ON NONLINEAR SYMMETRICAL STABILITY AND THE NONLINEAR SATURATION OF SYMMETRICAL INSTABILITY

A nonlinear symmetric stability theorem is derived in the context of t he f-plane Boussinesq equations, recovering an earlier result of Xu wi thin a more general framework. The theorem applies to symmetric distur bances to a baroclinic basic flow, the disturbances having arbitrary s tructure and magnitude. The criteria for nonlinear stability are virtu ally identical to those for linear stability. As in Xu, the nonlinear stability theorem can be used to obtain rigorous upper bounds on the s aturation amplitude of symmetric instabilities. In a simple example, t he bounds are found to compare favorably with heuristic parcel-based e stimates in both the hydrostatic and non-hydrostatic limits.