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 “diabatic 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 pola...