The Vortex Tracking Semispectral model is a computationally and conceptually streamlined formulation for simulation of hurricanes. "Vortex tracking" means that the model is cast in cylindrical coordinates that move with the vortex. "Semispectral" means that the fields vary sinusoidally in azimuth, but not in radius. In this formulation, the problem reduces to a set of linear equations for each azimuthal wavenumber, forced by the environmental flow and coupled by wave-wave interactions that account for all of the nonlinearity.
The vortex moves primarily through advection by the surrounding wind and propagation due to wavenumber one (WN1) asymmetries, called the beta gyres, forced by environmental potential vorticity (PV) gradients. In many cases nonlinearity plays a dissipative role. It prevents unphysical acceleration of the vortex in the planetary vorticity gradient. Although the tempo of vortex evolution and its speed of motion increase with increased environmental forcing, the combined effect of two PV gradients acting on the vortex simultaneously is weaker than the sum of their individual effects. In still surroundings or uniform flows on a beta plane, the energy spectrum falls off smoothly with increasing wavenumber and little energy cascades beyond WN6, where the model is generally truncated.
In anticyclonic environmental shear, the WN2 asymmetry induced by the deformation field interferes destructively with WN2 induced by wave-wave interaction so that the spectrum drops off quickly beyond WN2. In cyclonic shear, the deformation-induced and nonlinearly induced asymmetries interfere constructively, resulting in a broader spectrum. The asymmetries are cyclonically curved spirals (trailing in a cyclonic circulation) that converge substantial cyclonic angular momentum into the vortex. They have many characteristics in common with the upper-tropospheric eddies hypothesized to play a role in tropical cyclone intensity change.
In cyclonic shear, asymmetric energy cascades from WN2 and beyond to WN1, changing the beta gyres and the motion. The cascade causes the track calculation to converge more slowly with increasing spectral resolution. When energy is supplied directly to the asymmetries in the middle of the spectrum by imposed mass sources and sinks, similar cascades to WN1 cause irregular trochoidal tracks. In an alternative treatment of the problem, the beta plane calculation is carried out in fixed coordinates, and the coordinates are repositioned periodically to track the vortex rather than translated continuously. All of the vortex motion requires interpolation, that causes spurious broadening of the wave-energy spectrum and meandering of the track