A comparative study of atmospheric and laboratory‐analogue numerical tornado‐vortex models

A detailed sensitivity study of a tornado‐vortex model developed by Howells and Smith is presented in order to draw a comparison between the results of various axisymmetric models that purport to simulate laboratory and tornadic vortices. The model incorporates a stretched finite‐difference mesh in both radial and vertical directions and this provides for an increase in resolution in the vicinity of the vortex core and lower‐boundary layer. The development of the vortex is studied for different values of two key parameters. These are the ratio of the applied tangential velocity to the mean vertical velocity (the swirl ratio) and the Reynolds' number based on the eddy diffusivity coefficient, the mean radial velocity, and the radius of the domain. Most of the simulations are for a no‐slip lower boundary, but a few free‐slip experiments are presented for comparison. These serve to highlight the importance of the radial inflow jet for the no‐slip case. Emphasis is placed in the no‐slip experiment on the relative importance of the primary meridional circulation associated directly with the applied forcing, and the secondary circulation induced by the lower‐boundary layer. For weak applied swirl (tangential) velocity (1ms⁻¹), the secondary circulation is relatively weak and the maximum tangential velocity is associated with the convergence produced by the primary circulation. Accordingly, this maximum occurs at a substantial height above the lower boundary. For moderate applied swirl velocity (4ms⁻¹), the secondary circulation is manifest as a strong radial inflow jet near the lower boundary. This jet advects rotating air close to the axis. The flow that evolves is dependent on the magnitude of the eddy turbulent diffusivity coefficient. For a relatively low diffusivity coefficient (10m²s⁻¹), a large amplitude centrifugal wave forms and breaks violently near the corner region. At higher values (20m²s⁻¹), a quasi‐steady toroidal vortex develops in the region where the stream surfaces expand, and the maximum swirl velocity is found to occur at low levels near the corner region. This breakdown feature is advected out of the domain when the diffusivity coefficient is increased to 30m²s⁻¹. When the simulations are performed using high imposed swirl velocities (10ms⁻¹), a very intense vortex forms with maximum tangential velocity exceeding 55ms⁻¹, despite the frictional losses near the ground. This is considerably stronger than the equivalent free‐slip vortex which attains a maximum tangential velocity of 44ms⁻¹. Although many of these results have been obtained in past numerical studies, a clear demonstration of the importance of the secondary circulation as compared with the primary circulation has not been forthcoming due to a wide variety of experimental configurations and external parameters.