CMS-Flow:Roller: Difference between revisions
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== Surface Roller == | == Surface Roller == | ||
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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>|1}} | |||
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 | 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}} | |||
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>|3}} | |||
where <math>a = (\cos{\theta}, \sin{\theta} )</math>. | where <math>a = (\cos{\theta}, \sin{\theta} )</math>. | ||
Revision as of 15:25, 22 October 2012
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 .
References
- Ruessink, B.G., Miles, J.R., Feddersen, F., Guza, R.T. and Elgar, S., 2001. Modeling the alongshore current on barred beaches. Journal of Geophysical Research, 106(C10): 22451-22464.
- Stive, M.J.F. and De Vriend, H.J., 1994. Shear stresses and mean flow in shoaling and breaking waves. ASCE, New York, pp. 594-608.