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T. Warn and H. Warn

Abstract

The asymptotics of the analysis of Dickinson (1970) on the development of a Rossby wave critical level are reexamined. These linear results are used to discuss certain aspects of the development of the nonlinear critical level for Rossby waves. In particular it is shown that the critical layer becomes fully nonlinear in a (nondimensional) time scale of O(e-??), where e is a parameter measuring the amplitude of the forced wave, and that all harmonies are likely to be important in the critical layer after this time.

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T. Warn and B. Brasnett

Abstract

The problem of long, quasi-geostrophic baroclinic waves interacting with topography is shown to reduce to an inhomogeneous, damped Korteweg-deVries equation. The soliton perturbation theory of Karpman and Maslov (1977, 1978) and Kaup and Newell (1978) is then used to examine the qualitative aspects of the interaction of travelling solitons with topography. The perturbation theory suggests and numerical experiments confirm that under certain conditions incident solitans can be simultaneously amplified and stalled by topography-a process which we interpret as a transition to a regional blocking configuration.

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G. Brunet and T. Warn

Abstract

It is argued using simple examples that while free, barotropic Rossby wave critical layers on unbounded stable monotone profiles are difficult to excite with smooth initial data, they are easily excited on stable jets when the background absolute-vorticity gradient is sufficiently weak. After sufficient time the critical layer, which is located at the jet maximum, becomes locally nonlinear in the absence of dissipation, regardless of the initial amplitude of the disturbance. Even though the nonlinear terms are smallest at the critical layer, they dominate due to the smallness of the linear terms there. We also speculate on how other nonmonotone profiles might be treated.

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M. Béland and T. Warn

Abstract

By means of a straightforward application of the Laplace transform, a radiation condition for transient Rossby waves is obtained. The condition is exact for linear problems and permits the numerical simulation of laterally propagating waves in a semi-infinite channel using a finite computational mesh. Linear and non-linear simulations using this condition compare favorably with double-domain integrations for periods of up to 20–40 days. It is shown that the rate of degradation of these simulations depends on both the intensity of the nonlinearities and the scale of motion near the computational boundary. Some possible applications to other problems are also discussed.

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A. Patoine and T. Warn

Abstract

It is shown that the interaction of long, quasi-stationary baroclinic waves with topography can be described by an inhomogeneous Korteweg-deVries equation whose solutions exhibit a variety of phenomena familiar from the study of baroclinic waves in other contexts. In particular solutions involving lee waves and upstream influence, multiple equilibria and soliton-like phase shifts between solitary waves and topography have been found under various parameter settings.

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P. E. Merilees and T. Warn

Abstract

No abstract available.

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