Inhomogeneous Turbulence Modelling in Rotor Wakes and in the Atmospheric Boundary Layer

The turbulence model recommended by the IEC 61400-1 standard is based on the assumptions of homogeneous, isotropic, and incompressible turbulence with an additional vortex stretching correction assuming a uniform constant shear rate. In industry practice, inhomogeneous turbulence in rotor wakes and in the Atmospheric Boundary Layer is modelled by applying a spatial scaling function to the homogeneous turbulence model, a process that violates the incompressibility assumption of the von Káarmáan spectral tensor. The aim of this work is to generalise the von Káarmáan spectral tensor to a differential form applicable to basis functions that are suitable for certain boundary conditions and coordinate systems. Two specific examples of such solenoidal turbulence models are presented, for rotor wakes and for the Atmospheric Boundary Layer. First results from aero-servo-elastic loads computations indicate that preserving the solenoidal structure of the turbulence leads to an increase in certain fatigue loads over those predicted by a scaled homogeneous turbulence model.