The nonlinear model of axisymmetric free-surface two-layered creeping flow

The nonlinear model based on the long-wave approximation of the Navier–Stokes equations is developed to investigate the evolution of free-surface two-layered creeping flow subjected by the initial topography of the surface and interface between layers. Using the method of asymptotic expansions for the governing equations, we study a long-time evolution of the flow and reveal the relation between the surface and interface displacements. The obtained results are applied to calculate the profile of the crust-mantle interface beneath the large-scale lunar basin.