ON THE TRANSFORMATION OF DISCONTINUITY WAVES FROM SPATIAL TO PRESSURECOORDINATES FOR THE PRIMITIVE SYSTEM OF GEOPHYSICAL FLUID-DYNAMICS

We give a complete analysis of the transformation of discontinuity wav es from spatial coordinates to pressure coordinates for the primitive equations of geophysical fluid dynamics, These waves are moving surfac es in physical space across which some or all of the fluid variables a re discontinuous, and therefore correspond to regions of steep gradien t in solutions of related models which incorporate frictional forces o r viscosity. Discontinuity waves consequently represent the most easil y discernable and frequently the most interesting and important featur es of the flow. Our results show that the primitive equations in eithe r coordinate system inherit from the underlying Euler equations all th e physically correct shear waves; that the acoustic waves are complete ly eliminated in pressure coordinates but not in spatial coordinates; and that unphysical, anomolous waves occur in both coordinate systems. (C) 1998 Elsevier Science B.V.