Let us begin with the momentum equation, Eq. 6-43, for a fluid on a rotating Earth and consider the magnitude of the various terms. First, we restrict attention to the free atmosphere and ocean (by which we mean away from boundary layers), where friction is negligible.1 Suppose each of the horizontal flow components u and v has a typical magnitude U, and that each varies in time with a characteristic time scale T and with horizontal position over a characteristic length scale L. Then the first two terms on the left side of the horizontal components of Eq. 6-43 scale as2:
Dt dt u2 J flr
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