16.3.10 Open Channel Wave Boundary Conditions

The open channel wave boundary condition allows you to simulate the propagation of waves, which is useful in the marine industry. This is an upstream boundary condition and is applied to the velocity inlet of the VOF model. The wave profile for an incident wave can be described as follows:

where $z$ is the wave height, $A$ is the wave amplitude, $\epsilon$ is the phase difference, $t$ is the time, and $k_x$ and $k_y$ are the wave numbers in the x and y directions, respectively, such that $k_x = k\cos \theta$ and $k_y = k\sin \theta$.

The wave number $k$ is defined as

where $\lambda$ is the wave length and the effective wave frequency $\omega_e$ is

$U$ is the uniform incident wave velocity and $\omega$, the wave frequency, is defined as

where $h$ is the liquid height and $g$ is the gravity magnitude.

The velocity components for the incident wave boundary condition can be described in terms of shallow waves and short gravity waves.

Shallow waves are defined as

Short gravity waves are defined as

where $u$, $v$, and $w$ are the velocity components. Note that direction specifications for the velocity components are such that $u$ is based on the flow direction specified in the wave velocity specification method, $w$ is based on the gravity direction, and $v$ is in the cross direction of the flow and gravity direction. For more information on how to use and set up this model, refer to this section in the separate User's Guide.