Frequency downshift in a viscous fluid

Carter, John D.; Govan, Alex

doi:10.1016/j.euromechflu.2016.06.002

Cited by 22 publications

(41 citation statements)

References 20 publications

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“…To test the accuracy of the models, we compare predictions of Fourier amplitudes M, P, ω p , and ω m , from the models, with data already in the literature and with two new experiments. Experiments A and B were presented in Segur et al [22] and reconsidered in Carter & Govan [4]. Experiments C and D are new.…”

Section: Experimental Apparatus and Resultsmentioning

confidence: 99%

“…One of the experiments exhibited frequency downshift while the other three did not. The models include: the classical cubic nonlinear Schrödinger equation [30,25] (NLS), the Dysthe equation [6] (Dysthe), the dissipative NLS equation [22,5] (dNLS), the viscous Dysthe equation [4] (vDysthe), the Islas-Schober equation [11] (IS), the Gordon equation [7] ( Gordon), and a new model presented herein, which we call the dissipative Gramstad-Trulsen equation (dGT), a dissipative generalization of the model derived by Gramstad-Trulsen [8]. We focus on FD and frequency upshift (FU) in both the spectral mean and spectral peak senses.…”

Section: Introduction 2 Introductionmentioning

confidence: 99%

“…The numerical results from the models are compared with the experimental results in Section 5.Figures 2 and 3 contain plots of the (dimensionless) amplitudes of the carrier wave and the six sidebands with largest amplitudes versus (dimensionless) χ for Expts C and D respectively. The corresponding plots for Experiments A and B are found in Carter & Govan[4], though they are presented in dimensional form Plots from every other gauge for Expt B. The first column contains plots of surface displacement (in cm) versus time (in sec).…”

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A comparison of frequency downshift models of wave trains on deep water

2019

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Frequency downshift (FD) in wave trains on deep water occurs when a measure of the frequency, typically the spectral peak or the spectral mean, decreases as the waves travel down a tank or across the ocean. Many FD models rely on wind or wave breaking. We consider seven models that do not include these effects and compare their predictions with four sets of experiments that also do not include these effects. The models are the (i) nonlinear Schrödinger equation (NLS), (ii) dissipative NLS equation (dNLS), (iii) Dysthe equation, (iv) viscous Dysthe equation (vDysthe), (v) Gordon equation (Gordon) (which has a free parameter), (vi) Islas-Schober equation (IS) (which has a free parameter), and (vii) a new model, the dissipative Gramstad-Trulsen (dGT) equation.The dGT equation has no free parameters and addresses some of the difficulties associated with the Dysthe and vDysthe equations. We compare a measure of overall error and the evolution of the spectral amplitudes, mean, and peak. We find: (i) The NLS and Dysthe equations do not accurately predict the measured spectral amplitudes. (ii) The Gordon equation, which is a successful model of FD in optics, does not accurately model FD in water waves, regardless of the choice of free parameter. (iii) The dNLS, vDysthe, dGT, and IS (with optimized free parameter) models all do a reasonable job predicting the measured spectral amplitudes, but none captures all spectral evolutions. (iv) The vDysthe, dGT, and IS (with optimized free parameter) models do the best at predicting the observed evolution of the spectral peak and the spectral mean. (v) The IS model, optimized over its free parameter, has the smallest overall error for three of the four experiments. The vDysthe equation has the smallest overall error in the other experiment.

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Section: Experimental Apparatus and Resultsmentioning

confidence: 99%

Section: Introduction 2 Introductionmentioning

confidence: 99%

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confidence: 99%

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A comparison of frequency downshift models of wave trains on deep water

2019

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“…For the sake of validation of experimental results, the envelope of the measured water surface dynamics has been reconstructed, using the Hilbert transform [23] and then compared to NLSE and MNLSE simulations, including dissipation. The dissipative MNLSE formalism can be described by [40] i Ψ x + 2k…”

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confidence: 99%

Nonconservative higher-order hydrodynamic modulation instability

et al. 2017

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The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy side-bands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary side-bands generate an infinite number of additional side-bands, forming a triangular side-band cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that are created are also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirm observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counter-intuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids and plasma.One possible explanation for the formation of extreme wave events for instance in the ocean and nonlinear optical media is the modulation instability (MI) [1][2][3]. Understanding the wave dynamics of modulationally unstable waves is of major significance for the sake of accurate modeling and prediction of localized structures as well as of rogue waves in particular [4,5]. The MI describes the disintegration of uni-directional and narrow-banded wave fields. Physically, the instability is driven, when sidebands that are located around the main carrier energy peak in a specific instability range are excited. The progressive focusing of the wave field is translated in spectral domain with an advancing formation of an infinite number of side-bands in form of a triangular cascade [6,7]. One deterministic way to study the MI is by use of the nonlinear Schrödinger equation (NLSE) [8,9]. The latter weakly nonlinear evolution equation is indeed very useful in the study of the problem, in view of its integrability [10]. In fact, the NLSE admits a family of exact solutions that model stationary, pulsating and modulationally unstable wave fields [11]. The standard model that describes the MI process are the family of Akhmediev breathers (ABs) [12]. Indeed, for each unstable modulation frequency, or unstable side-band, one can assign an exact analytical AB expression to study the spatiotemporal evolution of the wave field. From an experimental perspective these universal type of solutions are very valuable, since the complex nonlinear physical processes can be controlled in time and space a...

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“…Later, deterministic wind forcing and viscous dissipation for weakly nonlinear surface gravity waves by means of a forced and damped NLS was considered by Kharif et al [40]. Higher order approximation of the nonlinear water wave envelope leads to Dysthe equations [41], for which fluid viscosity has been included in [42].…”

Section: Introductionmentioning

confidence: 99%

Study on the behavior of weakly nonlinear water waves in the presence of random wind forcing

2019

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Specific solutions of the nonlinear Schrödinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the presence of gusty wind. Using the method of multiple scales, a nonlinear Schrödinger equation is obtained for the case of wind forced weakly nonlinear deep water waves. Thereby, the wind forcing is modeled as a stochastic process. This leads to a stochastic nonlinear Schrödinger equation, which is calculated for different wind regimes. For the case of wind forcing which is either random in time or random in space, it is shown that breather type solutions such as the Peregrine breather occur even in strong gusty wind conditions.

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Frequency downshift in a viscous fluid

Cited by 22 publications

References 20 publications

A comparison of frequency downshift models of wave trains on deep water

A comparison of frequency downshift models of wave trains on deep water

Nonconservative higher-order hydrodynamic modulation instability

Study on the behavior of weakly nonlinear water waves in the presence of random wind forcing

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