Browsing by Author "Buldakov, Eugeny"
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Item Open Access Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents(Cambridge University Press, 2019-12-17) Steer, James N.; Borthwick, Alistair G. L.; Stagonas, Dimitris; Buldakov, EugenyThis 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.Item Open Access Numerical models for evolution of extreme wave groups(Elsevier, 2019-05-23) Buldakov, Eugeny; Higuera, Pablo; Stagonas, DimitrisThe paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method for treating spilling breaking is introduced and includes dissipative suppression of the breaker and correction of crest shape to improve the post breaking behaviour. The model is used to create a Lagrangian numerical wave tank, to reproduce experimental results of wave group evolution. The same set of experiments is modelled using a novel VoF numerical wave tank created using OpenFOAM. Lagrangian numerical results are validated against experiments and VoF computations and good agreement is demonstrated. Differences are observed only for a small region around the breaking crest.