By Victor Shrira, Sergei Nazarenko
Wave or vulnerable turbulence is a department of technological know-how fascinated by the evolution of random wave fields of all types and on all scales, from waves in galaxies to capillary waves on water floor, from waves in nonlinear optics to quantum fluids. inspite of the large variety of wave fields in nature, there's a universal conceptual and mathematical middle which permits to explain the procedures of random wave interactions in the comparable conceptual paradigm, and within the similar language. the improvement of this middle and its hyperlinks with the purposes is the essence of wave turbulence technological know-how (WT) that is a longtime imperative a part of nonlinear technological know-how.
The ebook comprising seven experiences goals at discussing new demanding situations in WT and views of its improvement. a different emphasis is made upon the hyperlinks among the idea and scan. all of the studies is dedicated to a selected box of software (there isn't any overlap), or a unique strategy or proposal. The experiences hide quite a few purposes of WT, together with water waves, optical fibers, WT experiments on a steel plate and observations of astrophysical WT.
Readership: Researchers, pros and graduate scholars in mathematical physics, power reviews, reliable & fluid mechanics, and complicated structures.
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Additional info for Advances in Wave Turbulence
As such they are rather reminiscent of “rogue” or “freak” waves, found in oceans and in nonlinear optical media. These coherent objects evolve in shape and in speed because they generate radiating tails (cf. Cerenkov radiation) which drain their power. As a result, their central wavenumber becomes larger and they evolve so as eventually to resemble quasisolitons whose q/k0 is small. At this stage, the feed to the radiating tail becomes exponentially small. If one posits that the ﬁeld is dominated by an ensemble of such objects at diﬀerent stages of their lifetimes, then the MMT spectrum is recovered.
5. 18) uniformly asymptotic in k, and that the ratio tL /tNL is uniformly small in k. With forcing and damping, the ﬁrst truncation leads to a statistically steady state except in cases such as acoustic waves or Alfv´en waves where the resonant manifolds foliate wavevector space. See the ﬁrst challenge in Sec. 6 and the shape of the KZ spectrum in Galtier et al. (2000). The kinetic equation dnk /dt = 4 T4 [nk ] is independent of the sign of 1 s2 s3 the coeﬃcient Gss kk1 k2 k3 , but the ﬁrst frequency correction is not.
In Q2d, we will discuss the highly important case of the MMT equation with λ = 1, which is Benjamin–Feir unstable, but has no collapses. Q2d. The Majda-McLaughlin-Tabak conundrum. MMT for λ = 1. , 2009) obtained a new understanding of anomalous results presented by Majda et al. (1997). Numerical simulations of this equation showed that for λ = −1, with suﬃciently small initial conditions, one would recover the KZ spectrum nk ∼ k −1 spectrum as long as collapse events were rare. However, for the case λ = 1, MMT found a statistical steady state with the spectrum nk ∼ k −5/4 , distinctly diﬀerent from KZ over the whole range of wavenumbers.