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The nonlinear evolution and breaking of vorticity waves may be viewed as an isentropic process, as long as the spatial scales are large enough to prevent irreversible potential temperature mixing and the temporal scales are small enough to be essentially uninfluenced by diabatic processes. These conditions are largely satisfied in synoptic-scale wave-breaking events, associated with baroclinic or barotropic eddies. Under these circumstances the wave breaking events will advect potential vorticity on isentropic surfaces. Due to the complicated behavior of the eddies, this advection will have a rather erratic character. This type of advection is called chaotic advection.
We can now imagine a situation where both homogenization and stripping occur. Suppose the potential vorticity front that is formed by the stripping processes exhibits large-scale aperiodic meridional motion. The source of the aperiodic motion might be orography, inducing a meridional background field, but again the source is immaterial. Any potential vorticity structure outside the potential vorticity front will get deformed and lengthened by the shear dispersion induced by the velocity maximum associated with the potential vorticity front. In this process it becomes effectively a passive tracer. Now the large-scale aperiodic velocity field will lead to chaotic mixing of the small-scale potential vorticity structures. This will eventually lead to a homogenized field, at least in a coarse-grained sense, on the timescale of the motion of the potential vorticity front. The global picture now is that of a more or less piecewise uniform potential vorticity field.
These processes, which lead to a piecewise uniform potential vorticity field, have mostly been described in an adiabatic context. The influence of diabatic processes on stripping has not been studied very much. Mariotti et al. (1994) study the effect of viscosity and hyperviscosity on the structure of a vortex that decayed under the influence of an external strain field. They observe that viscosity leads to the constant production of weak vorticity skirts at the outer side of the vortex. These skirts get stripped away, leaving a smaller bare vortex. Eventually this process destroys the vortex. Furthermore, the introduction of viscosity limits the maximum vorticity gradient. The stripping processes cannot increase the vorticity gradients indefinitely, because diffusive processes, which become stronger with higher gradients, tend to smooth gradients. A simple argument that dissipative processes generally tend to decrease the potential vorticity gradient can be found in the appendix. So the average vorticity gradient at the boundary of the vortex is determined by a dynamical equilibrium between stripping and dissipation. Note that in general this dynamical equilibrium may not be as clear-cut as in the case studied by Mariotti et al. (1994), or by Haynes and Ward (1993). The latter observed how gradient enhancing processes, which they model as a simple strain, can come to an equilibrium with realistic dissipative processes. In the case of the polar vortex or the tropopause, the advective processes are generally chaotic, leading to a stripping that is intermittent, spatially as well as temporally.
This model was implemented numerically as a spectral model on the sphere. In the experiments shown, a T85 spectral truncation was used. The high truncation was chosen in order to resolve small-scale eddies explicitly. Time stepping was done with a leapfrog scheme, using a time step of 15 min. A small fourth-order hyperviscosity was included, in order to improve the inertial range of the energy spectrum. The hyperviscosity damps the wavenumber 85 spherical harmonics on a timescale of 40 h. Numerical stability for this term was obtained by implementing it semi-implicitly. Mariotti et al. (1994) warned that hyperviscosity could lead to spurious effects in the process of vortex stripping. This warning does not apply to our case; in the present model, the effects of hyperviscosity on the stripping processes are swamped by the effects of the much stronger thermal damping. 2b1af7f3a8