Author(s): J. B. Christoffersen; I. G. Jonsson

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Abstract: The energy principle known from steady hydraulics (i.e. the concept of an energy or total head line and a horizontal energy reference line) has been successfully extended to a dissipative current wave motion over an arbitrary bottom. The shear stress is assumed confined to a thin bottom layer, and the current is vertically uniform. However, it is allowed to have vorticity about vertical axes. The waves are described by a second order Stokian approach. The important new energy height equation states that the sum of a total current wave (energy) head and a current wave dissipation head is constant along a streamline. The total head is a sum of four terms: The mean/water surface height above datum, plus a current velocity head, plus a mean wave velocity head, and minus an interaction term head. The current-wave dissipation head is a sum of two terms: A current dissipation head minus a wave dissipation head. The usefulness of this new energy height equation, when calculating current depth refraction, is demonstrated. Some significant new results for a pure wave motion are also shown. Firstly that the total head minus the wave dissipation head is constant along a wave orthogonal, and secondly that the total head is constant along a wave front. By choosing proper initial conditions, the above two findings show that it is possible to find a horizontal energy reference level also for a dissipative wave motion, which is useful for the calculation of depth refraction of water waves.

DOI: https://doi.org/10.1080/00221688109499528

Year: 1981