It was shown that for perfect hydrostatic conditions
Under normal conditions, the ocean rarely if ever achieves such a simple balance due to the presence of extraneous forces other than gravity. These forces induce deviations of the orientation of the isobaric surfaces from level and introduce relative motions of the water. Furthermore, due to thermal and advectional processes, the isopycnal surfaces are not necessarily parallel to the isobaric surfaces. Therefore, Eq. (20) does not apply under usual conditions in the ocean.
If, however, the magnitude of the currents associated with the inclined isobaric surfaces are of small magnitude, and if the vertical accelerations of the water are negligible compared with gravity, then the scalar relation
is approximately valid even though the isobaric surfaces are inclined slightly with respect to the level surfaces. If Eq. (25) holds under these conditions, we have the situation of quasi-hydrostatic conditions. Eq. (25) is one of the most useful tools in physical oceanography since it is only through this equation that it is possible to infer, by indirect means, something about the inclination of the isobaric surfaces in the oceanic regions where a fixed reference level is lacking.
It will be shown in Ch. IV that Eq. (25) is a good approximation when dealing with the distribution of pressure associated with the ocean currents. However, when one deals with the pressure distribution associated with surface waves in deep water, the conditions can no longer be considered quasi-static and Eq. (25) is not applicable. The reason for this is that the vertical accelerations of the fluid are significant compared with gravity.
In studies of acoustical vibrations Eq. (25) is approximately valid only from the standpoint of the mean pressure distribution, for here again the accelerations associated with the vibrations of the fluid particles induces anomalies of the instantaneous pressure from that of quasi-hydrostatic equilibrium.