The Effect of the Earth's Rotation on Wave-Induced Drift in Finite-Depth Water
The Role of Unsteadiness
J. Mol (TU Delft - Civil Engineering & Geosciences)
J. J.M. Slot (Eindhoven University of Technology)
P. A. Sanders (Eindhoven University of Technology)
M. Duran-Matute (Eindhoven University of Technology)
T. S. van den Bremer (TU Delft - Civil Engineering & Geosciences)
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Abstract
Wave-induced transport in the coastal zone can play an important role in the distribution of nutrients, plankton, and pollutants including plastic litter. The effect of the water depth, unsteadiness of the wave field, and the rotation of the Earth on the wave-induced drift is investigated in this paper. We derive a model for the time-dependent drift velocity in finite-depth water for a time-varying wave forcing, where we include the effect of rotation and a constant eddy viscosity. The solution is given in the form of a finite-depth Ekman-Stokes kernel. Convolution of this kernel with a time series of the Stokes drift gives the wave-induced Eulerian-mean velocity. The resulting unsteady flow contains damped inertial oscillations, where the amplitude of the oscillations is influenced by the rate of change of the wave forcing. Both a decrease in water depth (lower (Formula presented.)) and a decrease in the relative importance of rotation compared to viscosity (lower (inverse) wave Ekman number (Formula presented.)) lead to faster decay of these oscillations. Applying the model to buoy data shows a large impact on the predicted transport in finite depth.
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