Permissible modes of non-thermal convection in planetary mantles

Boundary conditions are imposed upon the solutions of the conservation equations for non-thermal convective motion in a self-gravitating, homogeneous, non-rotating sphere of radiusR, consisting of a core extending to a fraction of the radius of the sphere and with a viscous mantle overlying the core. It is shown that convective modes are permissible in the mantle only for certain values ofn and .