Numerical simulation of wake vortex detection using a radio acoustic sounding system

A parallel, two-dimensional Euler, one-dimensional Maxwell code is developed to numerically simulate wake vortex detection using a radio acoustic sounding system. The code is written in Fortran 90 with the message passing interface for parallel implementation. The main difficulty with a time-accurate simulation is the number of samples required to resolve the Doppler shift in the scattered electromagnetic signal. Even for a one-dimensional simulation with typical scatterer size, the CPU time required to run the code is far beyond currently available computer resources. Two alternatives that overcome this problem are described. In the first, the code is run for a fictitious speed of light. Second, the governing differential equations are recast in order to remove the carrier frequency and solve only for the frequency shift using an implicit scheme with large time steps. The numerical stability characteristics of the resulting discretized equation with complex coefficients are shown. The code is run for both the approaches with Taylor and Oseen vortex velocity profiles. Finally, the Abel transform is applied to the outputs of both explicit and implicit schemes, and the wake vortex velocity field is retrieved with very good accuracy.