Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents

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dc.contributor.authorSteer, James N.
dc.contributor.authorBorthwick, Alistair G. L.
dc.contributor.authorStagonas, Dimitris
dc.contributor.authorBuldakov, Eugeny
dc.date.accessioned2020-03-10T12:36:43Z
dc.date.available2020-03-10T12:36:43Z
dc.date.issued2019-12-17
dc.description.abstractThis 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_UK
dc.identifier.citationSteer JN, Borthwick AGL, Stagonas D, et al., (2020) Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents. Journal of Fluid Mechanics, Volume 884, February 2020, Article number A40en_UK
dc.identifier.issn0022-1120
dc.identifier.urihttps://doi.org/10.1017/jfm.2019.951
dc.identifier.urihttp://dspace.lib.cranfield.ac.uk/handle/1826/15256
dc.language.isoenen_UK
dc.publisherCambridge University Pressen_UK
dc.rightsAttribution-NonCommercial 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/*
dc.subjectWave - current interactionen_UK
dc.subjectShear currentsen_UK
dc.subjectNon-linear instabilityen_UK
dc.titleExperimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currentsen_UK
dc.typeArticleen_UK

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