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Steady Deep‐Water Waves on a Linear Shear Current
Author(s) -
Simmen J. A.,
Saffman P. G.
Publication year - 1985
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198573135
Subject(s) - amplitude , limiting , mechanics , shear waves , longitudinal wave , mechanical wave , shear (geology) , physics , gravity wave , rogue wave , current (fluid) , love wave , classical mechanics , geology , wave propagation , nonlinear system , optics , thermodynamics , engineering , mechanical engineering , petrology , quantum mechanics
The properties of steady, periodic, deep‐water gravity waves on a linear shear current are investigated. Numerical solutions for all waveheights, up to and including the limiting ones, are computed from a formulation which involves only the wave profile (parametrized in a natural way) and some constants of the motion. It is found that for some shear currents the highest waves are not necessarily those waves with sharp crests known as extreme waves. Furthermore a certain nonuniqueness in the sense of a fold is shown to exist, and a new type of limiting wave is discovered. For both small‐amplitude waves and extreme waves the numerical results are compared with theoretical predictions.