*Article* **On Modelling Wind-Farm Wake Turbulence Autospectra and Coherence from a Database**

#### **Kyle A. Schau 1, Gopal Gaonkar 2 and Vaishakh Krishnan 2,\***


Received: 30 November 2018; Accepted: 29 December 2018; Published: 30 December 2018

**Abstract:** This study addresses the feasibility of modeling wind-farm wake-turbulence autospectra and coherences from a database: flow velocity points from experimental and computational fluid dynamics (CFD) investigations. Specifically, it first applies an earlier-exercised framework to construct the autospectral models from a database and then it adopts a recently proposed framework to construct the coherence models from a database. While this proposed framework has not been tested against a database, the methodology has been completely formulated with a theoretical basis. These models of autospectrum and coherence are interpretive, and in closed form. Both frameworks basically involve the perturbation series expansion of the autospectra and coherences. The framework for modeling autospectra is tested against a demanding database of wake turbulence inside a wind farm over a complex terrain from a full-scale test. The suitability of these autospectral models for simulation through white-noise driven filters is also demonstrated. Finally, coherence models are generated for assumed values of the perturbation series constants, and these coherence models are used to demonstrate how the coherence models of homogeneous isotropic turbulence deviate from the coherence models of non-homogeneous non-isotropic turbulence such as wind-farm wake turbulence. This feasibility of extracting both the one-point statistics of autospectral models and the two-point statistics of coherence models from a database represents a research avenue that is new and promising in the treatment of wind-farm wake turbulence. This paper also demonstrates the feasibility of fruitfully exploiting the wake treatment methods developed in other fields.

**Keywords:** turbulence; statistical modelling
