A Simple Vortex Model Applied to an Idealized Rotor in Sheared Inflow

Mac Gaunaa, Niels Troldborg, Emmanuel Branlard

Research output: Contribution to journalArticlepeer-review

1 Scopus Citations


A simple analytical vortex model is presented and used to study an idealized wind turbine rotor in uniform and sheared inflow, respectively. Our model predicts that 1D momentum theory should be applied locally when modelling a non-uniformly loaded rotor in a sheared inflow. Hence the maximum local power coefficient (expressed with respect to the local, upstream velocity) of an ideal rotor is not affected by the presence of shear. We study the interaction between the wake vorticity generated by the rotor and the wind shear vorticity and find that their mutual interaction results in no net generation of axial vorticity: the wake effects and the shear effects exactly cancel each other out. This means that there are no resulting cross-shear-induced velocities and therefore also no cross-shear deflection of the wake in this model.

Original languageAmerican English
Pages (from-to)505-513
Number of pages9
JournalWind Energy Science
Issue number4
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Mac Gaunaa et al.

NREL Publication Number

  • NREL/JA-5000-86253


  • sheared inflow
  • vortex model
  • wind turbine rotors


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