Simulations of Vortex Genesis in Stretched Shear Flow


These simulations were motivated by observations of velocity fields observed several minutes prior to tornadogenesis in Doppler on Wheels (DOW) data on May 15, 2003 and in the simulations by Lou Wicker, conducted for the NOVA TV program. In the data, an elongated area of shear appeared on the interface between the rear flank downdraft (RFD) air and the inflow air, on the cyclonic shear side of the RFD. Soon thereafter, two tornadoes appeared on this shear zone, one of which soon dissipated, while the other grew in both size and intensity. The same process happened about a half hour later, and this time, brief tornadoes appeared on the anticyclonic shear side of the RFD, and more presistent tornadoes formed on the cyclonic shear side.

Preliminary Hypothesis

Hypothesis is subject to change, as I study the 2-D turbulence problem further. The hypothesis is that intense shear along the interface between the RFD and inflow of a supercell causes turbulence generation in the flow. The stretching process and resulting deformation field that occurs under the updraft of a supercell weakens horizontal vorticity and intensifies vertical vorticity, thereby constraining the flow to a quasi-2d columnar form. Under such constraints, the turbulence cascade process is forced into a 2-D regime with energy moving upscale. Within such a regime, the vortex exists to remove intense gradients of velocity that develop, and once once they are removed and/or the stretching process ceases, the vortex weakens or dissipates.

LES Setup

The LES setup involved a domain of 2.56km x 2.56km x 1.6 km on a 128x128x80 grid. With grid cells of 20 meters on all sides. The vertical coordinate system is cartesian, and no grid stretching was used. The LES solves the filtered, Boussinesq, Navier-Stokes equations using finite, centered differencing, an Asselin-filtered, Leapfrog time-stepping scheme, and a diagnostic equation for pressure. The initial flow consisted of u, which changed linearly from +5 m/s along the left boundary to -5 m/s along the right boundary, and v, which was -5 m/s in the left half of the domain and +5 m/s in the right half of the domain. w was set to ensure nondivergence of the flow field (du/dx = -dw/dz). Boundary conditions for velocity were Dirichlet conditions on the sides, periodic in the north-south direction, no-slip at the bottom (with M-O similarity applied locally), and Neumann (zero gradient) conditions at the top. A surface heat flux of 0.3 Km/s was also used.

Simulation Results

The simulations showed that the intense shear zone at the center of the domain developed five vortices initially, and these vortices then merged sequentially, leaving a single, intense vortex about 20-30 minutes into the simulation. This single vortex intensified and had 10-m winds that reached at least 57 m/s in the latter portion of the simulation. The following animations show the evolution of the temperature and vertical velocity fields in the flow:

x-y cross-section of temperature near the surface

y-z cross-section of temperature through the center of the domain

y-z cross-section of vertical velocity

Simulations were also conducted with the surface heat flux turned off. These simulations qualitatively proceeded in about the same manner, except the vortex only reached 45 m/s. If u and v are doubled in the initial flow (10,10) with the same 0.3 Km/s surface heating, the vortex wind speeds peak at 74 m/s

Initial Thoughts and Future Work

Initially, the appearance of such a well-developed, intense vortex in the first simulation was a bit of a surprise, as I was not expecting to find anything so intense. After further thought, the initial flow setup is such that the vortex is strongly forced to develop. The initial v-shear in the flow is constrained to a north-south zone only 20 meters wide, and this gradient probably needs to be relaxed in order to be realistic, and the surface heat flux under a thunderstorm is not likely to be as large as it was in the first simulations. However, other features of the flow certainly seem to be well within the range of what might occur under the updraft region of a supercell thunderstorm. My future plans, contingent on funding for this activity, would be to further explore the parameter space in this experiment. This would include variations in the convergence (change in u) and vorticity (change in v), and to change the vertical profile of u,v. In this experiment, u and v were initially constant with height, but it would also be interesting to look at vertical changes of these variables. One limitation of the experiment is that the flow field is highly constrained by the boundary conditions-- the larger scale flow field is not allowed to evolve and interact with the changes that occur in the simulation domain.

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