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 Cramér 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.