Far-wake meandering induced by atmospheric eddies in flow past a wind turbine

Xiaojian Mao*, J. N. Sorensen

*Corresponding author for this work

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A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency omega = 0.8-2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re
Original languageEnglish
JournalJournal of Fluid Mechanics
Pages (from-to)190-209
Number of pages20
Publication statusPublished - 2018

Bibliographical note

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.


  • Nonlinear instability
  • Vortex shedding
  • Wakes


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