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  • Cambridge University Press  (10)
  • American Institute of Physics  (5)
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  • 11
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    Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves (2018)
    Cambridge University Press
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    Publication Date: 2018-11-26
    Description: In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events. © 2018 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 12
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    On a random time series analysis valid for arbitrary spectral shape (2014)
    Cambridge University Press
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    Publication Date: 2014-10-23
    Description: While studying the problem of predicting freak waves it was realized that it would be advantageous to introduce a simple measure for such extreme events. Although it is customary to characterize extremes in terms of wave height or its maximum it is argued in this paper that wave height is an ill-defined quantity in contrast to, for example, the envelope of a wave train. Also, the last measure has physical relevance, because the square of the envelope is the potential energy of the wave train. The well-known representation of a narrow-band wave train is given in terms of a slowly varying envelope function ρ and a slowly varying frequency ω = -∂φ/∂t where φ is the phase of the wave train. The key point is now that the notion of a local frequency and envelope is generalized by also applying the same definitions for a wave train with a broad-banded spectrum. It turns out that this reduction of a complicated signal to only two parameters, namely envelope and frequency, still provides useful information on how to characterize extreme events in a time series. As an example, for a linear wave train the joint probability distribution of envelope height and period is obtained and is validated against results from a Monte Carlo simulation. The extension to the nonlinear regime is, as will be seen, fairly straightforward. © Cambridge University Press 2014.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 13
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    Quasilinear approximation for the spectrum of wind-generated water waves (1982)
    Cambridge University Press
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    Publication Date: 1982-04-01
    Description: According to Miles’ theory of wind-wave generation, water waves grow if the curvature of the wind profile at the critical height is negative. As a result, the wind profile changes in time owing to the transfer of energy to the waves. In thequasilinear approximation (where the interaction of the waves with one another is neglected) equations for the coupled air-water system are obtained by means of a multiple-time-scale analysis. In this way the validity of Miles’ calculationsis extended, thereby allowing a study of the large-time behaviour.While the water waves grow owing to the energy transfer from the air flow, the waves in turn modify the flow in such a way that for large times the curvature of the velocity profile vanishes. The amplitude of the waves is then limited because the energy transfer is quenched.In the high-frequency range the asymptotic wave spectrum is given by a ‘ - 4’ law in the frequency domain rather than the ‘ classical ‘ ‘ - 5 ‘ law. © 1982, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 14
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    On phase velocity and growth rate of wind-induced gravity-capillary waves (1985)
    Cambridge University Press
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    Publication Date: 1985-12-01
    Description: The generation and growth of gravity—capillary waves (A « 1 cm) by wind are reconsidered using linear instability theory to describe the process. For all friction velocities we solve the resulting Orr—Sommerfeld equation using asymptoticmethods. New elements in our theory, compared with the work of Benjamin (1959) andMiles (1962), aremore stress onmathematical rigour and the incorporation of the wind-induced shear current. We find that the growth rate of the initial wavelets, the first waves to be generated by the wind, is proportional to u. We also study the effect of changes in the shape of the profiles of wind and wind-induced current. In doing this we compare results ofMiles (1962), Larson & Wright (1975), Valenzuela (1976), Kawai (1979), Plant & Wright (1980) and our study. We find that the growth rate is very sensitive to the shape of the wind profile while the influence of changes in the current profile ismuch smaller. To determine correctly the phase velocity, the value of current and current shear at the interface are very important,muchmore so than the shape of either wind or current profile. © 1985, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 15
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    The initial evolution of gravity-capillary waves (1987)
    Cambridge University Press
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    Publication Date: 1987-11-01
    Description: In this paper we discuss the initial evolution of wind-generated, gravity-capillary waves by means of a dynamical model that includes the effects of wind input, viscous dissipation and three-wave interactions. In particular, we study the generation of the initial wavelets by wind and the subsequent migration of the peak of the spectrum to lower wavenumbers. Under certain conditions a sudden migration of the peak wavenumber is found. It is argued that this sudden migration is related to the phenomenon of second-harmonic resonance. We also observe that during the generation of the initial wavelets by wind, nonlinear three-wave interactions may be important. Therefore, the experimental determination of the growth rate of the waves by wind by just analysing the time series of the surface elevation (as is done by e.g. Kawai 1979 and Plant & Wright 1977) might be in error. © 1987, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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