Numerical Modeling of Atmospheric Vortices

Sudeep Dasari, David Murphy, Colin Redman
Los Alamos High School
New Mexico Supercomputing Challenge, 2013


   title={Numerical Modeling of Atmospheric Vortices},

   author={Dasari, Sudeep and Murphy, David and Redman, Colin},



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Tornadoes such as Joplin, Mo (2011), Spencer, SD (1998), and Dallas, Texas (1957) induce extremely high wind velocities that devastate structures and lift off large objects in their path. Typically, a tornado takes up to an hour to materialize in the form of a narrow axisymmetric vortex and sustains that structure for 10-20 minutes after which the tornado dies down. Near real time simulation of tornado core flow could significantly improve accuracy of Dopplar on Wheels (DOW) radar measurements which in turn would enable more effective warning and evacuation strategies. Presently very simplified vortex models, such as the algebraic Wood-White model and the modified Rankine model, are being used to simulate radar signatures necessary to reconstruct real world tornadoes with limited success. Other alternatives, such as commercial CFD tools, may provide more accurate results but take long periods of time to compute. We believe that mathematical frameworks developed by Drs. Sullivan and Kuo provide an optimum approach to bridge this gap because they are based on fluid-mechanically and thermodynamically self-consistent physics to model atmospheric vortices with sufficient accuracy. Implementation of their models required the solving of multiple and coupled nonlinear boundary value fourth order ordinary differential equations (ODEs) using a fourth-order iterative Runge-Kutta method (RK4). Because certain sub-models consisted of differentialintegrals, we had to effectively implement Euler integration and Newton’s finite differentiation algorithms, as well as create a coordinate transformation system to easily move data from polar coordinates used for tornado computations and the Cartesian system for all other operations. Combining all these methods and building on the works of scientists such as Kuo and Sullivan we created a series of programs that accurately simulated vortex flow, examined dynamics of particles with pre-defined mass and drag coefficients when subjected to said vortex, and exported the data for use in visualization with Paraview, a multi-platform scientific visualization software being developed by Sandia and Los Alamos National Labs. Furthermore, we validated the models by comparing their predictions for wind velocities with measurements reported in the literature for the 1998-Spencer and 1957-Dallas tornadoes. A surprisingly good comparison was observed: which established validity of our implementation of Kuo’s models. Once these computer models were built, it was quickly realized that they can be very time consuming by modern standards and at the same time had tremendous potential for successful optimization work. As such, we conducted a series of optimization tasks designed to speed up the execution of our code including: (a) utilized the graphics processing unit (GPU) to accelerate the RK4 and Euler integration computations, and finally the entire Kuo model, (b) used CPU multi-threading feature to accelerate the particle tracing algorithm; and (c) implemented a new data format system to reduce the size of the exported file and decrease write times. The optimization tasks proved to be extraordinarily effective, as the GPU optimization dropped computing time by over 2000 percent, CPU multithreading proved to shave significant amounts of time from the particle computing, and the data formats allowed the writing of large volumes of data while taking smaller amounts of disk space as well as write time.
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