Capture and Resonant Forcing of Solitary Waves by the Interaction of a Baroclinic Current with Topography

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  • 1 CSIRO Division of Atmospheric Research, Aspendale, Victoria, Australia
  • | 2 Department of Mathematics, Monash University, Claylon, Victoria, Australia
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Abstract

The authors have demonstrated that a large amplitude, nearly stationary solitary wave can be induced either by direct resonant forcing or by the capture of a traveling wave over the forcing region, using a two-layer model in a weakly nonlinear, long-wave limit. This two-layer model consists of a thin upper layer (where the motion is relatively strong) and a deep lower layer. From this system, an evolution equation of the KdV-type is derived to describe the upper-layer motion, while the deep lower-layer motion is described by a linear long-wave vorticity equation. The authors are particularly interested in the role of baroclinic instability in the evolution of solitary waves, as well as the effects of topographic forcing and frictional dissipation.

Resonant forcing occurs within a bandwidth of a detuning parameter that scales with the square root of the (nondimensional) forcing amplitude. On the other hand, the capture of traveling waves, whose amplitude is larger than a critical value, occurs when the detuning parameter is outside the resonant band, and it is in this range that multiple equilibria (coexistence of the large and small amplitude stationary states for a given parameter set) can be realized. Whether the large amplitude stationary state appears upstream or downstream from the forcing region depends on the relative importance of baroclinic energy conversion, topographic forcing, and frictional dissipation. Further, a topographic feature can trigger baroclinic instability, which can then induce not only large amplitude stationary waves but also large amplitude traveling waves going away from the forcing region. The model results are suggestive of the bimodality of Kuroshio upstream from the Izu Ridge.

Abstract

The authors have demonstrated that a large amplitude, nearly stationary solitary wave can be induced either by direct resonant forcing or by the capture of a traveling wave over the forcing region, using a two-layer model in a weakly nonlinear, long-wave limit. This two-layer model consists of a thin upper layer (where the motion is relatively strong) and a deep lower layer. From this system, an evolution equation of the KdV-type is derived to describe the upper-layer motion, while the deep lower-layer motion is described by a linear long-wave vorticity equation. The authors are particularly interested in the role of baroclinic instability in the evolution of solitary waves, as well as the effects of topographic forcing and frictional dissipation.

Resonant forcing occurs within a bandwidth of a detuning parameter that scales with the square root of the (nondimensional) forcing amplitude. On the other hand, the capture of traveling waves, whose amplitude is larger than a critical value, occurs when the detuning parameter is outside the resonant band, and it is in this range that multiple equilibria (coexistence of the large and small amplitude stationary states for a given parameter set) can be realized. Whether the large amplitude stationary state appears upstream or downstream from the forcing region depends on the relative importance of baroclinic energy conversion, topographic forcing, and frictional dissipation. Further, a topographic feature can trigger baroclinic instability, which can then induce not only large amplitude stationary waves but also large amplitude traveling waves going away from the forcing region. The model results are suggestive of the bimodality of Kuroshio upstream from the Izu Ridge.

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