Strong conservative form of the incompressible Navier-Stokes equations in a rotating frame with a solution procedure

The Navier-Stokes equations in a rotating frame of reference have been formulated in the so-called strong conservative form, i.e., without the traditional source terms, viz., the Coriolis and centrifugal forces, These equations have been coupled with the continuity equation by using the modified artificial compressibility method in order to develop an implicit numerical scheme that has third order accuracy in space and second order accuracy in time. This scheme uses the Roe fluxes and the MUSCL extrapolation techniques to obtain the desired accuracies in space and the backward Euler formula to obtain the desired time accuracy. The flux Jacobians and their eigensystem are presented which are required in the development of the numerical scheme, The resulting scheme was used to solve the Ekman boundary layer problems with (a) no slip and (b) applied surface stress boundary conditions and excellent agreement between computed and exact solutions has been obtained, supporting the new formulation of the governing equations as well as the solution procedure. (C) 1996 Academic Press, Inc.