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A discussion of momentum balances in the surf-zone.

A discussion of momentum balances in the surf-zone. How can a alongshore current be driven by a normally incident wave field. Equations. 1 : cross-shore momentum balance 2 : alongshore momentum balance. We can drop: -the wind stress term -the turbulent stress terms

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A discussion of momentum balances in the surf-zone.

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  1. A discussion of momentum balances in the surf-zone. How can a alongshore current be driven by a normally incident wave field.

  2. Equations • 1 : cross-shore momentum balance • 2 : alongshore momentum balance

  3. We can drop: -the wind stress term -the turbulent stress terms -we assume a steady state The alongshore balance becomes  3

  4. What about neglecting the bottom stress? • Studies showed that set-up was under predicted close to the shoreline and errors in the calculations of set-up were 3 times larger when the bottom stress is neglected than when it is included.

  5. Otherwise, studies were done and it appears that if we use the momentum equation (3) on a barred beach, the set-up location is not well predicted. And the predicted currents flow opposite to those observed.

  6. Why? • At first, the beach floor is not uniform, so the incident wave field is not uniform either. So, the bottom stress is important.

  7. Wave rollers • these are passive regions of circulating water carried by breaking waves. • Including these wave rollers causes a spatial lag between the dissipation of wave energy and the transfer of momentum to steady currents, thus shifting the alongshore current maximum shoreward.

  8. Including the wave rollers, the radiation stress is: (4) • The wave roller energy is (5) • The alongshore momentum balance becomes:(6) With the radiation stress component Syy : (7)

  9. Conclusion • We have a good prediction of the currents and set-up with a 1-D model that neglects the component Sxy but that includes the set-up gradient in the cross-shore radiation stress component Sxx, the bottom stress and the wave rollers in the radiation stress equations.

  10. References • Effect of wave rollers and bottom stress on wave setup. A. Apotsos, B.Raubenheimer…:2007. Journal of Geophysical research. Vol 112, C02003, doi:10.1029/2006JC003549 • Wave-driven setup and alongshore flows observed onshore of a submarine canyonA.Apotsos, B. Raubenheimer…:2008. Journal of Geophysical research. Vol 113, C07025,doi:10.1029/2007JC004514   • Modeling the alongshore current on barred beaches. B. G. Ruessink, J. R. Miles…:2001.Journal of geophysical research,VOL. 106,C10, p22,451-22,4 • Pressure Gradient-Dominated Nearshore Circulation on an Inlet-Adjacent Beach. F. Shi, D. M. Hanes…Journal of geophysical research, VOL. ???, XXXX, DOI:10.1029.

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