CMS-Wave:Wave Radiation Stresses: Difference between revisions
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(Created page with "=Wave Radiation Stresses= The wave radiation stresses <math>(S_{ij})</math> are calculated using linear wave theory as (Longuet-Higgins and Stewart 1961; Dean and Dalrymple 1...") |
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:<math>\theta</math> = the wave direction [rad] | :<math>\theta</math> = the wave direction [rad] | ||
:<math> | :<math>E_w</math> = wave energy = <math>1/16\ \rho g H_s^2</math> [N/m] | ||
:<math>H_s</math> = significant wave height [m] | :<math>H_s</math> = significant wave height [m] | ||
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&0\ for\ i \neq j | &0\ for\ i \neq j | ||
\end{align}\right.</math> | \end{align}\right.</math> | ||
| Line 36: | Line 30: | ||
:<math>c_g</math> = wave group velocity [m/s] | :<math>c_g</math> = wave group velocity [m/s] | ||
:<math>c</math> = wave | :<math>c</math> = wave celerity [m/s] | ||
:<math>k</math> = wave number [rad/s] | :<math>k</math> = wave number [rad/s] | ||
The wave radiation stresses and their gradients are computed within the wave model and interpolated in space and time in the flow model. | The wave radiation stresses and their gradients are computed within the wave model and interpolated in space and time in the flow model. | ||
=References= | |||
*Dean, R. G., and R. A. Dalrymple. 1984. Water wave mechanics for engineers and scientists. Englewood Cliffs, NJ: Prentice-Hall. | |||
*Longuet-Higgins, M. S., and R. W. Stewart. 1961. The changes in amplitude of short gravity waves on steady non-uniform currents. Journal of Fluid Mechanics 10(4):529–549. | |||
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[[category:CMS-Wave]] | |||
Latest revision as of 16:09, 23 January 2023
Wave Radiation Stresses
The wave radiation stresses are calculated using linear wave theory as (Longuet-Higgins and Stewart 1961; Dean and Dalrymple 1984)
| (1) |
![{\displaystyle S_{ij}=\int \int E_{w}(f,\theta )\left[n_{g}\omega _{i}\omega _{j}+\delta _{ij}\left(n_{g}-{\frac {1}{2}}\right)\right]dfd\theta }](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/4722f26e547f5e44429182eae50673704c5325ed)
where:
- f = the wave frequency [1/s]
- = the wave direction [rad]
- = wave energy = [N/m]
- = significant wave height [m]
- = wave unit vector = [-]
![{\displaystyle n_{g}={\frac {c_{g}}{c}}={\frac {1}{2}}\left(1+{\frac {2kh}{sinh\ 2kn}}\right)[-]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/09055d77e38b08369697d50bbaabceadb3edd316)
- = wave group velocity [m/s]
- = wave celerity [m/s]
- = wave number [rad/s]
The wave radiation stresses and their gradients are computed within the wave model and interpolated in space and time in the flow model.
References
- Dean, R. G., and R. A. Dalrymple. 1984. Water wave mechanics for engineers and scientists. Englewood Cliffs, NJ: Prentice-Hall.
- Longuet-Higgins, M. S., and R. W. Stewart. 1961. The changes in amplitude of short gravity waves on steady non-uniform currents. Journal of Fluid Mechanics 10(4):529–549.