CMS-Flow:Roller: Difference between revisions
(Created page with big __NOTOC__ == Surface Roller == As the wave transitions from nonbreaking to fully breaking, part of the wave energy is transformed into momentum which goes an aerated regio...) |
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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. | 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 math \theta /math, the evolution and dissipation of the surface roller energy is given by an energy balance equation (Stive and De Vriend 1994, Ruessink 2001) | Under the assumption that the surface moves in the mean wave direction <math> \theta </math>, the evolution and dissipation of the surface roller energy is given by an energy balance equation (Stive and De Vriend 1994, Ruessink 2001) | ||
{{Equation|math \frac{\partial 2 E_{sr} c_j }{\partial x_j } = -D_{sr} + f_e D_{br} /math|2=1}} | {{Equation|<math> \frac{\partial 2 E_{sr} c_j }{\partial x_j } = -D_{sr} + f_e D_{br} </math>|2=1}} | ||
where | where <math>E_{sr}</math> is the roller energy density, <math>c</math> is the roller propogation speed, <math>D_{sr}</math> is the roller dissipation, <math>D_{br}</math> is the wave breaking dissipation (from wave model), and <math>f_{e}</math> is an efficiency factor. The roller dissipation is approximated as | ||
{{Equation|math D_{sr} = \frac{2 g E_{sr} \beta_D }{c} /math|2=2}} | {{Equation|<math> D_{sr} = \frac{2 g E_{sr} \beta_D }{c} </math>|2=2}} | ||
The roller contribution to the wave radiation stresses is given by | The roller contribution to the wave radiation stresses is given by | ||
{{Equation|math R_{ij} = 2 E_{sr} a_i a_j /math|2=3}} | {{Equation|<math> R_{ij} = 2 E_{sr} a_i a_j </math>|2=3}} | ||
where | where <math>a = (\cos{\theta}, \sin{\theta} )</math>. | ||
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[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 15:30, 22 October 2010
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 , the evolution and dissipation of the surface roller energy is given by an energy balance equation (Stive and De Vriend 1994, Ruessink 2001)
| (1) |
where is the roller energy density, is the roller propogation speed, is the roller dissipation, is the wave breaking dissipation (from wave model), and is an efficiency factor. The roller dissipation is approximated as
| (2) |
The roller contribution to the wave radiation stresses is given by
| (3) |
where .
