WAVE HEIGHT DISTRIBUTION IN CONSTANT AND FINITE DEPTHS

Sofia Caires, Marcel R.A. Van Gent

Abstract


Several alternatives to the Rayleigh distribution have been proposed for describing individual wave heights in regions where depth-induced wave breaking occurs. The most widely used of these is the so-called Battjes and Groenendijk distribution. This distribution has been derived and validated in a context of a shallow water foreshore waves propagating over a gently sloping shallow region towards the shore. Its validity for waves propagating in regions with
shallow flat bottoms is investigated here. It is concluded that the distribution on average underestimates (outside its range of validity) high wave height measurements in shallow flat bottoms by as much as 15%.

Keywords


Wave height distribution; flat bottoms; depth limited; flume data; field data; waves; shallow water

References


Battjes, J.A., and H.W. Groenendijk. 2000. Wave height distributions on shallow foreshores, Coastal Engineering, 40, 61-182.http://dx.doi.org/10.1016/S0378-3839(00)00007-7

Bottema, M. 2007. Measured wind-wave climatology Lake IJssel (NL). Main results for the period 1997-2006, Report RWS RIZA 2007.020, July 2007.

Bottema, M., and G.P. van Vledder. 2009. A ten-year data set for fetch- and depth-limited wave growth, Coastal Engineering, 56, doi:10.1016/j.coastaleng.2009.01.012.http://dx.doi.org/10.1016/j.coastaleng.2009.01.012

Goda, Y. 1979. A review on statistical interpretation of wave data, In: Report of the Port and Harbour Research Institute, Japan, 18, 5–32.

Goda, Y. 1985. Random seas and design of maritime structures, University of Tokyo Press.

Holthuijsen, L.H. 2007. Waves in oceanic and coastal waters, Cambridge University Press.http://dx.doi.org/10.1017/CBO9780511618536

Janssen, P. A. E M. 2009. On some consequences of the canonical transformation in the Hamiltonian theory of water waves, J. Fluid Mech., 637, 1–44.http://dx.doi.org/10.1017/S0022112009008131

Janssen, P. A. E. M. and J.-R. Bidlot. 2009. On the extension of the freak wave warning system and its veri¿cation, Technical Report 588, European Centre for Medium-rangeWeather Forecasting.

Longuet-Higgins, M.S. 1952. On the statistical distribution of the heights of sea waves, J. Mar. Research, 11, 385-398.

Rattanapitikon, W. 2010. Verification of conversion formulas for computing representative wave heights, Ocean Engineering, 37, 1554-1563.http://dx.doi.org/10.1016/j.oceaneng.2010.09.013

Van der Westhuysen, A.J. 2010. Modelling of depth-induced wave breaking under finite-depth wave growth conditions, J. Geophys. Res., 115, C01008, doi:10.1029/2009JC005433.http://dx.doi.org/10.1029/2009JC005433


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.