Baroclinic Eady wave and fronts. Part III: Unbalanced dynamics - Departures from viscous semigeostrophy

By subtracting the viscous semigeostrophic (SG) equations from the primitiv e 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 equa tions shows that the unbalanced perturbation is generated by a Vector forci ng, called the SG forcing, whose components are defined by the SG Lagrangia n time derivatives of three ageostrophic components in the cross-frontal wi nd, along-frontal wind and buoyancy fields, respectively. It is found that the unbalanced perturbations are generated almost totally by the wind-forci ng components and the buoyancy forcing is always negligibly small. In the f ree-slip case, the along-frontal wind forcing is weaker than the cross-fron tal one and the unbalanced perturbations are generated largely as a linear response in the form of inertial gravity waves to die forcing. In the nonsl ip 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 f arther away from the front. In both cases, the unbalanced perturbations are much weaker than their balanced counterparts even when the fronts are full y developed.