A generalized time-dependent local convection theory

The time-dependent convection theory given in 1] is generalized to include non-radial oscillations. Under some reasonable assumptions, dynamic equations are derived of the auto-correlation and cross-correlation functions of the velocity and temperature fluctuations. Steady and pulsating components are separated and solved for. Our steady component agrees with Vitense's formulae. The pulsating component contains a phase-lag, due to the inertia of the convective motion.