Quantitative Nondimensional Properties of the Gradient Wind

Abstract

Elementary gradient wind balance has been discussed in all dynamic meteorology texts and many papers since the turn of the century. It has nearly escaped notice, however, that if one fully nondimensionalizes the gradient balance equation with the inertia velocity fR, then it contains only two dimensionless variables: a gradient wind and a geostrophic wind measured in inertia velocity units. A single square root expression gives the gradient wind for all four classes of flow as a 1?1 function of the dimensionless geostrophic wind and numerical tables are easily constructed showing numerical ratios and the approach to cyclostrophic balance. Such numerical tables apply to any horizontal scale from micro- to meso- to synoptic or larger as long as the elementary physical assumptions are reasonably satisfied. Examples suggesting that anomalous anticyclonic flows can occur on mesoscales are discussed.