Nonlinear Dynamics Of Rossby Waves In A
Western Boundary Current
Author(s)
L. J. Campbell
Abstract
This paper examines the nonlinear dynamics of a Rossby wave propagating longitudinally
in a north-south shear flow. The flow configuration is an idealized model
for a western boundary current in an ocean basin. It is assumed that there is a critical
layer in the flow, where the shear flow speed is the same as the wave phase
speed. The nonlinear critical-layer evolution of the wave depends on the direction
of propagation of the wave. Numerical simulations show that an eastwardpropagating
wave incident on the critical layer from the west is absorbed by the
mean flow at early times. This is the same situation that is known to occur for
small-amplitude waves, according to the linear theory. At later times, however,
nonlinear waves may be reflected from the critical layer. In contrast, a westwardpropagatingwave
incident on the critical layer from the east passes through largely
unaffected. An approximate analytic solution of the linearized equations is also
presented to give further insight into the evolution of the critical layer.
Keywords: critical layer, Rossby waves, nonlinear wave interactions, western
boundary current, shear flow, numerical simulations.
1 Introduction
An idealized model for the dynamics of Rossby waves in a western boundary current
in an ocean basin consists of a latitudinally-periodicRossby wave propagating
horizontally in the zonal direction in a north-south shear flow [6, 7, 8]. This paper
examines the nonlinear interactions between the waves and the current in the vicinity
of a critical layer. A critical layer is a region surrounding a longitude at which
the shear flow velocity is equal to the phase speed of the wave.When the governing
linearized inviscid equations are solved numerically or analytically it is seen that
Keywords
critical layer, Rossby waves, nonlinear wave interactions, western
boundary current, shear flow, numerical simulations.
Related Book
Other papers in this volume
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