By Victor Shrira, Sergei Nazarenko
Wave or vulnerable turbulence is a department of technology 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. despite the big variety 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 comparable conceptual paradigm, and within the related language. the advance of this center and its hyperlinks with the functions is the essence of wave turbulence technological know-how (WT) that is a longtime fundamental a part of nonlinear technological know-how.
The ebook comprising seven reports goals at discussing new demanding situations in WT and views of its improvement. a different emphasis is made upon the hyperlinks among the speculation and test. all of the experiences is dedicated to a selected box of software (there isn't any overlap), or a singular method or suggestion. The reports conceal a number of 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, strength stories, good & fluid mechanics, and intricate structures.
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Extra resources for Advances in Wave Turbulence
Collapses and the cycle of intermittency. The model, applicable for optical waves of diﬀraction in a Kerr nonlinear medium, is the NLS equation with Hamiltonian 12 (|∇u|2 + λ|u|4 )dx. For power input Q0 and energy input P0 (here energy is the spectral density of the Hamiltonian) put in at middle scales ω0 , the power cascades to low wavenumbers. The KZ inverse cascade suﬀers breakdown at low wavenumbers. 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.
If the Fourier transforms of v(x) and w(x) are V (k) and W (k), then the Fourier transform of v(x)w(x) is V (k1 )W (k2 )δ(k1 + k2 − k)dk1 dk2 . 5) 1 ∂φ 2 ∂z 2 + gη − σ∇2 η/(1 + (∇η)2 )3/2 = 0. 6) are applied at the surface z = η(x, t). Here g is gravity and σ = S/ρ, the surface tension divided by density. 6) about z = η and keep only terms to quadratic order. 7) 2 at z = 0. 8) April 4, 2013 15:56 9in x 6in Advances in Wave Turbulence b1517-ch01 Advances in Wave Turbulence 40 Let Nk and Fk be the Fourier transforms of η(x, t) and φ(x, 0, t).
Vibrating plate turbulence: can one hear the Kolmogorov spectrum? During et al. (2006) derived and analyzed the wave turbulence of vibrations ωk ∝ |k|2 on large, thin, elastic plates with normal deformations η(x, t) governed by the von Karman–Donnell equations. 21), but with the distinct feature that, unlike gravity waves and optical waves of diﬀraction, the restriction that the four wave interaction preserves wavenumbers is no longer required. As a result, there is only one equipartition solution nk = T /ωk ∝ k −2 and the KZ direct energy ﬂux solution nk ∝ k −2 .
Advances in Wave Turbulence by Victor Shrira, Sergei Nazarenko