Dynamics of Rossby Wave Breaking

Rossby wave breaking is an essential mechanism by which waves (eddies) induce mixing of potential vorticity and alter the mean flow irreversibly. In the linear theory, critical lines are often thought of as absorbers of wave activity and thus are associated with wave breaking. At finite amplitude, waves often break before they encounter a critical line or even when there is no critical line. To examine the mechanisms that govern the location, timing, and magnitude of wave breaking, we analyze two sets of idealized simulation of nonlinear decay of barotropic Rossby waves on a sphere: one with no background flow and hence no critical line, and the other with a shear flow that embeds a critical line at low latitudes. In each case, meridionally confined finite-amplitude Rossby waves are placed at midlatitudes of the Northern Hemisphere and allowed to evolve freely except for a hyperviscosity that removes enstrophy at small scales. We analyze the spatio-temporal structure of finite-amplitude wave activity (pseudomomentum) and its dissipation as diagnostics of group propagation and wave breaking, varying the initial amplitude of the Rossby waves. With no background flow, the waves split into a weak northward moving packet and several southward moving packets. At small amplitudes, a large fraction of wave activity enters the Southern Hemisphere in the southward moving packets and accumulates near the turning latitude. As the initial amplitude of the waves is increased, the southward moving wave activity is trapped around 30N and dissipated there. The magnitude and meridional extent of dissipation increase with the wave amplitude with distinctive characteristics of wave breaking, despite the absence of a critical line in the initial condition. With the background shear flow, northward and southward moving wave packets are generated but very little wave activity enters the Southern Hemisphere. At high amplitudes, almost all of the southward moving wave activity is trapped in the subtropics of the Northern Hemisphere and dissipated there as the waves break. The maximum dissipation occurs at a latitude higher than the critical line. It moves further north as the amplitude of the waves increases. In either case the linear critical line is not a good predictor of wave breaking location. We propose the notion of self-induced nonlinear critical line -- where the speed of the mean flow modified by the finite-amplitude waves matches the average effective phase speed of the waves -- as the location of maximum wave activity dissipation. Although the kinematics of nonlinear critical line is analogous to the linear critical line, the former is accessible to the waves in finite time.