Breaking internal waves and fronts in rotating fluids

We consider the evolution of nonlinear Kelvin waves using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to breaking. We find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in the absence of rotation. The onset of breaking occurs almost simultaneously over a distance comparable to the Rossby radius of deformation. We also study three-dimensional hydraulic jumps travelling near boundaries in rotating fluids. The transverse structure of the wave field behind such jumps is similar to the transverse structure of Kelvin waves. We obtain the jump relations and derive an evolution equation for the jump as it moves along the boundary. The model is suitable for describing the propagation of oceanic and atmospheric fronts. We show that after some initial adjustment the Kelvin-type jump assumes a permanent form and travels with a constant velocity along the boundary or the coast. The jump is normal to the boundary, but within one Rossby radius it becomes oblique to the coastline.