A Semigeostrophic Eady-Wave Frontal Model Incorporating Momentum Diffusion. Part II: Kinetic Energy and Enstrophy Dissipation

Abstract

Momentum diffusion has been introduced into a semigeostrophic Eady-wave frontal model by Blumen (Part I). This model is used to determine the kinetic energy and enstrophy dissipations within a frontal zone that extends from the ground to a midtropospheric level. The largest amount of kinetic energy dissipation occurs when a relatively small nondimensional eddy viscosity coefficient is used, and the front attains an equilibrated state?a balance between unstable growth and momentum diffusion. The magnitude of kinetic energy dissipation ranges from about 50 to 250 W m?2 for parameter values that characterize surface-based fronts. These values are comparable to the 75 W m?2 determined by Kennedy and Shapiro from observations in an upper-level front, but are about one to two orders of magnitude larger than previous estimates of kinetic energy dissipated locally in clear-air turbulence zones and in the planetary boundary layer. An estimate of global kinetic energy dissipation in the planetary boundary layer is provided. A comparison establishes that fronts may make a relatively large contribution to the dissipation occurring during the life cycle of a cyclone, but the global contribution is less than that associated with the planetary boundary layer. Frontal equilibration is characterized by a balance between production and dissipation of enstrophy. However, as frontolysis sets in, the dissipation of enstrophy becomes the dominant feature. Finally, it is noted that the physical process associated with the cascade of energy and enstrophy to dissipative scales differs from the cascade process described by the theory of homogeneous turbulence, and a different spectral decay law is realized.