Solving the nonlinear shallow-water equations in physical space

Journal of Fluid Mechanics

Volumn 643, Issue , 2010, Pages 207-232

  Antuono, M ^a   Brocchini, M ^b  

^a ITALIAN SHIP MODEL BASIN   (Italy)

^b UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

Solitary waves; Surface gravity waves; Wave breaking

Indexed keywords

BOUNDARY VALUE PROBLEMS; EQUATIONS OF MOTION; GRAVITY WAVES; KINEMATICS; LIQUID WAVES; MATHEMATICAL TRANSFORMATIONS; OCEANOGRAPHY; SOLITONS;

ANALYTICAL CONDITIONS; FIRST-ORDER CONDITIONS; HODOGRAPH TRANSFORMATIONS; NON-LINEAR SHALLOW WATER EQUATIONS; SECOND-ORDER CONDITIONS; SURFACE GRAVITY WAVES; WAVE-WAVE INTERACTIONS; WAVEBREAKING;

NONLINEAR EQUATIONS;

BEACH; GRAVITY WAVE; NONLINEAR WAVE; PERTURBATION; SHALLOW-WATER EQUATION; SOLITARY WAVE; SURFACE WAVE; WAVE BREAKING;

EID: 76349107124     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009992096     Document Type: Article

References (15)

1. Abramowitz, M. & Ste gun, I. 1964 Handbook of Mathematical Functions. Dover.
2. Antuono, M. & Brocchini, M. 2007 The boundary value problem for the nonlinear shallow water equation. Stud. Appl. Maths. 119 71-91.
3. Antuono, M. & Brocchini, M. 2008 Maximum run-up, breaking conditions and dynamical forces in the swash zone: a boundary value approach. Coast. Engng 55 (9), 732-740.
4. Bellotti, G. & Brocchini, M. 2002 On using Boussinesq-type equations near the shoreline: a note of caution. Ocean Engng 29 1569-1575.
5. Brocchini, M. & Peregrine, D. H. 1996 Integral flow properties of the swash zone and averaging. J. Fluid Mech. 317 241-273.
6. Carrier, G. F. & Greenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4, 97-109.
7. Hubbard, M. E. & Dodd, N. 2002 A two-dimensional numerical model of wave run-up and overtopping. Coast. Engng 47, 1-26.
8. Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. John Wiley.
9. Meyer, E. R. 1986a On the shore singularity of water waves. Part I. The local model. Phys. Fluids 29 (10), 3152-3163.
10. Meyer, E. R. 1986b On the shore singularity of water waves. Part II. Small waves do not break on gentle beaches. Phys. Fluids 29 (10), 3164-3171.
11. Pritchard, D. & Dickinson, L. 2007 The near-shore behaviour of shallow-water waves with localized initial conditions. J. Fluid Mech. 591, 413-436.
12. Shen, M. C. & Meyer, E. R. 1963 Climb of a bore on a beach. Part 3. Run-up. J. Fluid Mech. 16, 113-125.
13. Synolakis, C. E. 1987 The run-up of solitary waves. J. Fluid Mech. 185, 523-545.
14. Tuck, E. O. & Hwang, L. S. 1972 Long wave generation on a sloping beach. J. Fluid Mech. 51, 449-461.
15. Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.