Multi-Shell Models of Celestial Bodies with an Intermediate Layer of Fluid: Dynamics in the Case of the Large Values of the Ekman Number

Abstract

We consider a mechanical system that is comprised of three parts: a rigid outer shell with a spherical cavity, a spherical core inside this cavity, and an intermediate layer of liquid between the core and the shell. Such a model provides an adequate description of the behavior of a wide variety of celestial bodies. The centers of the inner and outer liquid’s spherical boundaries are assumed to coincide. Assuming that the viscosity of the liquid is high, we obtained an approximate solution to the Navier–Stokes equations that describes a so called creeping flow of the liquid, which sets on after all transient processes die out. We note that the effect of the liquid on the rotational motion of the system can be modeled as a special torque acting upon the system with “solidified” fluid.