By Victor Shrira, Sergei Nazarenko
Wave or vulnerable turbulence is a department of technology serious about 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 range of wave fields in nature, there's a universal conceptual and mathematical middle which permits to explain the methods of random wave interactions in the related conceptual paradigm, and within the comparable language. the improvement of this center and its hyperlinks with the functions is the essence of wave turbulence technology (WT) that is a longtime quintessential a part of nonlinear technology.
The publication 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 speculation and scan. all of the studies is dedicated to a specific box of program (there isn't any overlap), or a singular procedure or thought. The experiences conceal 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, execs and graduate scholars in mathematical physics, power reports, strong & fluid mechanics, and intricate platforms.
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Extra info for Advances in Wave Turbulence
There is clear evidence of the theoretically predicted pure KZ energy ﬂux frequency spectrum I(ω) = (2π)−1 η(x, t)η(x, t + τ ) exp(−iωτ )dτ = cP 1/2 (S/ρ)1/6 ω −17/6 over at least a decade of frequencies in the ﬁrst experiment and over two decades in the second. 2 for narrowband input and is shown in Fig. 1. , 2007b) is almost Gaussian with the usual Tayfun correction expected from second harmonics excited by quadratic interactions. , 2010). However, the dependence of I(ω) on P , the energy ﬂux, is neither P 1/2 (nor P 1/3 ) as predicted but seems to be proportional to P .
Condensate Formation Modeled by the defocussing (λ = −1) NLS equation, this is an open and hot topic. , 2001)? (ii) Given a ﬁnite total energy and number of particles (and an ultraviolet cutoﬀ kc ), can one ﬁnd in the subcritical temperature range T < Tc , (at T = Tc , µ, the chemical potential is zero; for T < Tc , µ would be positive and the Rayleigh–Jeans equilibrium nk = T /(ωk − µ) singular), a wave turbulence description with a gradual transition from free April 4, 2013 38 15:56 9in x 6in Advances in Wave Turbulence b1517-ch01 Advances in Wave Turbulence waves (ωk = k 2 ) to Bogoliubov waves (ω = ± 2|λ|n0 k 2 + k 4 ) where n0 is the number of particles in the condensate?
Some parts of the initial ﬁeld behave as wavetrains made incoherent by interactions with the random medium. Because of their random phases, these parts are trapped (cf. Anderson localization). For them the medium is opaque. But another part of the initial pulse, the soliton component, can synchronize the ensemble of random oscillators and cause them to oscillate in lock step with each other and with the central frequency of the incoming pulse. For them, the medium is transparent. There is no Anderson localization.
Advances in Wave Turbulence by Victor Shrira, Sergei Nazarenko