The helix wake and its properties: reduced order modeling through dynamic mode decomposition

Abstract. Wind turbine wakes can be treated as a complex system of helical vortices. When this system destabilizes, the wake recovers its velocity deficit through mixing and entertainment of energy from the surrounding flow. How fast and effectively that happens depends on the inflow characteristics and can also be influenced by how the turbines are operated. Dynamic induction control techniques such as the helix affect the onset of instability and the transition from near to far wake, but the exact mechanisms are still unclear. Its potential in a wind farm context has been proved both numerically and experimentally, but a helix wake model does not exist yet. The goal of this study is to derive a data-driven model of the helix wake and characterize it. Dynamic mode decomposition of data generated with large eddy simulations is performed. We simulate the DTU 10 MW model turbine under a range of helix excitation frequencies and different inflows. We show that the helix modes are dominantly present both in laminar and turbulent flow. However, as turbulence intensity increases, they exhibit larger spatial decay and temporal amplitude. Additionally, we identify inflow modes related to the turbulence length scales of the inflow. We show that a very limited number of modes allows us to reconstruct the initial flow field accurately and that the optimum excitation frequency for the control technique depends on the turbulence intensity and on the position of the downstream turbines.