Monte Carlo turbulence simulation using rational approximations to von Karman spectra
Abstract
Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp 5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left halfplane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the 2 power is closest to the 5/3 power, the rational approximation should roll off as the 2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.
 Publication:

AIAA Journal
 Pub Date:
 January 1986
 DOI:
 10.2514/3.9223
 Bibcode:
 1986AIAAJ..24...62C
 Keywords:

 Approximation;
 Computational Fluid Dynamics;
 Monte Carlo Method;
 Rational Functions;
 Turbulent Flow;
 Von Karman Equation;
 Coefficients;
 Differential Equations;
 Transfer Functions;
 Fluid Mechanics and Heat Transfer