| Helicity, as a combined measure of the intensity and persistence of turbulent eddies, is likely to be the most important kinematical characteristic of tornadolike vortices. It is shown that in simplified form a maximally helical vortex can be described by two Fourier waves with the same sign of helicity and a fixed amplitude and phase relationship.; Tornadolike vortices tend to occur in the vicinity of strong horizontal gradients of velocity. It is therefore assumed that they are generated primarily by instabilities of these intense shear zones of the storm system. Consequently significant variability of the storm flow is on the scale of the embedded vortex rather than on the scale of the storm circulation itself.; The velocity field is separated into a slowly evolving part representing the storm flow, and a rapidly evolving part representing the tornadolike vortex. A three-dimensional dynamical system is then obtained from the equations of motion for the vortex flow by Fourier transformation and truncation, restricting the fast flow to the two vortex waves and a nonhelical catalyst wave. The two equilibria of the dynamical system are the phase space origin, referred to as the ground state, and a nonvanishing vortex state. The system parameters depend on the expansion coefficients of the slow background flow. The stability of the equilibria can therefore be analysed as a function of the background flow state. With a stable ground state perturbations of the fast velocity field are damped out. As the ground state loses stability in a transcritical bifurcation the vortex state simultaneously gains stability and weak vortical perturbations are intensified, approaching a steady state as long as the vortex equilibrium is maintained by the background flow.; In the simple model the most relevant changes in the background flow affecting vortex stability are changes in the horizontal shear of horizontal velocity. It is shown that for a given background updraft strength a certain minimum amount of horizontal shear is necessary to spin up an intense vortex. However, as the horizontal shear increases relative to the updraft strength, at a certain point the coherent vortex is destroyed. |
