REVISITING THE JONSWAP BOTTOM FRICTION FORMULATION

Gerbrant van Vledder, Marcel Zijlema, Leo Holthuijsen

Abstract


The derivation of the JONSWAP bottom friction for wind-driven seas is revisited. This is motivated by the fact that
in the literature two different values for the corresponding coefficient are recommended, one value applicable for
swell conditions and a significantly higher value for wind-driven sea conditions. The value applicable for winddriven
seas was originally determined by Bouws and Komen (1983) who studied the source term balance of a
remarkably stationary storm in shallow water. We used a more accurate interpretation of these observations by
hindcasting this storm with the third-generation wave model SWAN. In addition, we compare wave model results
with measurements in the Wadden Sea and with parametric growth curves, some of which were obtained in Lake
George, Australia. The results strongly suggest that the lower bottom friction value of Cb=0.038 m2s-3 is applicable
for both wind-sea and swell conditions.

Keywords


Wave modelling; bottom friction; TMA scaling;SWAN; JONSWAP; North Sea

References


Battjes, J.A. and J.P.F.M. Janssen, 1978: Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. on Coastal Engineering, ASCE, 569-587.

Booij, N., R.C. Ris, and L.H. Holthuijsen, 1999: A third-generation wave prediction model for coastal regions, Part I, Model description and validation. J. Geoph. Res, Vol. 104, C4, 7649-7666. http://dx.doi.org/10.1029/98JC02622

Bouws, E., 1979: Spectra of extreme wave conditions in the Southern North Sea considering the influence of water depth. Proc. Conf. on Sea Climatology. Paris, 1979: Collection Colloquia at Seminars, Vol. 34, 51-69.

Bouws, E, and G.J. Komen, 1983: On the balance between growth and dissipation in an extreme, depthlimited wind-sea in the southern North Sea. J. Phys. Oceanogr., Vol. 13, 1653-1658. http://dx.doi.org/10.1175/1520-0485(1983)013<1653:OTBBGA>2.0.CO;2

Bouws, E., H. G√ľnther, W. Rosenthal and C.L. Vincent, 1985: Similarity of the wind wave spectrum in finite depth water. 1. Spectral form. J. Geophys. Res., Vol. 90, C1, 975-986. http://dx.doi.org/10.1029/JC090iC01p00975

Bretschneider, 1973: See SPM, 1973.

Brown, J., 2010: A case study of combined wave and water levels under storm conditions using WAM and SWAN in a shallow water application. In press Ocean Modelling. http://dx.doi.org/10.1016/j.ocemod.2010.07.009

Deltares, 2010: SWAN Calibration and Validation for HBC2011, Report 1200103-020.

Hasselmann, K, et al., 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP), Deutch. Hydrogr. Z. Suppl. A8, 12, 95 pp.

Hasselmann, S., K. Hasselmann, K., J.H. Allender and T.P. Barnett, 1985: Computations and parameterizations of the nonlinear energy transfer in a gravity wave spectrum. Part II: parameterizations of the nonlinear transfer for application in wave models. J. Phys. Oceanogr., Vol. 15 (11): 1378-1391. http://dx.doi.org/10.1175/1520-0485(1985)015<1378:CAPOTN>2.0.CO;2

Holthuijsen, L.H., 1980: Methods of wave prediction, part I and II (Methoden voor golfvoorspelling, deel I en II, in Dutch), Technical Advisory Commission against Inundation (Technische Adviescommissie voor de Waterkeringen, in Dutch), Den Haag, The Netherlands.

Large, W. G., and S. Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Ocean., Vol. 11, 324-481. http://dx.doi.org/10.1175/1520-0485(1981)011<0324:OOMFMI>2.0.CO;2

Rogers, W.E., P.A. Hwang, and D.W. Wang, 2003: Investigation of wave growth and decay in the SWAN model: three regional-scale applications. J. Phys. Oceanogr., Vol. 33, 366-389. http://dx.doi.org/10.1175/1520-0485(2003)033<0366:IOWGAD>2.0.CO;2

SPM, 1973: Shore Protection Manual, U.S. Army Coastal Engineering Research Center.

Van Vledder, G.Ph., J. Adema, O.R. Koop, F.J.M. Enet and A.J. van der Westhuysen, 2009: Lowfrequency wind wave penetration in a tidal inlet system during a severe winter storm. Proc. 11th Int. Workshop on Wave Hindcasting and Forecasting, Halifax, Canada.

Wieringa, J., 1976: An objective exposure correction method for average wind speeds measured at a sheltered location. Quart. J. Roy. Soc., Vol. 102, 241-253. http://dx.doi.org/10.1002/qj.49710243119

Wu, J., 1982: Wind-stress coefficients over sea surface from breeze to hurricane, J. Geophys. Res., Vol. 87, C12, 9704-9706. http://dx.doi.org/10.1029/JC087iC12p09704

Young, I.R. and L.A. Verhagen, 1996: The growth of fetch limited waves in water of finite depth. Part 1: Total energy and peak frequency. Coastal Engineering, Vol. 29, 47-78. http://dx.doi.org/10.1016/S0378-3839(96)00006-3

Zijlema, M., 2009: Multiscale simulations using unstructured mesh SWAN model for wave hindcasting in the Dutch Wadden Sea. Paper 2, Coastal Dynamics, Tokyo, Japan.


Full Text: PDF

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