Template Function es::coles_wake

Function Documentation

template <typename T_z, typename T_param>
T_z es::coles_wake(T_z const &eta, T_param const &pi_coles)

Compute coles wake parameter.

Used by Perry and Marusic 1995.

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.

\[\begin{split} W_c[\eta, \Pi_j] & = & 2 \eta^2 \left( 3 - 2\eta \right) - \frac{1}{3\Pi_j}\eta^3 \\ \eta & = & \frac{z+z_0}{\delta + z_0} \end{split}\]

Translated from MATLAB: 

function wc = colesWake(eta, Pi)
    wc = 2*eta.^2.*(3-2*eta) - (1/Pi).*eta.^2.*(1-eta).*(1-2*eta);
end

Parameters
  • eta: Nondimensional height values
  • pi_coles: The coles wake parameter Pi