Rossby Waves on a Shear Flow with Recirculation Cores

Derzho, Oleg G.; Grimshaw, Roger

doi:10.1111/j.1467-9590.2005.00318.x

Cited by 14 publications

(14 citation statements)

References 7 publications

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“…The case when the trapped core and multiscaling are combined together is beyond the scope of the present study and will be presented elsewhere. It is noted that multiscaling phenomena exist for solitary waves in various physical contexts, for example, for Rossby waves on a shear flow (Derzho and Grimshaw, 2005) or inertial waves in swirling flows (Derzho and Grimshaw, 2002).…”

Section: Discussionmentioning

confidence: 99%

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Brief communication: Multiscaled solitary waves

Derzho

2017

Nonlin. Processes Geophys.

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Abstract. It is analytically shown how competing nonlinearities yield multiscaled structures for internal solitary waves in stratified shallow fluids. These solitary waves only exist for large amplitudes beyond the limit of applicability of the Korteweg-de Vries (KdV) equation or its usual extensions. The multiscaling phenomenon exists or does not exist for almost identical density profiles. The trapped core inside the wave prevents the appearance of such multiple scales within the core area. The structural stability of waves of large amplitudes is briefly discussed. Waves of large amplitudes displaying quadratic, cubic and higher-order nonlinear terms have stable and unstable branches. Multiscaled waves without a vortex core are shown to be structurally unstable. It is anticipated that multiscaling phenomena will exist for solitary waves in various physical contexts.

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Section: Discussionmentioning

confidence: 99%

“…Derzho and Grimshaw (2005) reported that solitary Rossby waves in channels obey the same KdV-type equation with complicated nonlinearity due to the mean shear variations. A Coriolis force for Rossby waves plays the same role as gravitational force for the internal gravity waves.…”

Section: Multiscalingmentioning

confidence: 99%

Brief communication: Multiscaled solitary waves

Derzho

2017

Nonlin. Processes Geophys.

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“…Following the pioneering work of Benney [2] and recent papers of Derzho and Grimshaw [10,11] and Clarke and Grimshaw [3], we discuss large amplitude Rossby waves riding on a background flow with a weak shear in a meridional channel bounded by rigid latitudinal boundaries at y = y 0 and y = y 0 + H . As |x| → ∞, the flow becomes a weakly mean shear flow given by…”

Section: Nonlinear Rossby Waves On a Weak Shear Flowmentioning

confidence: 99%

“…These studies are based on the assumption that there is no stagnation point or closed streamlines in the flow, that is, there is an implicit limitation on the amplitude of the waves. On the other hand, Derzho and Grimshaw [10] generalized Benney's work to the case of Rossby waves containing stagnation points in the interior.…”

Section: Introductionmentioning

confidence: 97%

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On linear and nonlinear Rossby waves in an ocean

Debnath¹

2007

Journal of Mathematical Analysis and Applications

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This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n = 1) analysis. An extension of the higher modes (n 2) of this work will be made in a subsequent paper.

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Trapped Vortex Cores in Internal Solitary Waves Propagating in a Thin Stratified Layer Embedded in a Deep Homogeneous Fluid

Derzho

IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

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Rossby Waves on a Shear Flow with Recirculation Cores

Cited by 14 publications

References 7 publications

Brief communication: Multiscaled solitary waves

Brief communication: Multiscaled solitary waves

On linear and nonlinear Rossby waves in an ocean

Trapped Vortex Cores in Internal Solitary Waves Propagating in a Thin Stratified Layer Embedded in a Deep Homogeneous Fluid

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