A method for calculations of nonlinear shear flow: Application to formation of giant planets in the solar nebula

We calculate the disturbance to an accretion disk flow that results from an embedded orbiting giant protoplanet. This involves nonlinear calculations of two-dimensional steady state flows with vorticity. The method we have developed for this purpose is a generalization of one often used in aerodynamics for potential flows. The velocity held is decomposed into components involving a vortical part and a potential part. Applications of conservation of vorticity and mass gives partial differential equations satisfied by the flow variables. The system is completed by the use of Bernoulli's equation, along with an equation of state and a momentum stream function. The method is fairly robust, efficient, and potentially applicable to a great many related problems of astrophysical fluid dynamics. The implications of our results for giant-planet formation are discussed, along with desirable improvements and extensions to the method.