Radiation stress and mass transport in gravity waves, with application to ‘surf beats’

  title={Radiation stress and mass transport in gravity waves, with application to ‘surf beats’},
  author={Michael Selwyn Longuet-Higgins and Robert William Stewart},
  journal={Journal of Fluid Mechanics},
  pages={481 - 504}
This paper studies the second-order currents and changes in mean surface level which are caused by gravity waves of non-uniform amplitude. The effects are interpreted in terms of the radiation stresses in the waves. The first example is of wave groups propagated in water of uniform mean depth. The problem is solved first by a perturbation analysis. In two special cases the second-order currents are found to be proportional simply to the square of the local wave amplitude: (a) when the lengths… 

Wave-Current Interaction: A Comparison of Radiation-Stress and Vortex-Force Representations

The eects of wind-generated surface gravity waves on more slowly evolving long waves, currents and material distributions in stratied coastal waters are investigated using the wave-averaged,

Wave–Current Interactions in Finite Depth

The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified.

The Depth-Dependent Current and Wave Interaction Equations: A Revision

AbstractThis is a revision of a previous paper dealing with three-dimensional wave-current interactions. It is shown that the continuity and momentum equations in the absence of surface waves can

Effects of wave‐current interaction on rip currents

[1] The time evolution of rip currents in the nearshore is studied by numerical experiments. The generation of rip currents is due to waves propagating and breaking over alongshore variable

Mass transport induced by internal Kelvin waves beneath shore‐fast ice

[1] A one-layer reduced-gravity model is used to investigate the wave-induced mass flux in internal Kelvin waves along a straight coast beneath shore-fast ice. The waves are generated by barotropic

On the instability leading to rip currents due to wave–current interaction

  • Jie Yu
  • Environmental Science, Physics
    Journal of Fluid Mechanics
  • 2006
We examine the instability leading to depth-averaged circulations, which are related to rip currents in the surf zone, due to wave–current interactions. Our intention is to clarify some issues which

Rip currents: 1. Theoretical investigations

  • A. Bowen
  • Environmental Science, Physics
  • 1969
The nearshore circulation of water on a plane beach produced by a wave train, normally incident on the beach, which has a longshore variation in wave height is investigated theoretically. The

On the mean motion induced by internal gravity waves

  • F. Bretherton
  • Physics, Environmental Science
    Journal of Fluid Mechanics
  • 1969
A train of internal gravity waves in a stratified liquid exerts a stress on the liquid and induces changes in the mean motion of second order in the wave amplitude. In those circumstances in which

Longshore currents generated by obliquely incident sea waves: 1

By using known results on the radiation stress associated with gravity waves, the total lateral thrust exerted by incoming waves on the beach and in the nearshore zone is rigorously shown to equal

An asymptotic theory for the interaction of waves and currents in coastal waters

A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside



Mass transport in water waves

  • M. Longuet-Higgins
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1953
It was shown by Stokes that in a water wave the particles of fluid possess, apart from their orbital motion, a steady second-order drift velocity (usually called the mass-transport velocity). Recent

Changes in the form of short gravity waves on long waves and tidal currents

Short gravity waves, when superposed on much longer waves of the same type, have a tendency to become both shorter and steeper at the crests of the longer waves, and correspondingly longer and lower


The purposes of this paper are: (a) to give a summary of useful relationships derived by means of the solitary wave theory, and to plot these relations using dimensionless parameters for the purpose

Mass transport in the boundary layer at a free oscillating surface

In a previous paper (1953b) it was shown theoretically that just below the boundary layer at the surface of a free wave the mass-transport gradient should be exactly twice that given by Stokes's

Mass, momentum and energy flux in water waves

This paper gives a direct derivation of some results obtained by Longuet-Higgins & Stewart (1960, 1961) on the amplitude variation of waves propagating on a non-uniform stream. The derivation raises

Standing waves on a contracting or expanding current

  • G. Taylor
  • Physics
    Journal of Fluid Mechanics
  • 1962
In a recent work Longuet-Higgins & Stewart (1961) have studied the changes in wavelength and amplitude of progressive waves of constant frequency as they are propagated into regions of surface

The refraction of sea waves in shallow water

This paper considers the changes that occur in the character of short-crested sea waves when they are refracted by a shallowing depth of water. Besides a change in mean wave-length and direction


  • Physics
Russell, as a result of his experiments, that the velocity of pro pagation of a series of oscillatory waves does not depend on the height of the waves*. A series of oscillatory waves, such as that

Surf beats: sea waves of 1 to 5 min. period

  • M. Tucker
  • Environmental Science, Geology
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1950
Long sea waves with periods of 2 to 3 min. and a few inches in amplitude have been measured. It has been shown that they are due to the varying height of groups of waves breaking on the shore. The

Total reflection of surface waves by deep water

A mechanism is described by which surface gravity waves generated in shallow water may be totally reflected from deep water. The mechanism by which waves generated in deep water may be “captured” is