By Victor Shrira, Sergei Nazarenko

Wave or vulnerable turbulence is a department of technology keen on 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. despite the large variety of wave fields in nature, there's a universal conceptual and mathematical middle which permits to explain the tactics of random wave interactions in the comparable conceptual paradigm, and within the related language. the advance of this middle and its hyperlinks with the functions is the essence of wave turbulence technological know-how (WT) that's a longtime quintessential a part of nonlinear technological know-how.

The booklet comprising seven reports goals at discussing new demanding situations in WT and views of its improvement. a distinct emphasis is made upon the hyperlinks among the speculation and test. all of the stories is dedicated to a specific box of program (there is not any overlap), or a unique procedure or suggestion. The reports conceal various functions 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 stories, good & fluid mechanics, and intricate structures.

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If there is no dissipation sink there (as there might be in semiconductor laser context where lasing occurs at the minimum bandgap, namely low k), then a condensate will build. We will discuss here what happens in the self-focusing case for which λ = −1. The condensate is Benjamin–Feir unstable, and the resulting structures which emerge are fully nonlinear coherent pulses which collapse by becoming singular (infinite amplitudes, infinitesimal width) in a finite time t∗ . The collapses are the mechanisms through which power is carried from low to high wavenumbers at which dissipation acts.

The front now travels as kf ∝ (t∗ − t)a , a < 0 and leaves in its wake a spectrum k −x where the exponent x = b/|a| is greater than the KZ value and can only be determined by solving a nonlinear eigenvalue problem. Only after the front hits the dissipation range, does, the KZ spectrum build up backwards from k = ∞. , 2003a; Connaughton and Newell, 2010). April 4, 2013 15:56 9in x 6in Advances in Wave Turbulence Wave Turbulence: A Story Far from Over b1517-ch01 21 5. Breakdown of KZ spectra. To test the validity of P3, let us compute tL /tNL = (nk ωk )−1 dnk /dt on the spectrum nk = ck −αx for the case where T2 [nk ] ≡ 0.

2. Are there situations for which the wave turbulence closure is not relevant at all, at any scale? If this were to be the case, and it is, can we identify what additional premises are needed, premises whose validity can be checked beforehand, which, together with P1, P2 and P3, would be sufficient to guarantee the self-consistency of the wave turbulence closure or to establish that transfer is achieved by processes entirely different from resonant wave interactions? The answers to these questions are: 1.

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