Analytic solutions for Stokes’ flow with lateral variations in viscosity

Abstract

SUMMARY Analytic solutions for 2-D incompressible Stokes’ flow with lateral variations in viscosity have been developed with a Green's function method and matrix propagator techniques. The analytic solutions are developed based on the observation that lateral variations in viscosity only result in mode coupling between viscosity and buoyancy in the horizontal dimension and not in the vertical dimension. The Green's function solution for flows with a viscosity that varies laterally with an exponential function indicates that, if the lateral variation in viscosity is within one order of magnitude, at very long wavelengths (for example degree 2) the mode coupling between viscosity and buoyancy does not greatly influence the geoid deduced from models ignoring the lateral variations in viscosity. The relatively short-wavelength geoid (degree 4 and higher modes), however, is seriously contaminated by mode coupling. The solutions for sharp lateral variations in viscosity calculated with propagator matrix techniques show that the topography varies rapidly across the viscosity boundaries.