Simulation of higher-order stochastic processes by spectral representation

The Spectral Representation Method is generalized for simulation of asymmetrically nonlinear (skewed higher order) stochastic processes. This is achieved by deriving new orthogonal increments for the spectral process in the Cramer spectral representation that include wave interactions and satisfy third-order orthogonality properties. These orthogonal increments are derived by introducing two new quantities the pure power spectrum and the partial bicoherence that decouple the contributions of single waves and wave interactions in the Fourier-type expansion of a stochastic process. The further extension to fourth and higher-order processes is discussed. Several mathematical examples demonstrate the capabilities of the proposed methodology to generate general third-order stochastic processes. The method is then applied to the generation of turbulent wind velocities characterized from Large Eddy Simulations of the atmospheric boundary layer.