Propagation and Breaking of Nonlinear Kelvin Waves

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  • 1 Scripps Institution of Oceanography, University of California San Diego, La Jolla, California
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Abstract

The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.

Abstract

The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.

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