Shear waves in a circular wave basin Public Deposited

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  • Shear waves, which are instabilities of the longshore current, are of interest to nearshore research because they can act as a cross-shore mixing mechanism for the current. The best method to study them is in a controlled environment, such as circular wave tank where continuous longshore currents can be generated. Conservation of vorticity is found from the linearized equations of motion in cylindrical coordinates. The flow field is expressed as a small perturbation superimposed upon a mean longshore current. Using streamfunction definitions for the perturbation velocities, solutions to the vorticity equation are frequency (eigenvalues) and cross-shore structure (eigenvectors). Solutions of a finite difference model, using cross-shore geometry suitable for laboratory testing, range from 0.0 to 0.8 Hz. Them fastest growing wave occurs at 0.4 Hz. The u-v phase difference of the unstable odes are nonquadrature in the area of steep offshore shear, moving toward quadrature further offshore. The dispersion shows that shear waves are shorter than natural tank modes. An experiment is designed to observe shear waves in a circular tank, using a cross-shore geometry similar to that of the model. Measurements are taken over sequential runs at seven cross-shore positions using one current meter. A composite profile of the longshore current shows that the measurement positions fall within a region of steep offshore shear that includes an extremum in the potential vorticity profile. The cross-shore power spectra of the demeaned velocity time series show an increase in energy below 0.4 Hz in both velocity components. The coherence spectra at the first three cross-shore positions show significant coherence below 0.4 Hz that correspond to nonquadrature phases over the same band. The positions fall over the steepest part of the shear. Longshore wavenumbers are found by regressing phase onto spacial lags for eleven sensor pairs. Time series are taken over sequential runs, with different sensor spacings for each run. Twelve wavenumber slopes are found for frequencies between .15 Hz and .39 Hz. The dispersion of the measured signals compares favorably with shear wave solutions and indicates that the waves are too short to be natural tank modes.
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