Wave Forcing

Surface gravity waves produce a forcing on mean surface flow driving wave-induced currents and changes to the water surface elevation (e.g. wave setup and setdown). Wave forcing is a new feature in HEC-RAS 6.6. Wave forcing is caused by gradients in the wave radiation stress tensor as (Longuet-Higgins and Stewart 1962, 1964)

1)	$\begin{array}{l}\displaystyle \boldsymbol{\tau}_w = - \nabla \cdot \boldsymbol{S}\end{array}$

where

$\begin{array}{l}\boldsymbol{S} = \left[ \begin{matrix} S_{xx} & S_{xy} \\ S_{yx} & S_{yy} \end{matrix} \right]\end{array}$ : wave radiation stress tensor

The wave radiation stresses tensor represents the depth-integrated and phase-averaged excess momentum flux due to surface gravity waves.

For spectral waves, the wave radiation stress components can be approximated using linear wave theory as

2)

$\begin{array}{l}S_{xx} = \rho g \iint E(f, \theta) \left [ \dfrac{c_g}{c_p} \left ( \text{cos}^2 \theta + 1 \right ) - \frac{1}{2} \right ] d f d \theta \\ S_{xy} = S_{yx} = \rho g \iint E(f, \theta) \left ( \dfrac{c_g}{c_p} \text{sin} \theta \text{cos} \theta \right ) d f d \theta \\ S_{yy} = \rho g \iint E(f, \theta)\left [ \dfrac{c_g}{c_p} \left ( \text{sin}^2 \theta + 1 \right ) - \frac{1}{2} \right ] d f d \theta\end{array}$

in which

$\begin{array}{l}\rho\end{array}$ : water density [M/L³]
$\begin{array}{l}g\end{array}$ : gravity [L/T²]
$\begin{array}{l}E(f, \theta)\end{array}$ : wave energy density [L]
$\begin{array}{l}c_g\end{array}$ : wave group velocity [L/T]
$\begin{array}{l}c_p\end{array}$ : wave phase velocity [L/T]
$\begin{array}{l}f\end{array}$ : wave frequency [1/T]
$\begin{array}{l}\theta\end{array}$ : wave direction [-]

HEC-RAS does not compute the wave forcing since it does not have a wave model. The wave forcing is specified by the user on a grid and interpolated onto the HEC-RAS mesh.

It is noted that HEC-RAS does not have other wave-current interaction terms such as wave-enhanced bottom friction, horizontal mixing, and wave-induced mass fluxes. Therefore, HEC-RAS should not be used to simulate near-shore wave-generated currents. The wave forcing feature is intended for simulating wave generated variations in the water surface elevation.

Instructions on how to enter wave forcing data in HEC-RAS can be found here Wind Forcing.