Wake Modelling Based on the Stokes Stream Function and the Toroidal-Poloidal Decomposition

The Stokes stream function and its generalisation, the Toroidal-Poloidal decomposition, are well-suited for the derivation of axisymmetric engineering wake models, as they are solenoidal and fulfil conservation of mass of an incompressible fluid by construction. The presented model consists of a time-independent contribution based on Laguerre basis functions with a simple parametrisation that is well-suited for the diffusion-dominated far wake. A time-dependent part can be added based on a poloidal component that can model either helical or toroidal vortex structures, and its parametrisation can be closed towards the total thrust force on the rotor. Despite requiring an external solver, the presented model shows potential as a drop-in replacement for the Ainslie wake model that is widely used in the Wind Energy industry as part of the Dynamic Wake Meandering model.