CMS-Flow:Roller

Surface Roller

As the wave transitions from nonbreaking to fully breaking, part of the wave energy is transformed into momentum which goes an aerated region of water known as the surface roller. The surface roller has the effect of storing energy from the breaker and releasing it closer to shore and helps account for the shift towards the shore in peak alongshore current with respect to the breaker line.

Under the assumption that the surface moves in the mean wave direction $\theta$, the evolution and dissipation of the surface roller energy is given by an energy balance equation (Stive and De Vriend 1994, Ruessink 2001)

${\frac {\partial (2E_{sr}c_{j})}{\partial x_{j}}}=-D_{sr}+f_{e}D_{br}$

(1)

where $E_{sr}$ is the roller energy density, $c$ is the roller propogation speed, $D_{sr}$ is the roller dissipation, $D_{br}$ is the wave breaking dissipation (from wave model), and $f_{e}$ is an efficiency factor. The roller dissipation is approximated as

$D_{sr}={\frac {2gE_{sr}\beta _{D}}{c}}$

(2)

The roller contribution to the wave radiation stresses is given by

$R_{ij}=2E_{sr}a_{i}a_{j}$

(3)

where $a=(\cos {\theta },\sin {\theta })$.

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