The nature of the perceived acceleration depends on the relative size of the acceleration of the relative velocity observed in the rotating frame and the Coriolis acceleration. We can make a preliminary estimate of the importance of the Coriolis acceleration by examining the order of magnitude of the ratio of these two accelerations. For this purpose we write the order of magnitude of each of these accelerations in terms of the characteristic velocity and length scales \(U\) and \(L\)

The Coriolis acceleration can be estimated as \[ 2\Omega \times \mathbf{u} = O(2\Omega U) \]

Assume \(\partial \mathbf{u} / \partial t\) is of the same order as \(\mathbf{u} \cdot \nabla \mathbf{u}\), the relative acceleration \[ \frac{d\mathbf{u}}{dt} = O\left( \frac{U^2}{L} \right) \]

The Coriolis acceleration is independent of the geometric scale and depends linearly on the velocity \(U\). The size of the relative acceleration decreases with increasing scale and depends quadratically on \(U\). The ratio of the relative to the Coriolis acceleration is the Rossby number \[ \epsilon = \frac{U}{2\Omega L} \]

¹ Pedlosky, J. (1982). Geophysical Fluid Dynamics. Springer study edition. Springer, Berlin, Heidelberg.