On convection onset in a self-gravitating fluid sphere with internal heating: PMM vol. 35, n≗6, pp. 1000–1014, 1971

Abstract

Proof is given that the loss of stability of the equilibrium state of a self-gravitating fluid filling a rigid sphere having uniformly distributed internal heat sources is accompanied by the onset of a stationary axisymmetric (correct to within an arbitrary rotation) flow which remains stable in the vicinity of the point of stability loss. This flow is numerically defined as a segment of the Liapunov-Schmidt series. The problem of thermal instability of a self-gravitating fluid sphere is associated with various theories and hypotheses of geo- and astro-physics, as well as with the study of fluid behavior in conditions of quasi-weightlessness. Earlier investigations were mainly directed toward the formulation and solution of the linearized problem and finding the limit of instability [1]. Their results were further developed in later publication([2, 3] and others). The method proposed by Chandrasekhar [1] was applied in [4] to the related nonlinear problem. The theory of solution branching of equations of stationary convection [5, 6] is applied below to the study of convection onset in a self-gravitating fluid sphere.