By Victor Shrira, Sergei Nazarenko
Wave or susceptible turbulence is a department of technology focused 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. even with the big variety of wave fields in nature, there's a universal conceptual and mathematical middle which permits to explain the approaches of random wave interactions in the related conceptual paradigm, and within the related language. the advance of this middle and its hyperlinks with the purposes is the essence of wave turbulence technological know-how (WT) that's a longtime necessary a part of nonlinear technological know-how.
The ebook comprising seven studies goals at discussing new demanding situations in WT and views of its improvement. a distinct emphasis is made upon the hyperlinks among the idea and scan. all of the reports is dedicated to a selected box of software (there is not any overlap), or a unique method or notion. The reports disguise numerous purposes of WT, together with water waves, optical fibers, WT experiments on a steel plate and observations of astrophysical WT.
Readership: Researchers, execs and graduate scholars in mathematical physics, power stories, good & fluid mechanics, and complicated structures.
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Extra info for Advances in Wave Turbulence
Since measurements usually involve the time signal at a given point, we have to settle for SN (0, τ ). For surface waves, the second-order structure function is ∞ S2 (τ ) = 2 0 I(ω)(1 − cos(ωτ ))dω, where I(ω) = (πω/2ν 2 )(dk2 /dω)nk (ω), ω 2 = kν 2 = gk + (S/ρ)k 3 is the Fourier transform of the two point correlation η(x, t)η(x, t + τ ) . For capillary waves, I(ω) = cP 1/2 (S/ρ)1/6 ω −17/6 is the direct energy ﬂux spectrum. If this shape was valid for the entire April 4, 2013 22 15:56 9in x 6in Advances in Wave Turbulence b1517-ch01 Advances in Wave Turbulence ∞ range, then S2 (τ ) = 2cP 1/2 (S/ρ)1/6 τ 11/6 0 ξ −17/6 (1 − cos ξ)dξ.
Three reasons might be given to explain the steeper spectrum. The ﬁrst has been suggested by Josserand (private communication) who included broadband damping and found that the spectrum indeed did decay as ω −s , s > 0 where s could be tuned by the choice of damping. The second is that the spectrum is steepened by ﬁnite size eﬀects. The third, an explanation more in tune with the discussion in Sec. 2 is that the plate deformation dynamics is dominated by d-cone singularities (Cerda and Mahadevan, 1998).
Mahadevan. 4. Condensates of classical light waves In a recent article Sun et al. (2011) have demonstrated experimentally that classical light waves can, via resonant nonlinear wave interactions, condense into a k = 0 plane wave mode. 25 Nb2 O6 whose coupling strength is controlled by applying a voltage. They show clearly that as the nonlinearity increases, there is a strong condensation. The system is isolated and indeed at high wavenumbers, they observe the familiar k −2 Rayleigh–Jeans spectrum with zero chemical potential.
Advances in Wave Turbulence by Victor Shrira, Sergei Nazarenko