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Journal of Computational Physics, 1995
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Studies in Applied Mathematics, 1979
An investigation is made of the properties of periodic and solitary waves for a simple atmospheric model.
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An investigation is made of the properties of periodic and solitary waves for a simple atmospheric model.
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1986
We shall now consider adiabatic motions without external forces. Then in the quasistatic and Boussinesq approximations the equations of motion, mass conservation, and entropy evolution have the form (see Kamenkovich and Monin, 1978, §§2 and 5): $$\frac{{du}}{{dt}} - \frac{{uv}}{a}\tan \varphi - fv = - \frac{1}{{{\varrho _0}}}\frac{{\partial p}}{{a ...
V. M. Kamenkovich +2 more
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We shall now consider adiabatic motions without external forces. Then in the quasistatic and Boussinesq approximations the equations of motion, mass conservation, and entropy evolution have the form (see Kamenkovich and Monin, 1978, §§2 and 5): $$\frac{{du}}{{dt}} - \frac{{uv}}{a}\tan \varphi - fv = - \frac{1}{{{\varrho _0}}}\frac{{\partial p}}{{a ...
V. M. Kamenkovich +2 more
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Journal of the Atmospheric Sciences, 1979
Abstract A variational principle and an associated integral invariant are constructed for two-dimensional (non-divergent) waves of permanent form in a Rossby β-plane. A solitary-wave solution is obtained, and it is shown that the effects of cubic nonlinearity may be comparable with those of quadratic nonlinearity and may limit the amplitude of the wave.
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Abstract A variational principle and an associated integral invariant are constructed for two-dimensional (non-divergent) waves of permanent form in a Rossby β-plane. A solitary-wave solution is obtained, and it is shown that the effects of cubic nonlinearity may be comparable with those of quadratic nonlinearity and may limit the amplitude of the wave.
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The stability of a Rossby wave
Geophysical & Astrophysical Fluid Dynamics, 1977Abstract The stability of a finite-amplitude Rossby wave on a β-plane with respect to a small amplitude perturbation is examined. Normal modes are defined, without further approximation, by a third-order Floquet system. The parametric instability exhibited by the system is examined analytically and numerically.
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The Scattering of Rossby Waves by Ocean Ridges
2002Overview and equation of motion. Rossby waves, or planetary waves, play a crucial role in global oceanic circulation. These waves propagate in regions of non-uniform ambient potential vorticity by conserving the potential vorticity of the flow. Bottom topography and the variation of the Coriolis parameter (a quantity proportional to the normal ...
Abrahams, ID, Owen, GW, Willmott, AJ
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Chaotic advection by Rossby-Haurwitz waves
Fluid Dynamics Research, 1996Summary: We study the kinematics of the mixing of particles passively advected by linear wave solutions of \textit{B. Haurwitz} [J. Marine Res. 3, 254 ff. (1940)] for an incompressible, inviscid, barotropic, horizontal flow on a sphere. We show, with the help of Poincaré maps, that the superposition of two waves is sufficient to produce chaotic ...
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A Rossby-wave dynamo for the sun, I
Solar Physics, 1969To make the analysis more tractable, we simplify the equations of Part I to apply to two superposed layers of fluid, with horizontal variations in the motion and magnetic field represented by a small number of Fourier harmonics. The resulting set of eighteen ordinary nonlinear differential equations in time for the Fourier amplitudes is integrated ...
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Abstract A second form of wave motion can be supported by background rotation, called Rossby waves. These take the form of a slow, quasi-geostrophic motion, and they play a critical role in the atmospheres of the earth and the gas giants.
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