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, const bool corrected = true)

Compute corner-corrected coles wake parameter W_c .

There are two alternative functional forms for the wake parameter. Perry and Marusic (1995) used the Lewkowicz (1982) wake function, where the second ( 1/… ) term is artificially applied to ensure that the velocity defect function has zero gradient at z= :

\[ W_c[\eta, \Pi] & = & 2 \eta^2 \left( 3 - 2\eta \right) - \frac{1}{\Pi}\eta^2 \left( 1 - \eta \right) \left( 1 - 2\eta \right) \]

Note: Jones, Marusic and Perry 2001 refer to this correction as the ‘corner’ function and use an alternative correction (recommended by Prof. Coles) to the pure wall flow (instead of the wake) which is not a function of Pi, allowing reversion to the original (Coles 1956) wake parameter W :

\[ W[\eta, \Pi] & = & 2 \eta^2 \left( 3 - 2\eta \right) \]

This function implements the former by default!

This function is templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (the latter via template specialisation) of z values.

Parameters
  • eta: Nondimensional height values
  • pi_coles: The coles wake parameter Pi
  • corrected: Boolean flag, default true. If true, return Lewkowicz (1982) corrected wake function. If false, return the original uncorrected wake parameter.