Hostname: page-component-f554764f5-8cg97 Total loading time: 0 Render date: 2025-04-12T11:46:45.882Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetries and Conservation Laws of a Spectral Nonlinear Modelfor Atmospheric Baroclinic Jets

Published online by Cambridge University Press:  17 July 2014

N.H. Ibragimov ,
R.N. Ibragimov  and
L.R. Galiakberova
N.H. Ibragimov
Affiliation:
Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, 450 000 Ufa, Russia Center for Mathematical Modeling with Lie Group Analysis (CeMMLiGA) Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden
R.N. Ibragimov*
Affiliation:
Department of Mathematics, University of Texas at Brownsville Brownsville, TX 78520, USA Pacific Northwest National Laboratory, Richland, WA 99352, USA
L.R. Galiakberova
Affiliation:
Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, 450 000 Ufa, Russia
*
⋆Corresponding author. E-mail: [email protected]
Get access

Abstract

In this paper, we shall obtain the symmetries of the mathematical model describingspontaneous relaxation of eastward jets into a meandering state and use these symmetriesfor constructing the conservation laws. The basic eastward jet is a spectral parameter ofthe model, which is in geostrophic equilibrium with the basic density structure and whichguarantees the existence of nontrivial conservation laws.

Keywords

76U0535Q3035Q3535Q86
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 111 - 118
Copyright
© EDP Sciences, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, R.F., Ali, S., Brandtmiller, L.L., Nielsen, S.H.H., Fleisher, M.Q.. Wind-driven upwelling in the Southern Ocean and the deglacial rise in atmospheric CO2. Science, 323 (2006), 1443-1448. CrossRefGoogle Scholar
Smith, R.D., Maltrud, M.E., Bryan, F.O., Hecht, M.W.. Numerical Simulation of the North Atlantic Ocean at 1/10°. J. Phys. Oceanogr., 30 (2000), 1532–1561. 2.0.CO;2>CrossRefGoogle Scholar
Ibragimov, R.N.. Nonlinear viscous fluid patterns in a thin rotating spherical domain and applications. Phys. Fluids, 23 (2010), 123102. CrossRefGoogle Scholar
Ibragimov, R.N., Ibragimov, N.H.. Rotationally symmetric internal gravity waves. Int. J. Nonlinear Mech. 47, (2012) 46-52. CrossRefGoogle Scholar
Ibragimov, R.N.. Generation of internal tides by an oscillating background flow along a corrugated slope. Phys. Scripta, 78, 065801. CrossRef
Maltrud, M.E., Smith, R. D., Semtner, A. J., Malone, R. C.. Global Eddy-Resolving Ocean Simulations Driven by 1985–1994 Atmospheric Winds. J.Geophys. Res., 102 (1998), 25203–25226. Google Scholar
Ibragimov, R.N.. Free boundary effects on stability of two phase planar fluid motion in annulus: Migration of the stable mode. Comm. Nonlinear Sci. Numer. Simulat. 15 (2010), no. 9, 2361-2374. CrossRefGoogle Scholar
Frederiksen, J., Webster, P.. Alternative Theories of Atmospheric Teleconnections and Low-Frequency Fluctuations. Rev. Geopphys. 26 (1998), no. 3, 459-494. CrossRefGoogle Scholar
Ibragimov, R.N., Pelinovsky, D.E.. Incompressible viscous flows in a thin spherical shell. J. Math. Fluid Mech., 11 (2009), 60-90. CrossRefGoogle Scholar
Ibragimov, N.H., Ibragimov, R.N.. Integration by quadratures of the nonlinear Euler equations modeling atmospheric flows in a thin rotating spherical shell. Phys. Lett. A., 375 (2011), 3858-3865. CrossRefGoogle Scholar
Ibragimov, R.N., Dameron, M., Dannangoda, C.. Sources and sinks of energy balance for nonlinear atmospheric motion perturbed by west-to-east winds progressing on a surface of rotating spherical shell. Discontinuity, Nonlinearity and Complexity, 1 (2012), no. 1, 41-55. CrossRefGoogle Scholar
Held, I.. 1978: The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parametrisations. J. Atmos. Sci., 35 (1978), 572-576. 2.0.CO;2>CrossRefGoogle Scholar
N.H. Ibragimov. Nonlinear self-adjointness in constructing conservation laws. Archives of ALGA 7/8, 1-99. See also arXiv:1109.1728v1[math-ph], 2011, 1-104.
Araslanov, A.M., Galiakberova, L.R., Ibragimov, N.H., Ibragimov, R.H.. Conserved vectors for a model of nonlinear atmospheric flows around the rotating spherical surface. Math. Model. Natur. Phenom., 8 (2013), no. 1, 32-48. Google Scholar
Dewar, W.K.. On “too fast” baroclinic planetary waves in the general circulation. J. Phys. Oceanogr., 29 (1998), 500-511. Google Scholar
Ibragimov, R.N., Jefferson, G., Carminati, J.. Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations. Spinger: Anal. Math. Phys., 3 (2013), no. 3, 201-294. Google Scholar
Ibragimov, N.H., Ibragimov, R.N.. Nonlinear whirlpools versus harmonic waves in a rotating column of stratified fluid. Math. Model. Nat. Phenom., 8 (2013), no. 1, 32-14. CrossRefGoogle Scholar
R.N. Ibragimov, M. Dameron. Spinning phenomena and energetics of spherically pulsating patterns in stratified fluids. Phys. Scripta 84, 2011 015402.
Simmons, A.J., Hoskins, B.J.. Baroclinic instability on the sphere: Normal modes of the primitive and quasi-geostrophic equations. J. Atmos. Sci., 33 (1975), 1454–1477. 2.0.CO;2>CrossRefGoogle Scholar
J. Pedlosky. Geophysical Fluid Dynamics. Springer-Verlag, Second Edition, (1986).
Ibragimov, N.H., Ibragimov, R.N.. Applications of Lie Group analysis to mathematical modeling in natural sciences”. Math. Model. Nat. Phenom., 7 (2012), no. 2, 52-65. CrossRefGoogle Scholar
Ibragimov, R.N.. Mechanism of energy transfers to smaller scales within the rotational internal wave field. Springer: Math. Phys. Anal. Geom., 13 (2010), no. 4, 331-355. Google Scholar
Ibragimov, R.N.. Shallow water theory and solution of the problem on the atmospheric motion around a celestial body. Phys. Scripta., 61 (2000), 391-395. CrossRefGoogle Scholar