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A note on the vertical distribution of momentum transport in water wavesa

Kołodko J., Gic-Grusza G.

Oceanological and Hydrobiological Studies

2015

Vol. 44, No. 4

563--568

In this paper, the classical problem of horizontal waveinduced momentum transport is analyzed once again. A new analytical approach has been employed to reveal the vertical variation of this transport in the Eulerian description. In mathematical terms, this variation is shown to have (after “smoothing out” the surface corrugation) the character of a generalized function (distribution) and is described by a classical function in the water depths and by an additional Dirac-delta-function component on the averaged free surface. In terms of physics, the considered variation consists of two entities: (i) a continuous distribution of the mean momentum transport flux density (tensorial radiation pressure) over the entire water column, and (ii) an additional momentum transport flux concentrated on the mean free surface level (tensorial radiation surface pressure). Simple analytical formulae describing this variation have been derived. This allowed a conventional expression to be derived, describing the depth-integrated excess of horizontal momentum flux due to the presence of waves (the so-called “radiation stress”), confirming to some extent the correctness of the whole analysis carried out. The results obtained may be important to the ocean dynamics, especially in view of their possible application in the field of hydrodynamics of wave-dominated coastal zones.

On Vertical Variations of Wave-Induced Radiation Stress Tensor

Chybicki W.

Archives of Hydro-Engineering and Environmental Mechanics

2008

Vol. 55, nr 3-4

83-93

The flux of momentum generated by an incident wave field, commonly known as the radiation stress, plays an important role in near-shore water circulation. Many researchers use the concept of radiation stress in the calculation of cross-shore and long-shore circulation. In this paper, the traditional concept is extended to the case of vertical variation of radiation stress, and analitycal expressions for the vertical profile of radiation stress are derived. The distributions of the wave-induced radiation stress tensor with depth are studied by linear wave theory. The application of radiation stress with vertical variation is expected to play an important role in further studies of the near-shore system. Information regarding the vertical distribution of the radiation stress components ( and ) resulting from obliquely incident, shoaling waves is provided. The results show that the vertical variations of the wave-induced radiation stress tensor are significant as regards of wave propagation.