The modulational instability in deep water under the action of wind and dissipation
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Citations
Interplay of the pseudo-Raman term and trapping potentials in the nonlinear Schrödinger equation
Progresses in the Research of Oceanic Freak Waves: Mechanism, Modeling, and Forecasting
Evolution of water wave groups with wind action
Three-dimensional surface gravity waves of a broad bandwidth on deep water
Evolution of Water Wave Groups in the Forced Benney–Roskes System
References
Linear and Nonlinear Waves
Linear and Nonlinear Waves
Stability of periodic waves of finite amplitude on the surface of a deep fluid
The disintegration of wave trains on deep water Part 1. Theory
Linear and nonlinear waves
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Frequently Asked Questions (10)
Q2. What is the recurrence of the Fermi–Pasta–Ul?
The evolution of a two-dimensional nonlinear wave train on deep water, in the absence of dissipative effects, exhibits the Fermi–Pasta–Ulam recurrence phenomenon.
Q3. Why did they assume that damping might affect the early development of rogue waves?
Since damping affects the modulational instability of waves in deep water, they assumed that it might affect the early development of rogue waves.
Q4. What is the phase shift between the wind and the water waves?
For an energy flux to occur from the wind to the water waves, there must be a phase shift between the fluctuating pressure and the interface.
Q5. What is the purpose of this paper?
The present paper is aimed at reporting on the behaviour of Benjamin–Feir instability when dissipation and wind input are both taken into account.
Q6. What is the effect of wind and dissipation on the modulation of a?
In the presence of wind and dissipation, the unstable domain shrinks for low-frequency regime: this means that young waves are more sensitive to modulational instability than old waves.
Q7. What is the email address for correspondence?
Email address for correspondence: kharif@irphe.univ-mrs.frnearly uniform wave trains become modulated and then demodulated until they are again nearly uniform.
Q8. How can damping stop the growth of the sidebands?
when the perturbations are small initially, they cannot grow large enough for nonlinear resonant interaction between the carrier and the sidebands to become important.
Q9. What is the name of the potential water wave problem?
Since Stokes (1847), it is well known that the potential water wave problem admits as solutions uniform wave trains of two-dimensional progressive waves.
Q10. What is the criterion for linear stability?
This situation was discussed by Segur et al. (2005a, see their comment (iii) p. 238), and it was claimed that even with substantial growth of the perturbation, the Stokes solution of (3.4) is still linearly stable: it is always possible to find a gap (denoted ∆) between unperturbed and perturbed solution that satisfies the linear stability criterion.