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A derivation of equations for wave propagation in water of variable depth

  • A. E. Green (a1) and P. M. Naghdi (a2)

Within the scope of the three-dimensional theory of homogeneous incompressible inviscid fluids, this paper contains a derivation of a system of equations for propagation of waves in water of variable depth. The derivation is effected by means of the incompressibility condition, the energy equation, the invariance requirements under superposed rigid-body motions, together with a single approximation for the (three-dimensional) velocity field.

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Green, A. E., Laws, N. & Naghdi, P. M. 1974 On the theory of water waves. Proc. Roy. Soc. A338, 43.
Green, A. E. & Naghdi, P. M. 1976 Directed fluid sheets. Proc. Roy. Soc. A347, 447.
Green, A. E. & Zerna, W. 1968 Theoretical Elasticity, 2nd edn. Oxford: Clarendon Press.
Grimshaw, R. 1970 The solitary wave in water of variable depth J. Fluid Mech. 42, 639.
Johnson, R. S. 1973 On the development of solitary wave moving over an uneven bottom Proc. Camb. Phil. Soc. 73, 183.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Naghdi, P. M. 1972 The theory of shells and plates. In Handbuch der Physik (ed. S. Flügge), vol. via/2, p. 425. Springer.
Peregrine, D. H. 1967 Long waves on a beach J. Fluid Mech. 27, 815.
Peregrine, D. H. 1972 Equations for water waves and the approximation behind them. In Waves on Beaches, p. 95. Academic.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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