A note on the adjustment to hydrostatic balance

This note investigates the problem of the relation between the initial conditions for the primitive equations and the full set of initial conditions for the Euler equations of adiabatic motion. We formulate for the primitive equations a problem analogous to the one that was considered by Rossby (1938) concerning the quasi geostrophic approximation: a problem which is now well known as the adjustment to geostrophy. The major conclusion is that the initial conditions for the primitive equations may be derived from a full set of initial conditions by solving a one-dimensional unsteady problem of vertical motion.