Simulation of Artificial Turbulence by the Vortex Method

First, a simple and accurate numerical method is presented to produce velocity fluctuations that are determined by the prescribed physical quantities and qualities of turbulence such as longitudinal and lateral spectra, and integral scales. The fluctuations are obtained by solving a system of nonlinear equations that are derived from the equations of energy spectra and of root mean square of the fluctuations. This method requires as many computer memories and computations as one-dimensional case even for the three dimensional calculations. It is shown that there is a strong resemblance of the simulated velocity fluctuations and experimental data. The energy spectra of these velocity fluctuations are quite accurate with less than 0.01% relative errors to the prescribed spectra. Secondly, these solutions are used to examine the capability of the vortex methods to produce turbulent flows with the prescribed parameters. It is found that although the energy spectra by the vortex method scatter to some extent, they are distributed along the prescribed spectra. It can be said that the vortex methods are able to simulate the target turbulence fairly well. Also it is found that the solutions with the LES model increase and deviate from the target spectrum at the higher frequency regions. This may suggest the nonessentiality of the LES model for the vortex method.