The Frontal Width Problem

Abstract

Observations of two low-level frontal passages by a hot-wire anemometer placed at 3 m above the ground provide evidence that frontal zones and the postfrontal regions exhibit enhanced kinetic energy dissipation. These observations support a postulated linear relationship between turbulent kinetic energy dissipation rate ? and a characteristic frontal width L. A rigorous theoretical development is not available to verify the postulate that an equilibrated frontal width is determined by a balance between frontogenetical forcing and turbulent dissipation of kinetic energy. Instead, a simple construct, based on a model of inviscid frontogenesis, is introduced. This model exhibits downscale spectral energy transfer that decreases with horizontal scale during frontogenesis. This model is invalid in the dissipative range of fully turbulent small-scale motions. In those cases, however, when frontal equilibration occurs at scales close to the scales where dissipation just begins to become significant, the inviscid model provides some theoretical support for the postulated relationship between ? and L. The analysis is then extended to show how the vertical scale L? in a surface-based front is related to ? and N (N is the Brunt?Väisälä frequency) when the earth?s rotation is not a factor, but L? depends on ?, N, and f (f is the Coriolis parameter) when rotation is retained. Questions that remain unanswered by the present analysis concern the appropriate definition of a frontal scale, the role of precipitation in frontal scaling, and the equilibration of broad-scale fronts L ≥ 105 m, when turbulent dissipation of kinetic energy may not be the controlling factor in the equilibration of a front.