Numerical models parametrise a wind turbine either as a sink of kinetic energy and source of turbulent kinetic energy, or by using an actuator disk method. There is however a third option and that involves using a linear model as described in Smith (2009). The linear model represents the boundary layer as a uniform flow, with the drag from the wind turbine being vertically distributed. The use of a linear model leads to the possibility of interesting consequences from the wind farm being derived from the analytical solution. This, however, is only possible if the results from the linear model are representative of flow through a wind farm. This work therefore aims to compare the results from the linear model to the Met Office boundary layer model BLASIUS. BLASIUS has been used extensively for examining orographic flow and flow through forest canopies. The wind farm parametrisation of Fitch et.al (2012) has been implemented in BLASIUS. Multiple simulations are carried out to examine how Froude number, Fr = u/√(g'zi), and vertically propagating gravity waves, defined by Z = Nzi/u, alter the agreement between the linear model and BLASIUS. This is quantified by looking at the difference in position of the velocity minimum, the magnitude of velocity perturbation and pressure gradient through the wind farm. Analysis will be presented to show how these flow statistics are altered by varying dynamical conditions such as velocity, inversion height and inversion strength.
The boundary layer in the linear model is represented by a one dimensional horizontal flow. There are limitations to this assumption, not only from the wind turbine drag being distributed uniformly within the boundary layer but also there is an implication to the total drag from the wind farm.