Phase Resolving Wave—Current Interactions with Improved Boussinesq-Type Equations

References

• Antuono, M. , Liapidevskii, V. & Brocchini, M. [2009] “Dispersive nonlinear shallow-water equations,” Stud. Appl. Math. 122, 1–28.
   Web of Science ®Google Scholar
• Beji, S. & Nadaoka, K. [1996] “A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth,” Ocean Eng. 23(8), 691–704.
   Google Scholar
• Brevik, I. [1980] “Flume experiments on waves and currents II. Smooth bed,” Coastal Eng. J. 4, 89–110.
   Google Scholar
• Chawla, A. & Kirby, J. T. [2000] “A source function method for generation of waves on currents in boussinesq models,” Appl. Ocean Res. 22, 75–83.
   Google Scholar
• Chen, Q. , Madsen, P. A. , Schaffer, H. A. & Basco, D. R. [1998] “Wave-current interaction based on enhanced boussinesq approach,” Coastal Eng. J. 33, 11–39.
   Google Scholar
• Dean, R. G. & Dalrymple, R. A. [1984] Water Wave Mechanics for Engineers and Scientists (Prentice-Hall, Inc., Englewoods Cliffs, New Jersey 07632).
   Google Scholar
• Galan, A. , Simarro, G. , Orfila, A. , Simarro, J. & Liu, P. [2012] “A fully nonlinear model for water wave propagation from deep to shallow waters,” J. Waterway Port Coast Ocean Eng. 138(5) 362–371.
   Google Scholar
• Gobbi, M. F. , Kirby, J. T. & Wei, G. [2000] “A fully nonlinear boussinesq model for surface waves: Part ii. extension to o(kh)4,” J. Fluid Mech. 405, 182–210.
   Google Scholar
• Green, A. E. & Naghdi, P. M. [1976] “A derivation of equations for wave propagation in water of variable depth,” J. Fluid Mech. 78, 237–246.
   Web of Science ®Google Scholar
• Karambas, T. V. & Memos, C. D. [2009] “Boussinesq model for weakly nonlinear fully dispersive water waves,” J. Waterway Port Coastal Ocean Eng. 135, 187–199.
   Web of Science ®Google Scholar
• Kim, D. H. , Lynett, P. J. & Socolofsky, S. A. [2009] “A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows,” Ocean Model. 27, 198–214.
   Google Scholar
• Kirby, J. T. [1997] Nonlinear dispersive long waves in water of variable depth, in Gravity waves in water of finite depth, Hunt, J. H. (ed.). Advances in Fluid Mechanics, 10, 55–125, Computational Mechanical Publications.
   Google Scholar
• Larsen, J. & Dancy, H. [1983] “Open boundaries in short wave simulations — a new approach,” Coastal Eng. J. 7, 185–197.
   Google Scholar
• Liu, P. L.-F. & Losada, I. [2002] “Wave propagation modeling in coastal engineering,” J. Hydraulic Res. 40, 229–240.
   Web of Science ®Google Scholar
• Lynett, P. & Liu, P. L.-F. [2004] “A two layer approach to wave modeling,” R. Soc. London A 460, 2637–2669.
   Google Scholar
• Madsen, P. A. , Murray, R. & Sorensen, O. R. [1991] “A new form of the boussinesq equations with improved linear dispersion characteristics,” Coastal Eng. J. 15(4), 371–388.
   Google Scholar
• Madsen, P. A. & Schaffer, H. A. [1998] “Higher-order boussinesq-type equations for surface gravity waves: Derivation and analysis,” Philos. Trans. R. Soc. London A 356, 3123–3184.
   Web of Science ®Google Scholar
• Madsen, P. A. & Sorensen, O. R. [1992] “A new form of the Boussinesq equations with improved linear dispersion characteristics, part 2: A slowly-varying bathymetry,” Coastal Eng. J. 18, 183–204.
   Google Scholar
• Mei, C. C. [1989] The Applied Dynamics of Ocean Surface Waves (World Scientific, Singapore).
   Google Scholar
• Nwogu, O. [1993] “Alternative form of Boussinesq equations for nearshore wave propagation,” J. Waterway Port Coastal Ocean Eng. 119(6), 618–638.
   Web of Science ®Google Scholar
• Peregrine, D. H. [1967] “Long waves on a beach,” J. Fluid Mech. 27, 815–827.
   Web of Science ®Google Scholar
• Simarro, G. , Orfila, A. & Galan, A. [2013] “Linear shoaling in Boussinesq-type wave propagation models,” Coastal Eng. J. 80, 100–106.
   Google Scholar
• Wei, G. & Kirby, J. T. [1995] “Time-dependent numerical code for extended Boussinesq equations,” J. Waterway Port Coastal Ocean Eng. 121(5), 251–261.
   Web of Science ®Google Scholar
• Wei, G. , Kirby, J. T. , Grilli, S. T. & Subramnya, R. [1995] “A fully nonlinear boussinesq model for surface waves 1. highly nonlinear unsteady waves,” J. Fluid Mech. 294, 71–92.
   Web of Science ®Google Scholar
• Wei, G. , Kirby, J. T. & Sinha, A. [1999] “Generation of wave in Boussinesq models using a source function method,” Coastal Eng. J. 36, 271–299.
   Google Scholar
• Zhang, Y. , Kennedy, A. B. , Panda, N. , Dawson, C. & Westerink, J. J. [2013] “Boussinesq-GreenNaghdi rotational water wave theory,” Coastal Eng. J. 73, 13–27.
   Google Scholar