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Growing Solitary Disturbance in a Baroclinic Boundary Current

Atsushi KubokawaDepartment of Geophysics, Faculty of Science, Tohoku University, Sendai, Japan

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Abstract

Weakly nonlinear longwaves in a horizontally sheared current flowing along a longitudinal boundary in a two-layer ocean are investigated by using a quasi-geostrophic β-plane model. Under the assumptions that the depth ratio of two layers is small, the β effect is weak and the waves are almost stationary, we obtain a set of coupled equations similar to that derived perviously by Kubokawa for a coastal current with a surface density front on an f-plane. This set of equations contains soliton and cnoidal wave solutions and allows baroclinic instability to occur.

Considering a perturbation around the marginally stable condition, we obtain an analytic solution of a growing solitary disturbance with an amplitude larger than a certain critical value in a linearly stable eastward current. This disturbance propagates eastward, and grows by a baroclinic energy conversion. A numerical computation on its further evolution shows that after the amplitude exceeds another certain critical value, the disturbance begins to propagate westward and to radiate Rossby waves. This Rossby wave radiation causes the disturbance to decay and the propagation speed approaches zero. Nonlinear evolution of linearly unstable waves in an eastward current is also briefly discussed. The theory is applied to the Kuroshio Current in a qualitative way.

Abstract

Weakly nonlinear longwaves in a horizontally sheared current flowing along a longitudinal boundary in a two-layer ocean are investigated by using a quasi-geostrophic β-plane model. Under the assumptions that the depth ratio of two layers is small, the β effect is weak and the waves are almost stationary, we obtain a set of coupled equations similar to that derived perviously by Kubokawa for a coastal current with a surface density front on an f-plane. This set of equations contains soliton and cnoidal wave solutions and allows baroclinic instability to occur.

Considering a perturbation around the marginally stable condition, we obtain an analytic solution of a growing solitary disturbance with an amplitude larger than a certain critical value in a linearly stable eastward current. This disturbance propagates eastward, and grows by a baroclinic energy conversion. A numerical computation on its further evolution shows that after the amplitude exceeds another certain critical value, the disturbance begins to propagate westward and to radiate Rossby waves. This Rossby wave radiation causes the disturbance to decay and the propagation speed approaches zero. Nonlinear evolution of linearly unstable waves in an eastward current is also briefly discussed. The theory is applied to the Kuroshio Current in a qualitative way.

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