Nonlinear Disturbances of Western Boundary Currents

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  • 1 Scripps institution of Oceanography-University of California, San Diego, La Jolla, California and Istituto FISBAT-CNR, Bologna, Italy
  • | 2 Institute of Geophysics and Planetary physics-University of California, San Diego, La Jolla, California
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Abstract

Viscous shear instability is proposed as a primary mechanism for generating time-dependent eddies at western boundaries. Thus, the authors examine the stability of the Munk flow with constant transport flowing along a straight coast, tilted at an angle with respect to the north-south direction. Various properties of the marginally unstable wave are calculated as a function of the tilting angle, such as the critical Reynolds number and the phase and group velocities. The effects of weak nonlinearity are also examined, and the authors find that the instability is supercritical for the whole range of tilting angles examined. Thus, the marginally unstable mode can equilibrate at a small finite amplitude, and we derive the equation governing its slow evolution. The flow that results after the disturbance has equilibrated to finite amplitude is in agreement with the eddying boundary currents obtained in many wind-driven general circulation models.

Abstract

Viscous shear instability is proposed as a primary mechanism for generating time-dependent eddies at western boundaries. Thus, the authors examine the stability of the Munk flow with constant transport flowing along a straight coast, tilted at an angle with respect to the north-south direction. Various properties of the marginally unstable wave are calculated as a function of the tilting angle, such as the critical Reynolds number and the phase and group velocities. The effects of weak nonlinearity are also examined, and the authors find that the instability is supercritical for the whole range of tilting angles examined. Thus, the marginally unstable mode can equilibrate at a small finite amplitude, and we derive the equation governing its slow evolution. The flow that results after the disturbance has equilibrated to finite amplitude is in agreement with the eddying boundary currents obtained in many wind-driven general circulation models.

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