A note on weakly-nonlinear equations of continental shelf waves

A note on weakly-nonlinear equations of continental shelf waves

O LR (1986)33 (3) A. Physical Oceanography 209 equations. The further approximation that nonlinearity and dispersion are comparably weak leads to a...

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O LR (1986)33 (3)

A. Physical Oceanography

209

equations. The further approximation that nonlinearity and dispersion are comparably weak leads to a canonical form of Boussinesq's equations that conserves consistent approximations to energy, momentum and potential vorticity. Inst. of Geophys. and Planet. Phys., Univ. of Calif., La Jolla, CA 92093, USA.

speed decay, and modon wavenumber increases, exponentially as the slow time increases. Resulting dissipation in the streamfunction and vorticity is qualitatively similar to McWilliams et al. (1981) numerical solution, although it is unable to describe the eventual transition to Rossby waves. Dept. of Math. and Oceanogr., Univ. of British Columbia, Vancouver, BC V6T IW5, Canada.

86:1441 Miyata, Hideaki and Shinichi Nishimura, 1985. Finite-difference simulation of nonlinear ship waves. J. Fluid Mech., 157:327-357. Dept. of Naval Architecture, Univ. of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan.

86:1445 Thompson, E.F. and C.L. Vincent, 1985. Significant wave height for shallow water design. J. Wat Way Port coast. Ocean Div., Am. Soc. cir. Engrs, 111(5):828-842.

86:1442 Naguszewski, Andrzej, Stanislaw Massel and Wojciech Trapp, 1985. Non-linear attenuation of gravity wind waves. Oceanologia, Warsz., 20:2949. Experimental data show that low frequencies are damped more slowly than predicted by linear theory; the opposite is observed in the high frequency range. The developed non-linear perturbation scheme offers a theoretical base for understanding of this unclassical attenuation mechanism. Inst. of Hydroengrg., Polish Acad. of Sci., GdanskOliwa, Poland. 86:1443 Nakamura, Shigehisa, 1985. A note on weaklynonlinear equations of continental sheff waves. Mer, Tokyo, 23(2):49-54. (In Japanese, English abstract.) Weakly-nonlinear equations for continental shelf waves, derived without rigid-lid approximation, coincide with Pierini's equations on an f-plane as a special case of that on a beta-plane. On the f-plane the zeroth-order approximation gives a linear differential equation for a Sturm-Liouville problem, the first-order approximation a Burger's equation and the second-order approximation a KdV equation. Shirahama Oeeanogr. Observ, DPRI, Kyoto Univ., Katada-Hatasaki, Shirahama, Wakayama, 649 Japan. 86:1444 Swaters, G.E., 1985. FJmmn layer dissipation in an eastward-traveling modon. J. phys. Oceanogr., 15(9):1212-1216. A perturbation solution for an eastward-traveling modon in the presence of a bottom Ekman boundary layer is presented. The modon radius, translation speed and wavenumber are allowed to be functions of a slow time. Modon amplitude and translation

Wave height parameters are grouped into three classes according to their definition bases: height statistics, energy, and monochromatic. Parameters within each class are easily interrelated for most engineering purposes; however, parameters from different classes are difficult to interrelate, particularly where waves are near breaking. A simple empirical method is developed to relate statistical and energy based significant height estimates. Since the two significant height estimates differ by over 40% in some laboratory cases, engineers should clearly recognize the distinction between them. U.S. Army Coastal Engrg. Res. Center, Waterways Experiment Sta., P.O. Box 631, Vicksburg, MS 39180, USA. 86:1446 Violante, R.A. and W.F. Tanner, 1985. Rain waves vs swash-zone ripple marks: why are they mutually exdnsive? J. coast. Res., 1(4):375-381. Serv. de Hidrogr. Naval, Div. of Geol., Avda. Montes de Oca 2124, (1271) Buenos Aires, Argentina.

86:1447 Worthy, A.L., 1984. Wind forcing of edge waves on a truncated exponential shelf. Dt. hydrogr. Z~ 37(6):235-243. The effects of wind forcing on high frequency edge waves over a truncated exponential shelf are examined. Two wind stress models are used; the results are compared to those obtained for the semi-infinite continental shelf profile. Univ. of Wollongong, Math. Dept., P.O. Box 1144, Wollongong NSW 2500, Australia.

86:1448 Wu, Yongcheng, Yimou Wang and Lei Li, 1985. Characterist~ of wind waves in the Gulf of Bohal under the inflnence of a cold wave. Oceanologia Limnoi. sin., 16(2):147-155. (In Chinese, English abstract.)