Scaling DMD modes for modeling Dynamic Induction Control wakes in various wind speeds

Dynamic Mode Decomposition (DMD) is a fully data-driven method to extract a linear system from experimental or numerical data. It has proven its suitability for modeling wind turbine wakes, particularly those generated with Dynamic Induction Control (DIC), a method to reduce the wake deficit by enhancing its mixing with the surrounding flow. In this context, DMD may be used to build computationally efficient aerodynamic models suitable for model-based wind farm control algorithms. However, these standard DMD models are only valid for the flow conditions of the training data. This paper presents a novel approach to generalize a DMD model for DIC wakes from the training wind speed to various wind speeds by scaling the DMD modes. For this purpose, we first extract the DMD modes from numerical simulations of a DIC wake at a constant, homogeneous wind speed. Then, we adapt the obtained modes to a different wind speed with a scaling law for the frequency and magnitude derived from the definition of the Strouhal number. This allows for a versatile, efficient application of the DMD model in heterogeneous wind conditions at low computational costs. For validating the presented method, we model a helix wake at 6 ms^-1 based on the DMD modes from Large Eddy Simulations (LES) at 9 ms^-1. The DMD model coincides at a high level with validation simulations, resolving even mid- to small-scale structures.