TABLE OF CONTENTS Atmospheric motions and ocean currents are called Geophysical Flows, which are significantly influenced by the rotation of the Earth and density stratifications of the atmosphere and ocean. We consider the flows in a rotating system and the influence of density stratification on flows compactly in this chapter. [1] This subject is becoming increasingly important in the age of space science and giant computers.
To study geophysical flows, we have to consider fluid motions in a rotating frame such as a frame fixed to the Earth, which is a non-inertial frame. The equation of motion on such a noninertial frame is described by introducing a centrifugal force and Coriolis force in addition to the forces of the inertial system. It is assumed that a frame of reference 
is rotating with angular velocity ? relative to an inertial frame 
fixed to the space. The Navier Stokes equation in the inertial frame is given by (4.10), which is reproduced here:
where p m is the modified pressure, defined originally by (4.11) for a constant ?, and g is the acceleration due to gravity expressed by ?? ? ( ?: the gravity potential). The formula of p m can be extended to variable density ?. Assuming that the atmosphere is barotropic, i.e. assuming ? = ?( p), one can write as ? ? 1 ? p = ?? by...
