Simplified calculation of wave orbital velocities

Soulsby, R.L. (2006) Simplified calculation of wave orbital velocities. Technical Report. HR Wallingford.

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Abstract

Many coastal problems require the calculation of wave-generated oscillatory (orbital) velocities at the sea-bed for applications such as sediment mobility, transport and suspension, bed protection measures, and forces on structures. This is most commonly performed by using linear wave theory to transform the wave height and period to the orbital velocity in a given water depth as described by e.g. Sleath (1984). Only nonbreaking waves are considered in this report. The use of linear wave theory to obtain orbital velocities is justified by the experimental work of Kirkgöz (1986), who found that linear theory gave reasonable agreement with observed orbital velocities under wave crests over his entire range of parameter settings, even at the transformation point of plunging breakers where higher-order theories might be expected to give significantly better results. The velocity under wave troughs was significantly smaller than the predicted linear-theory value. Depending on the complexity of the problem, either a regular (monochromatic) wave or irregular (spectral) waves may be considered. However, the expression for the orbital velocity amplitude cannot be written explicitly in terms of depth, wave height and period, so indirect methods must be used. This report extends earlier work by Soulsby and Smallman (1986) and Soulsby (1987) to give calculation methods which are simple enough to be written in a single cell of a spreadsheet, for ease of use in practical applications using spreadsheet methods. It is less accurate than some methods, but is adequate to give at least a reasonable estimate for many desk-study applications. Despite enormous increases in computer speed and power since 1986, it is still often a limitation when using fine grids, long-term simulations, multiple sensitivity tests, or stochastic simulations in present day studies. Efficiency of repeated computations is thus still a desirable goal, especially when wave orbital velocities need to be calculated at every grid point and every time-step of a numerical model. The simple methods may therefore sometimes be preferred to more accurate methods even in numerical models.

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