A Nonlinear Model of Monochromatic Waves on Steady Currents Over Gradually Varying Bottoms

References

• Baddour, R. E. and Song, S. W. (1990). Interaction of high-order water waves with uniform currents. Ocean Eng. 17, 6, pp. 551–568.
   Google Scholar
• Booij, N. (1981). Gravity waves on water with non-uniform depth and current. Rep. No. 81–1, Dept. Civ. Eng., Delft Univ. of Tech., Delft.
   Google Scholar
• Bowen, A. J. (1969). The generation of longshore currents on a plane beach. J. Mar. Res. 27, 2, pp. 206–215.
   Google Scholar
• Bretherton, F. P. and Garrett, C. J. R. (1969). Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. Lond. Ser. A, 302: 529–554.
   Google Scholar
• Conte, S. D. and Boor, C. (1981). Elementary Numerical Analysis: An Algorithmic Approach, McGraw-Hill International, Singapore.
   Google Scholar
• Dean, R. G. and Dalrymple, R. A. (1991). Water Wave Mechanics for Engineers and Scientists. World Scientific Publishing Co., Singapore.
   Google Scholar
• Horikawa, K. (1989). Nearshore Dynamics and Coastal Processes: Theory, Measurement and Predictive Model. University of Tokyo Press, Tokyo.
   Google Scholar
• Hedges, T. S. (1976). An empirical modification to linear wave theory. Proc. Inst. Civ. Engrs. Part 2, 61, 575–579.
   Google Scholar
• Hedges, T. S. and Lee, B. W. (1992). The equivalent uniform current in wave-current computations, Coast. Eng. 16, 3, pp. 301–311.
   Google Scholar
• Isobe, M. (1994). Comparative study of equations for analyzing coastal wave transformation. Proc. Japan Soc. Civ. Engrs. Part 2, 27: 1–14 (in Japanese).
   Google Scholar
• Jonsson, I. G. (1990). Wave-Current interactions. The Sea: Ocean Engineering Science (ed. B. LeMehaute and D. M. Hanes ) 9: 65–119.
   Google Scholar
• Jonsson, I. G. and Arneborg, L. (1995). Energy properties and shoaling of higher order Stokes waves on a current. Ocean Eng. 22, 8: 819–857.
   Google Scholar
• Kirby, J. T. (1984). A note on linear surface wave-current interaction over slowly varying topography. J. Geophy. Res. 89(C), 1: 745–747.
   Google Scholar
• Liu, P. L.-F. (1983). Wave-current interactions on a slowly varying topography. J. Geophy. Res. 88(C), 7: 4421–4426.
   Google Scholar
• Liu, P. L.-F. (1990). Wave transformation. In: The Sea: Ocean Engineering Science (ed. B. LeMehaute and D. M. Hanes ) 9: 27–63.
   Google Scholar
• Longuet-Higgins, M. S. (1970). Longshore currents generated by obliquely incident sea waves, 1 & 2. J. Geophys. Res. 75, 33: 6778–6801.
   Google Scholar
• Longuet-Higgins, M. S. and Stewart, R. W. (1961). Changes in the amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10: 529–549.
   Web of Science ®Google Scholar
• Longuet-Higgins, M. S. and Stewart, R. W. (1964). Radiation stresses in water waves; a physical discussion with applications. Deep-Sea Res. 11: 529–562.
   Google Scholar
• Madsen, P. A. , Murray, R. and Sorensen, O. R. (1991). A new form of Boussinesq equations with improved linear dispersion characteristics. Coast. Eng. 15: 371–388.
   Web of Science ®Google Scholar
• Madsen, P. A. and Sorensen, O. R. (1992). A new form of Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coast. Eng. 18: 183–204.
   Web of Science ®Google Scholar
• Mahmood, K. and Yevjevich, V. (1975). Unsteady Flows in Open Channels. Vol. 1, Water Resources Pub., Colorado.
   Google Scholar
• Mei, C. C. (1989). The Applied Dynamics of Ocean Surface Waves. World Scientific Publishing Co., Singapore.
   Google Scholar
• Nadaoka, K. , Beji, S. and Nakagawa, Y. (1997). A fully dispersive weakly nonlinear model for water waves. Proc. Roy. Soc. Lond. Ser. A, 453: 303–318.
   Google Scholar
• Nwogu, O. (1993). Alternative form of Boussinesq equations for nearshore wave propagation. J. Wtrwy., Port, Coast and Ocean Eng. 119, 6: 618–638.
   Web of Science ®Google Scholar
• Peregrine, D. H. (1976). Interaction of water waves and currents. Adv. Appi. Mech. (ed. C. S. Yih ) 16: 9–117.
   Google Scholar
• Phillips, O. M. (1977). The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge.
   Google Scholar
• Radder, A. C. and Dingemans, M. W. (1985). Canonical equations for almost periodic, weakly nonlinear gravity waves. Wave Motion 7: 473–485.
   Google Scholar
• Sakai, S. , Saeki, H. and Ozaki, A. (1982). Effects of current on wave shoaling. Proc. 29th Japanese Conf. Coast. Eng. JSCE, pp. 70–74 (in Japanese).
   Google Scholar
• Stoker, J. J. (1957). Water Waves. Interscience Publisher, New York.
   Google Scholar
• Suh, K. D. , Kim, Y.-Y. and Lee, D. Y. (1994). Equilibrium-range spectrum of waves propagating on currents, J. Wtrwy., Port, Coast, and Ocean Eng. 120, 5, pp. 434–450.
   Google Scholar
• Wei, G. , Kirby, J. T. , Grilli, S. T. and Subramanya, R. (1995). A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. J. Fluid Mech. 294: 71–92.
   Web of Science ®Google Scholar
• Yu, X. (1995). Numerical methods for the dispersion equation of waves riding on a steady current. Rep., Fac. Eng., Nagasaki Univ. 25, 45, pp. 211–218.
   Google Scholar
• Yu, X. , Isobe, M. and Watanabe A. (1992) Numerical computation of wave transformation over beaches. Coast. Eng. Japan 35, 1, pp. 1–19.
   Google Scholar