Wave–current interactions: an experimental and numerical study. Part 2. Nonlinear waves

The interaction between a regular wavetrain and an adverse current containing an arbitrary distribution of vorticity, in two dimensions, is studied using a linear theory. The model is used to predict the wavelength and the particle velocities under the waves and these are found to agree well with experimentally obtained data for a number of current profiles. Surprisingly accurate predictions, for the profiles considered, were also obtained from an irrotational wave–current model in which the constant current has a value equal to the depth-averaged mean of the measured current profile. The changes in the wave amplitude as the current magnitude increases are predicted using an irrotational slowly varying model with good agreement being found between theory and experiment.

[1]  R. W. Stewart,et al.  Interaction between gravity waves and a shear flow , 1961, Journal of Fluid Mechanics.

[2]  I. Brevik,et al.  Flume experiment on waves and currents. I. Rippled bed , 1979 .

[3]  Yi-Yuan Yu.  Breaking of waves by an opposing current , 1952 .

[4]  G. Crapper.  Energy and momentum integrals for progressive capillary-gravity waves , 1979, Journal of Fluid Mechanics.

[5]  Robert A. Dalrymple,et al.  A finite amplitude wave on a linear shear current , 1974 .

[6]  T. Benjamin.  The solitary wave on a stream with an arbitrary distribution of vorticity , 1962, Journal of Fluid Mechanics.

[7]  J. T. Evans,et al.  Pneumatic and similar breakwaters , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  R. Simons,et al.  The interaction between waves and a turbulent current: waves propagating with the current , 1982, Journal of Fluid Mechanics.

[9]  R. Dalrymple.  A numerical model for periodic finite amplitude waves on a rotational fluid , 1977 .

[10]  Geoffrey Ingram Taylor,et al.  The action of a surface current used as a breakwater , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  F. Bretherton,et al.  Wavetrains in inhomogeneous moving media , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  I. Brevik.  Flume experiment on waves and currents II. Smooth bed , 1980 .

[13]  R. G. Dean,et al.  Forced small-amplitude water waves: a comparison of theory and experiment , 1960, Journal of Fluid Mechanics.

[14]  J. Fenton.  Some Results for Surface Gravity Waves on Shear Flows , 1973 .

[15]  G. Thomas,et al.  Wave action and set-down for waves on a shear current , 1978, Journal of Fluid Mechanics.

[16]  D. H. Peregrine,et al.  Interaction of Water Waves and Currents , 1976 .

[17]  M. Longuet-Higgins,et al.  The changes in amplitude of short gravity waves on steady non-uniform currents , 1961, Journal of Fluid Mechanics.

[18]  Turgut Sarpkaya,et al.  Oscillatory Gravity Waves in Flowing Water , 1957 .

[19]  Robert A. Dalrymple,et al.  Water wave models and wave forces with shear currents , 1973 .