Baroclinic Eady Wave and Fronts. Part III: Unbalanced Dynamics—Departures from Viscous Semigeostrophy

Abstract

By subtracting the viscous semigeostrophic (SG) equations from the primitive equations, a set of nonlinear perturbation equations is derived and used to study the unbalanced perturbations generated during the process of Eady wave frontogenesis and quantify the errors in the viscous SG solutions with two types (free slip and nonslip) of boundary conditions. This set of equations shows that the unbalanced perturbation is generated by a vector forcing, called the SG forcing, whose components are defined by the SG Lagrangian time derivatives of three ageostrophic components in the cross-frontal wind, along-frontal wind, and buoyancy fields, respectively. It is found that the unbalanced perturbations are generated almost totally by the wind-forcing components and the buoyancy forcing is always negligibly small. In the free-slip case, the along-frontal wind forcing is weaker than the cross-frontal one and the unbalanced perturbations are generated largely as a linear response in the form of inertial gravity waves to the forcing. In the nonslip case, the along-frontal wind-forcing component is slightly stronger than the cross-frontal forcing, but the unbalanced perturbations are generated in the form of enhanced planetary boundary layer pumping immediately ahead of the front and in the form of inertial gravity waves in the warm sector farther away from the front. In both cases, the unbalanced perturbations are much weaker than their balanced counterparts even when the fronts are fully developed.