Spatial quasilinear analysis of an isolated axisymmetric turbulent wake.

With several offshore wind farms under construction near large population centers in the U.S., guaranteeing reliability while maximizing power output remains a top priority. Specifically, turbulent wakes from upstream wind turbines can cause damage to downstream rotors and induce power losses of up to 10%. As part of a larger effort to create reduced-order models of wind-farm wake arrays, here we consider the spreading of an isolated axisymmetric wake using a novel spatial quasilinear (QL) formulation. The QL reduction is formally derived via multiple scales analysis by exploiting the slow streamwise development of the time-mean wake flow, which satisfies parabolic equations that can be marched in the streamwise direction. Reynolds stress divergences from the time-harmonic fluctuations are computed self-consistently by solving a spatial stability problem using the local radially-varying time-mean wake profile at each streamwise grid point. The model can be readily extended to incorporate azimuthally-varying perturbations and both swirl and slow-time pulsatility of the mean flow.