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Zakharov, Yu. V.; Okhotkin, K. G.

doi:10.1023/a:1019800205519

Cited by 22 publications

(9 citation statements)

References 2 publications

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“…For narrow-band waves, the asymptotic solution of Nonlinear Schrödinger equation (NLS) is fully determined by the BFI value. For the Dysthe or Zakharov equation [13,14] the BFI is still relevant if the spectrum is sufficiently narrow. Here we investigate whether the quadratic relation proposed by Janssen [12] is valid after an episode of wind.…”

Section: Introductionmentioning

confidence: 99%

Single-spectrum prediction of kurtosis of water waves in a nonconservative model

et al. 2019

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We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher order Nonlinear Schrödinger equation (NLS). During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted. * maura.brunetti@unige.ch

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Section: Introductionmentioning

confidence: 99%

Single-spectrum prediction of kurtosis of water waves in a nonconservative model

et al. 2019

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“…To our knowledge, within the realm of physics these ''mythical functions'' [36] occur mainly in the theory of various problems in classical dynamics and electronic/optical oscillators [36][37][38], with only a limited number of applications in statics, e.g. for the bending of thin rods [39]. The mathematical background features ''notations and conventions that are often contradictory or difficult to understand by physicists'' [36].…”

Section: Jacobi Functionsmentioning

confidence: 99%

Description of the buckling of a chain of hard spheres in terms of Jacobi functions

Weaire

Mughal

Ryan-Purcell

et al. 2022

Physica D: Nonlinear Phenomena

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“…For s 0 < s < L the nonlinear differential equation for the shape of the hair can be solved in terms of elliptic functions [34].…”

Section: The Free Energymentioning

confidence: 99%

“…In order for these equilibria to be stable we require dθY d L > 0, in analogy with Eqn. (34), or equivalently that d L dθY > 0. However, examination of the righthand side of Eqn.…”

Section: Singletsmentioning

confidence: 99%

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Superhydrophobicity on Hairy Surfaces

Blow

Yeomans

2010

Langmuir

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We investigate the wetting properties of surfaces patterned with fine elastic hairs, with an emphasis on identifying superhydrophobic states on hydrophilic hairs. We formulate a 2D model of a large drop in contact with a row of equispaced elastic hairs and, by minimizing the free energy of the model, identify the stable and metastable states. In particular, we concentrate on partially suspended states, where the hairs bend to support the drop--singlet states, where all hairs bend in the same direction, and doublet states, where neighboring hairs bend in opposite directions--and find the limits of stability of these configurations in terms of the material contact angle, hair flexibility, and system geometry. The drop can remain suspended in a singlet state at hydrophilic contact angles, but doublets exist only when the hairs are hydrophobic. The system is more likely to evolve into a singlet state if the hairs are inclined at the root. We discuss how, under limited circumstances, the results can be modified to describe an array of hairs in three dimensions. We find that now both singlets and doublets can exhibit superhydrophobic behavior on hydrophilic hairs. We discuss the limitations of our approach and the directions for future work.

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Untitled

Cited by 22 publications

References 2 publications

Single-spectrum prediction of kurtosis of water waves in a nonconservative model

Single-spectrum prediction of kurtosis of water waves in a nonconservative model

Description of the buckling of a chain of hard spheres in terms of Jacobi functions

Superhydrophobicity on Hairy Surfaces

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