The effect of energy generation fluctuations on the onset of thermal instability in a Boussinesq fluid sphere

The Boussinesq perturbation equations are modified to include the effect of energy generation fluctuations. The equations are then solved for the motion within a sphere of radius R subject to free and rigid boundary conditions. A transcendental equation is derived connecting the growth rate, Rayleigh number, Prandtl number and an energy generation number for each mode. Various cases are considered for the l = 1 mode with free boundary conditions and a good approximation is given for the Rayleigh number at high energy generation rates. (author)