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Original Articles

Water Waves near a Shoreline in a Flow with Vorticity: Two Classical Examples

Pages 133-156 | Received 25 Apr 2008, Published online: 21 Jan 2013

References

  • Burns , J C . 1953 . Long waves in running water . Proc. Camb. Phil. Soc. , 49 : 695 – 706 .
  • Constantin , A . 2001 . Edge waves along a sloping beach . J. Phys. A Maths. Gen. , 34 : 9723 – 9731 .
  • Constantin , A and Johnson , R S . 2008 . Propagation of very long waves, with vorticity, over variable depth, with applications to tsunamis . Fluid Dyn. Res. , 40 : 175 – 211 .
  • Drazin , P G and Johnson , R S . 1989 . Solitons: an Introduction , Cambridge : Cambridge University Press .
  • Evans , D V . 1988 . Edge Waves Over a sloping beach . Q. J. Mech. Appl. Maths. , 42 : 131 – 142 .
  • Freeman , N C and Johnson , R S . 1970 . Shallow water waves on shear flows . J. Fluid Mech. , 42 : 401 – 409 .
  • Gerstner , F . 1809 . Theorie der Wellen, Abh. D.k. böhm. Ges. D. Wiss . Also Ann. Phys. Lpz. , 2 : 412
  • Johnson , R S . 1986 . On the nonlinear critical layer below a nonlinear unsteady surface wave . J. Fluid Mech. , 167 : 327 – 351 .
  • Johnson , R S . 1997 . A Modern Introduction to the Mathematical Theory of Water Waves , Cambridge : Cambridge University Press .
  • Johnson , R S . 1997 . “ Nonlinear gravity waves on the surface of an arbitrary shear flow with variable depth ” . In Nonlinear Instability Analysis , 221 – 243 . Southampton : Adv. Fluid Mech .
  • Johnson , R S . 2005 . Some Contributions to the theory of edge waves . J. Fluid Mech. , 524 : 81 – 97 .
  • Johnson , R S . 2007 . Edge Waves: theories past and present . Phil. Trans. R. Soc. A , 365 : 2359 – 2376 .
  • Korteweg , D J and De Vries , G . 1895 . On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves . Phil. Mag , 39 : 422 – 443 .
  • Mollo-Christensen , E . 1982 . Allowable discontinuities in a Gerstner wave . Phys. Fluids , 25 : 586587
  • Stokes , G G . 1846 . Report On Recent researches in hydrodynamics . Rep. 16th Brit. Assoc. Adv. Sci , : 1 – 20 .
  • Stokes , G G . 1847 . On The Theory of oscillatory waves . Trans. Camb. Phil. Soc. , 8 : 441 – 455 .
  • Ursell , F . 1952 . Edge Waves On A sloping beach . Proc. R. Soc. A , 214 : 79 – 97 .
  • Whitham , G B . 1976 . Nonlinear Effects in edge waves . J. Fluid Mech. , 74 : 353 – 368 .
  • Yih , C-S . 1966 . Note On Edge Waves in a stratified fluid . J. Fluid Mech. , 24 : 765 – 767 .

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