The Influence of Unsteady Depths and Currents of Tides on Wind-Wave Propagation in Shelf Seas

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  • 1 Faculty of Civil Engineering, Delft University of Technology
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Abstract

The influence of unsteady depths and currents on wind wave propagation on the scale of shelf seas such as the North Sea is investigated. The attention is focused on depth and current variations due to tides, which are essentially stationary at the scale of a single wave but unsteady at the scale of wave propagation. Analytical solutions are derived for changes of monochromatic unidirectional linear waves due to a one-dimensional tide in water with a constant bottom level. It is shown that the change of absolute frequency due to variations of depth and current in time is of the same order of magnitude as the Doppler shift, and that it is not negligible, as assumed in a quasi-stationary approximation. The common quasi-stationary approximation leads to large errors in the predicted change of wave parameters in all situations considered here.

Abstract

The influence of unsteady depths and currents on wind wave propagation on the scale of shelf seas such as the North Sea is investigated. The attention is focused on depth and current variations due to tides, which are essentially stationary at the scale of a single wave but unsteady at the scale of wave propagation. Analytical solutions are derived for changes of monochromatic unidirectional linear waves due to a one-dimensional tide in water with a constant bottom level. It is shown that the change of absolute frequency due to variations of depth and current in time is of the same order of magnitude as the Doppler shift, and that it is not negligible, as assumed in a quasi-stationary approximation. The common quasi-stationary approximation leads to large errors in the predicted change of wave parameters in all situations considered here.

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