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Analytical solution for large-scale rotating fluid layer with thermal convection. (English. Russian original) Zbl 1434.76144
Fluid Dyn. 54, No. 6, 741-748 (2019); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2019, No. 6, 3-11 (2019).
Summary: A soliton-like solution is obtained by using the auxiliary Riccati equation method for the evolution equation describing the deformation of the upper surface of a large-scale rotating fluid layer with the thermal convection. This solution reveals that the long-lived structure of the rotating fluid layer depends on the nonlinear term associated with the beta effect and the diffusion term resulted from the thermal convection.
76U05 General theory of rotating fluids
76R05 Forced convection
76E20 Stability and instability of geophysical and astrophysical flows
80A19 Diffusive and convective heat and mass transfer, heat flow
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[1] Chandrasekhar, S., The instability of layer of fluid heated below subject to Coriolis forces, Proc. R. Soc. London A, 217, 306-327 (1953) · Zbl 0053.19102
[2] Zhang, K.; Roberts, Ph, Thermal inertial waves in a rotating fluid layer: exact and asymptotic solutions, Phys. Fluids, 9, 1980-1987 (1997) · Zbl 1185.76907
[3] Petviashvili, V. I., Red spot of Jupiter and the drift soliton in a plasma, Sov. JETP Lett., 32, 619-622 (1980)
[4] Tan, B.; Boyd, J. P., Dynamics of the Flierl-Petviashvili monopoles in a barotropic model with topographic forcing, Wave Motion, 26, 239-251 (1997) · Zbl 0928.76119
[5] Qiang, Z.; Yuan, Z.; Shi-Kuo, L., Two-dimensional Rossby waves: Exact solutions to Petviashvili equation, Commun. Theor. Phys., 45, 414-416 (2006)
[6] Busse, F. H., Thermal instabilities in rapidly rotating layer systems, J. Fluid Mech., 44, 441-460 (1970) · Zbl 0224.76041
[7] Busse, F. H., Convection driven zonal flows and vortices in the major planets, Chaos, 4, 123-134 (1994)
[8] Tikhomolov, E. M., Sustenance of vortex structures in a rotating fluid layer heated from below, JETP Lett., 59, 163-167 (1994)
[9] Tikhomolov, E. M., Short-scale convection and long-scale deformationally unstable Rossby wave in a rotating fluid layer heated from below, Phys. Fluids, 8, 3329-3337 (1996) · Zbl 1027.76550
[10] Sun, Z. P.; Schubert, G.; Glatzmaier, G. A., Banded surface flow maintained by convection in a model of rapidly rotating giant planets, Science, 260, 661-664 (1993)
[11] Gilman, P. A., Nonlinear Boussinesq convective model for large scale solar circulations, Sol. Phys., 27, 3-26 (1972)
[12] Gilman, P. A.; Miller, J., Nonlinear convection of a compressible fluid in a rotating spherical shell, Astrphys. J. Suppl., 61, 585-608 (1986)
[13] Bekir, A., New exact traveling wave solutions for regularized long-wave, Phi-Four and Drinfeld-Sokolov equation, Int. J. Nonlinear Sci., 6, 46-52 (2008) · Zbl 1159.35407
[14] Sirendaoreji, S., Auxiliary equation method and new solutions of Klein-Gordon equation, Chaos, Solitons & Fractals, 31, 943-950 (2007) · Zbl 1143.35341
[15] Pinar, Z.; Özis, T., Solutions of modified equal width equation by means of the auxiliary equation with a sixth-degree nonlinear term, Proc. Sixth ICMSEM, Lecture Notes in Electrical Engineering, 185, 139-148 (2013)
[16] Yong, C.; Biao, L.; Hong-King, Z., Generalized Riccati equation expansion method and its application to the Bogoyavlenskii’s generalized breaking soliton equation, Chin. Phys. Soc., 12, 940-946 (2003)
[17] Feng, D., Exact solutions of Kuramoto-Sivashinsky equation, Int. J. Education and Management Engineering, 2, 61-66 (2012)
[18] Nezlin, M. V.; Snezhkin, E. N., Rossby Vortices, Spiral Structures, Solitons: Astrophysics and Plasma Physics in Shallow Water Experiments (1993), Berlin: Springer-Verlag, Berlin
[19] Nezlin, M. V., Rossby solitary vortices on giant planets and in the laboratory, Chaos, 4, 187-202 (1994)
[20] Pedlosky, J., Geophysical Fluid Dynamics (1987), New York: Springer-Verlag, New York · Zbl 0713.76005
[21] Pokhotelov, O. A.; Kaladze, T. D.; Shukla, Pk; Stenflo, L., Three Dimensional Solitary Vortex Structures in the upper Atmosphere, Phys. Scr., 64, 245-252 (2001) · Zbl 1057.86007
[22] Kukharkin, N.; Orszag, S. A., Generation and Structure of Rossby Vortices in Rotating Fluids, Phys. Rev. E, 54, R4524-R4527 (1996)
[23] Julien, K.; Knobloch, E.; Werne, J., A new class of equations for rotationally constrained flows, Theor Comp Fluid Dyn, 11, 251-261 (1998) · Zbl 0923.76338
[24] King, E. M.; Stellmach, S.; Buffett, B., Scaling behavior in Rayleigh-Bénard convection with and without rotation, J. Fluid Mech., 717, 449-471 (2012) · Zbl 1284.76345
[25] Aubert, J.; Gillet, N.; Cardin, P., Quasigeostrophic models of convection in rotating spherical shells, Geochem. Geophys. Geosyst., 4, 1052-1071 (2003)
[26] Cardin, P.; Olson, P., Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core, Phys. Earth Planet. Inter., 82, 235-259 (1994)
[27] Gillet, N.; Jones, C. A., The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder, J. Fluid Mech., 554, 343-369 (2006) · Zbl 1091.76063
[28] Newell, A. C.; Whitehead, J. A., Finite bandwidth, finite amplitude convection, J. Fluid Mech., 38, 279-303 (1969) · Zbl 0187.25102
[29] Stone, P. H.; Baker, D. J., Concerning the existence of Taylor Columns in atmosphere, Q. J. Royal Meteorol. Soc., 94, 576-580 (1968)
[30] Flasar, F. M.; Conrath, B. J.; Piragila, J. A.; Clark, P. C.; French, R. G.; Gierasch, P. J., Thermal Structure and Dynamics of the Jovian Atmosphere I. The Great Red Spot, J. Geophys. Res., 86, 8759-8767 (1981)
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