Abstract
Thermal convection in vertical tubes has been studied theoretically as an initial value problem using numerical techniques. The thermal and viscous boundary layers at the wall are taken into account approximately. Special emphasis is placed on the Geophysical application of this problem, particularly in examining the convective theories of geyser eruptions from a hydrodynamic point of view and determining the forms of convection during the preliminary stage before boiling starts. The proper time scales and other associated properties are explained through determining the appropriate eddy coefficients.