Function es::reynolds_stress_13¶
- Defined in File stress.h
Function Documentation¶
-
void
es
::
reynolds_stress_13
(Eigen::ArrayXd &r13_a, Eigen::ArrayXd &r13_b, const double beta, const Eigen::ArrayXd &eta, const double kappa, const double pi_coles, const double shear_ratio, const double zeta)¶ Compute Horizontal-Vertical Reynolds Stress R13 profile.
Gets Reynolds Stress profiles due to Type A and B eddies.
Can use either the Lewkowicz formulation for velocity deficit (per Perry and Marusic 1995) or
TODO - presently, the integrations here are sensitive to the chosen eta distribution. Refactor according to issue #38
TODO - Determine whether it will be an advantage to template this function 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 eta values.
References
[1] Perry AE and Marusic I (1995) A wall-wake model for turbulent boundary layers. Part 1. Extension of the attached eddy hypothesis J Fluid Mech vol 298 pp 361-388
Future Improvements
[1] Optional different mean profile formulations including account for the free surface
[2] Support directional variation with height; i.e. compatible with mean profile formulations using U(y)
[3] Added formulation for contribution of smaller Type C eddies
[4] For the given wall formulation, can f be calculated more efficiently? See schlichting and gersten p. 593
- Parameters
beta
: Clauser parameter \( \Beta \), representing acceleration/decelaration of the boundary layereta
: Nondimensional vertical coordinates at which you want to get stress \( R_{13} \). Values must ascend but not necessarily be monotonic.kappa
: von Karman constant.pi_coles
: Coles wake parameter \( \Pi \)shear_ratio
: Ratio between free-stream and skin friction velocities \( S = U_{inf}/U_{\tau} \)zeta
: Scaled streamwise derivative \( \zeta \) of the Coles wake parameter \( \Pi \)