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Forecasting of wind generated waves
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cgWindWaves, Methodology and references

Directional spectrum effects

In narrow fetch areas there is a dominant fetch for the wave prediction. In restricted fetch areas, there is not one dominant fetch to predict the waves. In this case three methods have been implemented in the program.

Effective fetch method
 

The effective fetch method is obtaining an equivalent fetch of the region by an weighted average process of the fetch of each sector, from this fetch the significant wave height and period are predicted, and from them the wave spectrum.

An effective fetch (Feff) obtained as a fetch weighted average, is used for the prediction of significant wave height and significant wave period. F is the fetch along a ray radiating from the point at which the waves is to be determined, and making an angle a with the main wind direction. The integral is over a wind sector area (usually from -p/2 to p/2)

Saville's Modified method

Saville's method obtains an equivalent significant wave height and period, by a weighted average process of the predicted significant wave height and period for each sector. From the significant wave height and period the wave spectrum is predicted

The significant wave height Hs obtained as weighted average, and the significant wave period as the energy weighted average. H(a) and T(a) are the wave height and wave period of waves generated along a ray radiating from the point at which the waves are determined, and making an angle a with the main wind direction. The integral is over a wind sector area (usually from -p/2 to p/2).

Seymour's method

According to this the wave spectrum is computed for each sector and the final predicted wave spectrum is obtained by adding up the energy of each sector's spectrum.

The water region is separated in small sectors at angles a around the main wind direction up to a boundary angle (usually from -p/2 to p/2). For each sector the significant wave height and significant wave period are computed, and from them a wave spectrum. The final wave spectrum is obtained from energy-average of all these spectrums, and from this spectrum the significant wave height and significant wave period are computed.

 

Significant wave height and period

The mechanics wave generation by winds acting over water surface is so complex factor that various semi-empirical methods have been developed. The wave forecasting methods are based on semi-empirical relations (SMB methods Sverdrup, Munk, and Bretschneider), which link the significant wave height Hs and significant wave period to wind speed, fetch, and water depth.

In the program are implemented three basic and commonly used methods.

In this methods F is the fetch, U the wind velocity, and g the acceleration of gravity, and D is the average depth f the region. the nondimensional terms for significant wave height H and significant wave period T are given as
Bretschneider's method

[Seymour, R.J. "Estimating Wave Generation in Restricted Fetches", J. ASME WW2, May 1977, pp251-263.]

Bretschneider's method with depth effect

[Seymour, R.J. "Estimating Wave Generation in Restricted Fetches", J. ASME WW2, May 1977, pp251-263.]

Wilson's method

[Bretschneider, Ch.I.."Topics in Ocean Engineering, Volume 1", p31-32, Gulf Publishing Company, Houston Texas, 1969.]

Wave spectra

Two commonly used wave spectral formulas are implemented in the program


References
  1. Bretschneider, C. I.."Topics in Ocean Engineering, Volume 1", Gulf Publishing Company, Houston Texas, 1969.
  2. Hallam M.G., Heaf N.J, Wootton, L.R., Dynamics of Marine Structures, Ciria Underwater Engineering Group, London 1977.
  3. Kinsman B., " Wind Waves." Prentice Hall, Inc., Englewood Cliffs, New Jersey 1965.
  4. Muga B., J., and Wilson J. F. ," Dynamic Analysis of Ocean Structures. " Plenum Press, New York, 1970
  5. Newman, J., N. " Marine Hydrodynamics", MIT Press, Cambridge, Massachusetts, 1977.
  6. Seymour, R.J. "Estimating Wave Generation in Restricted fetches", J. ASME WW2, May 1977, pp251-263.
  7. World Meteorological Organization, "Handbook on Wave Analysis and Forecasting", WMO No 446, Geneva Switzerland 1976

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