Turbulence Kinetic Energy Budget and Conditional Sampling of Momentum, Scalar, and Intermittency Fluxes in Thermally Stratified Wind Farms

Nicholas Hamilton, Naseem Ali, Marc Calaf, Raul Cal

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20 Scopus Citations


A description of the turbulence kinetic energy budget is investigated to understand the dynamics and turbulence energy transfer between the atmospheric boundary layer and large wind farms. The turbulence kinetic energy budget terms are a dominant factor in explaining the energy supply process in wind farms. Large eddy simulations are used to generate the thermally stratified wind turbine array boundary layer, where stable and unstable conditions are considered. The wakes represent a sink of mean kinetic energy, and turbulence transport redistributes energy in the wake region. The energy balance between the budget terms is dependent on the physical location in the wind farm. During the unstable scenario, turbulence is driven by the production, transport, and buoyancy terms. Further, the contribution of the turbulence kinetic energy budget terms is reduced with increasing atmospheric stability, especially above the shear layer, where the mechanical production is the dominant term. Pressure diffusion redistributes the turbulent energy from the streamwise direction into the other components of the normal Reynolds stresses. This distinctive feature of the changing thermal stratification is presented through the quadrant analysis. The momentum ejection and sweep frequencies are both comparable and dominant. The scalar flux shows an increase in the contribution of the negative correlation in the quadrants. The quadrant analysis is extended to account for intermittency based on the pointwise Hölder exponents. Positive correlations are dominant in the wake and in higher layers of the domain for both considered cases.

Original languageAmerican English
Pages (from-to)32-63
Number of pages32
JournalJournal of Turbulence
Issue number1
StatePublished - 2 Jan 2019

Bibliographical note

Publisher Copyright:
©, Employees of Alliance, under Contract No. DE-AC36-08GO28308 with the U.S. Dept. of Energy, have authored this work. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes. Naseem Ali, Marc Calaf and Raúl Bayoán Cal hereby waive their right to assert copyright, but not their right to be named as co-authors in the article.

NREL Publication Number

  • NREL/JA-5000-72248


  • Atmospheric turbulence
  • large Eddy simulation
  • passive scalar turbulence
  • wind energy


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