  Motivated by the need for compact descriptions of the evolution of
non-classical wakes behind yawed wind turbines, we develop an analytical model
to predict the shape of curled wakes. Interest in such modelling arises due to
the potential of wake steering as a strategy for mitigating power reduction and
unsteady loading of downstream turbines in wind farms. We first estimate the
distribution of the shed vorticity at the wake edge due to both yaw offset and
rotating blades. By considering the wake edge as an ideally thin vortex sheet,
we describe its evolution in time moving with the flow. Vortex sheet equations
are solved using a power series expansion method, and an approximate solution
for the wake shape is obtained. The vortex sheet time evolution is then mapped
into a spatial evolution by using a convection velocity. Apart from the wake
shape, the lateral deflection of the wake including ground effects is modelled.
Our results show that there exists a universal solution for the shape of curled
wakes if suitable dimensionless variables are employed. For the case of
turbulent boundary layer inflow, the decay of vortex sheet circulation due to
turbulent diffusion is included. Finally, we modify the Gaussian wake model by
incorporating the predicted shape and deflection of the curled wake, so that we
can calculate the wake profiles behind yawed turbines. Model predictions are
validated against large-eddy simulations and laboratory experiments for
turbines with various operating conditions.
