A Semigeostrophic Eady-Wave Frontal Model Incorporating Momentum Diffusion. Part III: Wave Dispersion and Dissipation

Abstract

The two-dimensional, semigeostrophic and uniform potential vorticity Eady model is considered. An unstable baroclinic wave develops large velocity and temperature gradients in a narrow zone. Momentum diffusion and wave dispersion are incorporated into the model to prevent the ultimate development of a discontinuity in the alongfront geostrophic velocity ?(?x = ∞). Diffusion and dispersion act to reduce the amplitude of the growing baroclinic wave, and these processes also act to expand the width of the frontal zone, where the maximum velocity gradient is located. Explicit relationships are derived that reveal how these processes are dependent on two parameters: ?, the nondimensional eddy diffusion coefficient, and ? the ratio of a dispersion coefficient ? to ?2. The total dissipation of kinetic energy D is separated into two parts,D1andD2:D1 provides the dissipation that is largely confined to the relatively narrow frontal zone, and D2 = D ? D1 provides the dissipation that is associated with the decaying waves that trail behind the front. These evaluations are carried out for a range of parameter values (?, ?). Results show that the dissipation is not confined exclusively to the frontal zone but that D2 ? D1 when ? is large. Limitations of the present model development are associated with the excessive growth of the unstable Eady wave in the absence of dissipation and the lack of fine-scale measurements that may be used to design a dynamical model of the frontal zone.