Convective Fluid Motions in a Rotating Sphere.

Abstract

In connection with the self-exciting dynamo problem studies in our previous papers (referred to as Paper I, II and III), the present paper deals with the stationary con- vection motion of fluid within a rotating sphere. In §3 and 4, preliminary surveys are made for plane boundary problems. In §5, 6 and 7, the problem is reduced to solve the equations (6.16)-(6.18) under the conditions (7.15) and (7.16). This is an eigen-value problem for the Rayleigh number λ= a4αβg/kν containing a parameter Ω= ωa2/ν. This eigen-value problem is solved in §8 in an approximate way.In §9, it is shown that the fluid motion required in Paper I-III is possible in the case when Ω-102. The corresponding kinematical viscosity ν of the earth's core comes out to be about ν-1011 poise.