A 3D Parabolic equation method for wind turbine noise propagation in moving inhomogeneous atmosphere

With the increasing deployment of large wind turbines, concerns continue to be raised regarding their potential adverse effects on the environment. This includes the noise they generate. This paper focuses on the development of a parabolic equation (PE) method for the prediction of long-range wind turbine noise propagation. Since wind turbine noise necessarily propagates in a moving inhomogeneous atmosphere, the propagation of the noise at a given frequency is controlled by the Helmholtz equation for an inhomogeneous atmosphere with wind. In the present paper, a new formulation of the Helmholtz equation for a moving inhomogeneous medium in cylindrical coordinates is derived. Based on this new formulation, a new parabolic equation is constructed. This result extends the homogeneous form of the Parabolic Equation (PE) method for atmospheric sound propagation problems. The resulting equation is solved by the Crank-Nicholson finite difference method. The new PE formulation can be used to simulate three-dimensional sound propagation with an arbitrary wind, including a cross wind, above a flat ground surface with both rigid and impedance boundary conditions. Numerical results are presented and compared with some simple benchmark analytical and numerical results to validate the methodology. Examples of more realistic propagation problems are included that demonstrate the importance of including the wind. Planned extensions of the new methodology, including sound propagation over irregular terrain, are discussed.