3101.1
23. Kuzmina N., Rudels B., Stipa T., Zhurbas V. The structure and driving mechanisms of the Baltic intrusions. J. Phys. Oceanogr. 2005, 35, 6, 1120–1137. doi: 10.1175/JPO2749.1
24. Ruddick Barry. Intrusive mixing in a Mediterranean salt lens — intrusion slopes and dynamical mechanisms. J. Phys. Oceanogr. 1992, 22, 1274–1285. doi: 10.1175/1520–0485(1992)022<1274:IMIAMS>2.0.CO;2
Review
For citations:
Kuzmina N.P., Zhurbas N.V. Symmetric instability of geostrophic currents with a finite transverse lengthscale. Fundamental and Applied Hydrophysics. 2021;14(4):3-13. https://doi.org/10.7868/S2073667321040018