×

Zonal flow generation by the stretching of Rossby modons. (English) Zbl 1236.76106

Summary: The numerical study is presented of the zonal flow generation in shallow rotating fluids and in magnetized plasmas, in a strongly nonlinear regime described by the Charney-Hasegawa-Mima equation. It is demonstrated that coherent vortices, often regarded as the building blocks of the strong turbulence, are unstable in the presence of inhomogeneities. While the monopolar vortices, both cyclones and anticyclones, are rapidly dispersed by a finite Rossby velocity, the dipolar vortices (or modons) undergo a qualitative modification by the action of the scalar nonlinearity arising from the \(\beta \) effect. The westward propagating modons rapidly topple, disintegrating into two monopoles that propagate independently and rapidly disperse. Conversely, for the eastward propagating modons, the \(\beta \)-effect produces the change of the direction of the propagation, followed by the stretching in the east-west direction. On a long time scale, such modons expand to a length equal to the size of the computational box, and essentially an one-dimensional zonal flow is created, whose transverse (north-south) scale is determined by the initial size of the modon.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
76B65 Rossby waves (MSC2010)
76B47 Vortex flows for incompressible inviscid fluids
76E30 Nonlinear effects in hydrodynamic stability
35Q35 PDEs in connection with fluid mechanics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nezlin, M. V.; Snezhkin, E. N.; Dobroslavsky, A.; Pletnev, A., Rossby Vortices, Spiral Structures, Solitons (1993)
[2] Sagdeev, R. Z., Nonlinear Phenomena in Plasma Physics and Hydrodynamics (1986), Mir Publishers: Mir Publishers Moscow, p. 224
[3] Onishchenko, O. G.; Pokhotelov, O. A.; Astafieva, N. M., Physics Uspekhi, 51, 577 (2008)
[4] Kukharkin, N.; Orszag, S. A., Phys. Rev. E, 54, 4524 (1996)
[5] Rossby, C.-G., Quart. J. Meteorolog. Soc., 66, 68 (1940)
[6] Vasavada, A. R.; Showman, A. P., Reports on Progress in Physics, 68, 1935 (2005)
[7] Bridges, A., Jupiter movie debut: Cassini spacecraft comes in for close-up (2000)
[8] Shukla, P. K.; Yu, M. Y.; Rahman, H. U.; Spatschek, K. H., Phys. Rev. A, 23, 321 (1981)
[9] Shukla, P. K.; Yu, M. Y.; Rahman, H. U.; Spatschek, K. H., Phys. Rep., 105, 227 (1984)
[10] Shukla, P. K.; Stenflo, L., European Physical Journal D, 20, 103 (2002)
[11] Shukla, P. K.; Shaikh, D., Physics Letters A, 374, 286 (2009), 0910.1635
[12] Diamond, P. H.; Itoh, S.; Itoh, K.; Hahm, T. S., Plasma Physics and Controlled Fusion, 47, 35 (2005)
[13] Cheng, C. Z.; Okuda, H., Physical Review Letters, 38, 708 (1977)
[14] Larichev, V. D.; Reznik, G. M., Dokl. Akad. Nauk SSSR, 231, 1077 (1976)
[15] van Heijst, G. J.F.; Kloosterziel, R. C., Nature (London), 338, 569 (1989)
[16] Pingree, R. D.; Le Cann, B., J. Geophys. Res., 97, 14353 (1992)
[17] Jovanović, D.; Shukla, P. K., Physics Letters A, 326, 267 (2004)
[18] Bergeron, D. J.; Benney, R. F., Stud. Appl. Math., 48, 181 (1969)
[19] Stuart, J. T., Journal of Fluid Mechanics, 29, 417 (1967)
[20] Jovanović, D.; Stenflo, L.; Shukla, P. K., Nonlinear Processes in Geophysics, 9, 333 (2002)
[21] Ivanov, A. Y.; Ginzburg, A. I., Journal of Earth System Science, 111, 281 (2002)
[22] Makino, M.; Kamimura, T.; Taniuti, T., Journal of the Physical Society of Japan, 50, 980 (1981)
[23] Antonova, R. A.; Zhvaniya, B. P.; Lominadze, D. G.; Nanobashvili, D. I.; Petviashvili, V. I., Soviet Journal of Experimental and Theoretical Physics Letters, 37, 651 (1983)
[24] Westerhof, E.; Rem, J.; Schep, T. J., Phys. Rev. E, 56, 947 (1997)
[25] Horton, W.; Su, X. N.; Morrison, P. J., Soviet Journal of Plasma Physics, 16, 969 (1990)
[26] Aburjania, G. D.; Chargazia, K. Z.; Zelenyi, L. M.; Zimbardo, G., Nonlinear Processes in Geophysics, 16, 11 (2009)
[27] Sommeria, J.; Meyers, S. D.; Swinney, H. L., Nature (London), 337, 58 (1989)
[28] Aubert, J.; Jung, S.; Swinney, H. L., Geophys. Res. Lett., 29, 180000 (2002)
[29] Manin, D. Y.; Nazarenko, S. V., Physics of Fluids, 6, 1158 (1994)
[30] Shukla, P. K.; Stenflo, L., Physics Letters A, 307, 154 (2003)
[31] Dewar, R. L.; Abdullatif, R. F., (Denier, J.; Frederiksen, J. S., Frontiers in Turbulence and Coherent Structures (2007), World Scientific: World Scientific Singapore), 415
[32] Jovanovic, D.; Shukla, P. K., Physics Letters A, 289, 219 (1991)
[33] Mikhailovskii, A. B.; Lominadze, J. G.; Erokhin, N. N.; Erokhin, N. S.; Smolyakov, A. I.; Tsypin, V. S., Physics Letters A, 369, 218 (2007)
[34] Mendonça, J. T.; Shukla, P. K.; Bingham, R., New Journal of Physics, 11, 073038 (2009)
[35] Kaladze, T. D.; Wu, D. J.; Pokhotelov, O. A.; Sagdeev, R. Z.; Stenflo, L.; Shukla, P. K., Physics of Plasmas, 12, 122311 (2005)
[36] Nezlin, M. V., Chaos, 4, 187 (1994)
[37] Nezlin, M. V.; Rylov, A. Y.; Trubnikov, A. S.; Khutoretski, A. V., Geophysical and Astrophysical Fluid Dynamics, 52, 211 (1990)
[38] Horton, W.; Su, X. N.; Morrison, P. J., Soviet Journal of Plasma Physics, 16, 969 (1990)
[39] Su, X. N.; Horton, W.; Morrison, P. J., Physics of Fluids B, 3, 921 (1991)
[40] Jovanovic, D.; Horton, W., Physics of Fluids B, 5, 9 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.