Airwake-downwash turbulence is nonhomogeneous and rapidly distorting, impacting on pilot workload and such critical aspects of helicopter shipboard operations. It requires both the one-point statistics of auto spectrum and the two-point statistics of coherence for a relatively complete description. While major strides have been made in generating databases of flow velocity points through computational fluid dynamics (CFD) and experimental investigations, in numerically computing auto spectra and coherences and in developing a framework for extracting auto spectral models from a database, relatively little is known about such a development for coherence models. Accordingly, this study presents a framework for extracting coherence models from a database using a perturbation series expansion of coherence; therein, the basis function or the first term on the right hand side of the series is represented by the corresponding coherence for HIT: homeogeneous isotropic turbulence for which the frozen turbulence hypothesis is applicable. The perturbation series coefficients are evaluated by satisfying the theoretical constraints and fitting a curve in a least squares sense on a set of numerically generated coherence points in the low-frequency bandwidth (0≤ω≤10 rad/s). These models are interpretive and in closed form. Compared to voluminous, numerically generated points, they bring better understanding and complement the experimental and CFD investigations as surrogate models. As for the basis functions, the literature on coherence for HIT is scattered and piecemeal, and the expressions for coherences vary from one study to the other. Therefore, this work presents a unified account of these coherences for all three velocity components from first principles. Although, the framework has not been tested against a database, it is formulated with a mathematical basis of perturbation theory. Finally, for the assumed values of perturbation series constants, this work describes how coherences of airwake-downwash turbulence and such flow-fields that weakly deviate from HIT compare to coherences of HIT.

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.