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dc.contributor.authorSteer, JNen
dc.contributor.authorBorthwick, AGLen
dc.contributor.authorStagonas, Den
dc.contributor.authorBuldakov, Een
dc.contributor.authorvan den Bremer, TSen
dc.date.accessioned2021-08-22T12:21:18Z
dc.date.available2021-08-22T12:21:18Z
dc.date.issued2020-01-01en
dc.identifier.issn0022-1120en
dc.identifier.urihttp://hdl.handle.net/10026.1/17668
dc.description.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 (1D + 1) 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 0 to −0.87 s−1. For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95 % 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 0 and −0.48 s−1. 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.

en
dc.language.isoenen
dc.titleExperimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currentsen
dc.typeJournal Article
plymouth.volume884en
plymouth.publication-statusPublisheden
plymouth.journalJournal of Fluid Mechanicsen
dc.identifier.doi10.1017/jfm.2019.951en
plymouth.organisational-group/Plymouth
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics
plymouth.organisational-group/Plymouth/Users by role
plymouth.organisational-group/Plymouth/Users by role/Academics
dc.identifier.eissn1469-7645en
dc.rights.embargoperiodNot knownen
rioxxterms.versionofrecord10.1017/jfm.2019.951en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.typeJournal Article/Reviewen


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