Analytical formulation of thermal convection within a body of spherical shape (Q1820066)

We modify Chandrasekhar's (1961) theory on convective motion by introducing an equation of state which depends both on pressure and temperature. We use this formulation to study the thermal convection within planetary masses of spherical shape. We proceed analytically to show that the flow field and the other geophysically relevant variables can be represented in terms of series of Bessel functions of the radial distance for those regimes which satisfy eigenvalue relations between the Rayleigh number and another nondimensional parameter. We provide numerical values for these eigenfunctions corresponding to the first six orders of harmonics.