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 westwardpropagating wave 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.

Additional Metadata
Keywords Critical layer, Nonlinear wave interactions, Numerical simulations, Rossby waves, Shear flow, Western boundary current
Persistent URL dx.doi.org/10.2495/AFM06045
Conference Sixth International Conference on Advances in Fluid Mechanics, AFM 2006, AFM06
Citation
Campbell, L. (2006). Nonlinear dynamics of Rossby waves in a western boundary current. Presented at the Sixth International Conference on Advances in Fluid Mechanics, AFM 2006, AFM06. doi:10.2495/AFM06045