Non-linear dynamics of the corotation torque

The excitation of spiral waves by an external perturbation in a disc deposi ts angular momentum in the vicinity of the corotation resonance (the radius where the speed of a rotating pattern matches the local rotation rate). We use matched asymptotic expansions to derive a reduced model that captures non-linear dynamics of the resulting torque and fluid motions. The model is similar to that derived for forced Rossby wave critical layers in geophysi cal fluid dynamics. Using the model we explore the saturation of the corota tion torque, which occurs when the background potential (specific) vorticit y is redistributed by the disturbance. We also consider the effects of diss ipation. If there is a radial transport of potential vorticity, the corotat ion torque does not saturate. The main application is to the creation, grow th and migration of protoplanets within discs like the primordial solar neb ula. The disturbance also nucleates vortices in the vicinity of corotation, which may spark further epochs of planet formation.