Revisiting vacillations in shallow-water models of the stratosphere using potential-vorticity-based numerical algorithms

Polar vortex vacillations are investigated using long-term simulations of potential-vorticity (PV)-based shallow-water (SW) models for the stratosphere. In the models examined, mechanical forcing is applied through a time-independent topography mimicking tropospheric excitation of the stratosphere. Thermal forcing is applied through a linear relaxation of the mass field to a time-independent equilibrium state mimicking the radiative relaxation taking place in the stratosphere. The SW equations in the PV, velocity divergence, and acceleration divergence representation are solved for a range of resolutions using the "dia-batic contour-advective semi-Lagrangian" (DCASL) algorithm and a standard pure semi-Lagrangian (SL) algorithm. Using very different numerical algorithms enables the determination of the degree of numerical sensitivity and the properties of the vacillations with much greater accuracy than in previous related studies. The focus here is on the Lagrangian or material evolution of the polar vortex. The authors examine quasi-Lagrangian diagnostics based on equivalent latitude, the mass enclosed by PV contours, and the terms involved in its time evolution. The PV field forms the basis for calculating quasi-Lagrangian diagnostics. Variations in the mass enclosed by a PV contour are associated with nonconservative processes such as diabatic heating, friction, and irreversible small-scale mixing. Generally, the mass of the polar vortex increases under the action of diabatic mass fluxes, whereas it decreases under the action of dissipative mass fluxes. The results herein differ from previous results reported at T42 resolution by Rong and Waugh in which a spectral transform algorithm is used to solve the SW equations in a vorticity-divergence-mass representation, and in which dissipation is provided by explicitly damping vorticity using hyperdiffusion. Except for the first large-amplitude oscillation, there is little sign of a clear, systematic phase shift between the dissipative and diabatic mass fluxes across the edge of the polar vortex, as proposed by Rong and Waugh as the main mechanism responsible for the vacillations. Concomitant with the absence of a phase shift, the vacillations tend to decay and occur intermittently. Rather than a phase shift, inherent fluctuations in both the diabatic and mass fluxes across the edge of the polar vortex appear to be responsible for the vacillations.