Template Function es::veer_lhs

Function Documentation

template <typename T>
T es::veer_lhs(T const &ui, const double ui_g, const double phi)

Computes the left hand side of the veer relations given u(z) or v(z).

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 u values.

The veer relations are:

\[\begin{split} 2 |\mathbf{\Omega}| sin(\phi) (\overline{v}_g - \overline{v}) & = & \frac{\partial}{\partial z} \bigg( \nu\frac{\partial\overline{u}}{\partial z} - \overline{u'w'}\bigg) \\ 2 |\mathbf{\Omega}| sin(\phi) (\overline{u}_g - \overline{u}) & = & \frac{\partial}{\partial z} \bigg(\nu\frac{\partial\overline{v}}{\partial z} - \overline{v'w'}\bigg) \end{split}\]

Parameters
  • ui: Mean velocity component at a given height (m/s)
  • ui_g: Mean geostrophic velocity component outside the atmospheric boundary layer (m/s)
  • phi: Latitude (degrees)