New 2D Spectral Framework Reveals Wake Turbulence Structure

Researchers from the Western Norway University of Applied Sciences and Helmholtz-Zentrum Hereon have developed a two-dimensional spectral framework to characterize the anisotropic turbulence within wind-turbine wakes. The study, currently under review for the journal Wind Energy Science, addresses a limitation in common analytical methods that collapse the underlying wavevector structure of turbulence. By retaining directional information and its variation across scales, the proposed model offers a more precise description of how turbulent energy is organized in the wake of wind turbines.

The central challenge in wake analysis is that one-dimensional spectra, widely used to compare measured and simulated turbulence, cannot fully describe the geometry of anisotropic energy organization. The authors propose a bidirectional, scale-dependent tensorial remapping of the planar wavenumber domain to overcome this. This approach allows for the representation of strong anisotropy observed at energy-containing scales and its gradual relaxation toward smaller-scale isotropic behavior.

The model utilizes two directional stretch factors that depend jointly on the streamwise and spanwise wavenumbers to describe the transition from anisotropic to isotropic behavior. A corresponding Jacobian correction ensures that the spectral density is transformed consistently under wavevector mapping. The scale dependence of the directional stretching is represented by using constrained Bernstein polynomial surfaces.

The model incorporates a cumulative softplus parameterization. This parameterization guarantees boundedness, smoothness, and monotonic decay throughout the fitting procedure. Parameters are estimated using a staged, coarse-to-fine constrained optimization of the planar spectra of the streamwise and wall-normal velocity components. Additional constraints, including component-energy limits and surface-smoothness regularization, are included to ensure the resulting model remains physically plausible.

The framework was applied independently to large-eddy simulation datasets representing wind-turbine wakes under high- and low-turbulence inflow conditions. A reference atmospheric boundary-layer case without turbine forcing was also included to provide a baseline for comparison. The results demonstrate that incoming turbulence intensity modifies the directional, scale-dependent organization of turbulent energy, with strong directional differences at larger scales weakening toward smaller scales.

Validation of the fitted spectra involved generating statistically equivalent synthetic turbulent fields to evaluate spatial correlations, integral scales, structure functions, and one-point statistics.

The study highlights that common methods can hide the directional structure of turbulence in wind-turbine wakes, which changes with scale. By using large-scale computer simulations, the team developed an approach that tracks how turbulence changes across directions and sizes. The findings indicate that the method can improve wake analysis and modeling by providing an interpretable and computationally practical way to quantify these complex interactions.

The framework provides a new tool for understanding how turbine wakes and inflow turbulence intensity interact to shape the turbulent energy landscape.

Subject of Research: Two-dimensional spectral analysis of anisotropic turbulence in wind-turbine wakes

Article Title: Scale-Dependent Anisotropy in Two-Dimensional Spectra of Wind-Turbine Wake Boundary-Layer Flows

Article References: Sadeghi, S., Ghane, M., & Ali, N. (2026). Scale-Dependent Anisotropy in Two-Dimensional Spectra of Wind-Turbine Wake Boundary-Layer Flows. https://doi.org/10.5194/wes-2026-152

Image Credits: AI Generated

DOI: 10.5194/wes-2026-152

Keywords: wind energy, turbulence, spectral analysis, wind turbine wakes, large-eddy simulation, anisotropy, boundary layer, computational fluid dynamics, Scale-Dependent, Two-Dimensional, Spectra, Wind-Turbine