Stokes wave

Surface elevation of a deep water wave according to Stokes' third-order theory. The wave steepness is: ka = 0.3, with k the wavenumber and a the wave amplitude. Typical for these surface gravity waves are the sharp crests and flat troughs.
Model testing with periodic waves in the wave–tow tank of the Jere A. Chase Ocean Engineering Laboratory, University of New Hampshire.
Undular bore and whelps near the mouth of Araguari River in north-eastern Brazil. View is oblique toward mouth from airplane at approximately 100 ft (30 m) altitude.[1] The undulations following behind the bore front appear as slowly modulated Stokes waves.

In fluid dynamics, a Stokes wave is a nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion.

Stokes's wave theory is of direct practical use for waves on intermediate and deep water. It is used in the design of coastal and offshore structures, in order to determine the wave kinematics (free surface elevation and flow velocities). The wave kinematics are subsequently needed in the design process to determine the wave loads on a structure.[2] For long waves (as compared to depth) – and using only a few terms in the Stokes expansion – its applicability is limited to waves of small amplitude. In such shallow water, a cnoidal wave theory often provides better periodic-wave approximations.

While, in the strict sense, Stokes wave refers to a progressive periodic wave of permanent form, the term is also used in connection with standing waves[3] and even random waves.[4][5]

  1. ^ Figure 5 in: Susan Bartsch-Winkler; David K. Lynch (1988), Catalog of worldwide tidal bore occurrences and characteristics (Circular 1022), U. S. Geological Survey
  2. ^ Chakrabarti, S.K. (2005), Handbook of Offshore Engineering, Elsevier, p. 235, ISBN 9780080445687
  3. ^ Grant, M.A. (1973), "Standing Stokes waves of maximum height", Journal of Fluid Mechanics, 60 (3): 593–604, Bibcode:1973JFM....60..593G, doi:10.1017/S0022112073000364, S2CID 123179735
  4. ^ Ochi, Michel K. (2003), Hurricane-generated seas, Elsevier, p. 119, ISBN 9780080443126
  5. ^ Tayfun, M.A. (1980), "Narrow-band nonlinear sea waves", Journal of Geophysical Research, 85 (C3): 1548–1552, Bibcode:1980JGR....85.1548T, doi:10.1029/JC085iC03p01548