Template Function es::power_law_speed

Function Documentation

template <typename T, typename Talf>
T es::power_law_speed(T const &z, const double u_ref, const double z_ref, Talf const &alpha)

Compute speed profile according to the power law.

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of z values (to obtain shear profile u/dz) and/or alpha values (to obtain variational jacobean for fitting parameter alpha).

Power law speed is computed as:

\[ \frac{\overline{U}}{\overline{U}_{ref}} = \left(\frac{z}{z_{ref}}\right)^{\alpha} \]

Parameters
  • z: Height(s) in m at which you want to get speed.
  • u_ref: Reference speed in m/s
  • z_ref: Reference height in m
  • alpha: Power law exponent. Must be of same type as input z (allows autodifferentiation).