Simulation of nonhomogeneous fluctuating wind speed field in two-spatial dimensions via an evolutionary wavenumber-frequency joint power spectrum

Spectral representation method (SRM) is a widely-used tool for the simulation of fluctuating wind speed fields. To circumvent the computational challenges of the Cholesky decomposition involved in the spectral representation method, a wavenumber-frequency joint power spectrum based SRM was proposed recently. The method can be used for the efficient simulation of homogeneous and nonhomogeneous wind fields in one spatial dimension. In this paper, the wavenumber-frequency joint power spectrum based SRM is extended to simulate nonhomogeneous wind fields in two spatial dimensions. To this end, a closed-form evolutionary wavenumber-frequency joint spectrum is first derived, and integrated readily with the updated spectral representation method. To enhance the computational efficiency with respect to the threefold summation over the one-dimensional frequency domain and the two-dimensional wavenumber domain, two uneven-discretization strategies are proposed. They are associated with a tensor-product scheme and an acceptance-rejection criterion. For illustrative purposes, a numerical example of simulating a fluctuating wind speed field in two spatial dimensions associated with the rotating blades of a 5-MW wind turbine is considered. It is shown that both the proposed methods have good accuracy and efficiency, and the rejection-acceptance criterion based uneven discretization method is preferred to practical applications.