Steer, JN;
Borthwick, AGL;
Stagonas, D;
Buldakov, E;
Bremer, TSVD;
(2020)
Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents.
Journal of Fluid Mechanics
, 884
(A40)
10.1017/jfm.2019.951.
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Abstract
This paper examines experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from to . For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between and . Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.
| Type: | Article |
|---|---|
| Title: | Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2019.951 |
| Publisher version: | https://doi.org/10.1017/jfm.2019.951 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10088389 |
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