By Victor Shrira, Sergei Nazarenko
Wave or susceptible turbulence is a department of technological know-how enthusiastic 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 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 quintessential a part of nonlinear technological know-how.
The publication comprising seven studies goals at discussing new demanding situations in WT and views of its improvement. a unique emphasis is made upon the hyperlinks among the idea and test. all of the reports is dedicated to a specific box of program (there is not any overlap), or a singular method or thought. The studies conceal quite a few 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, strength stories, reliable & fluid mechanics, and intricate platforms.
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Additional resources for Advances in Wave Turbulence
24), it is the only spectrum for which the ratio ttNL is independent of k. Thus, it has no low k high k breakdowns. April 4, 2013 30 15:56 9in x 6in Advances in Wave Turbulence b1517-ch01 Advances in Wave Turbulence 3. As we have shown (Newell and Zakharov, 2008), it is the spectrum that allows us to balance the nonlinear transfer S(ω) or T4 [nk ] with ∂p k dissipation. To see this, write the kinetic equation as ∂E ∂t = − ∂k − γk where ωk nk dk = Ek dk, p is the angle average ﬂux and γk is −αx k dissipation.
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 .
While there is some evidence of consistency between theory and experiment, much remains to be done. In particular, it would be valuable to measure the joint space–time power spectrum Φ(k, ω), the Fourier transform of η(x, t)η(x + r, t + τ ) . A necessary condition for a valid theory is that its support be concentrated upon the modiﬁed dispersion relation. 1. Capillary wave turbulence Weakly nonlinear capillary waves support three wave resonances. , 2007a, 2007b, 2008a, 2008b, 2009) April 4, 2013 15:56 9in x 6in Advances in Wave Turbulence 10 −3 10 −4 10 −5 10 −6 10 −7 10 −8 10 −9 10 −10 23 −3 2 PSD ( V / Hz ) Power Spectrum Density ( V 2 / Hz ) Wave Turbulence: A Story Far from Over b1517-ch01 10 −5 10 −7 10 −9 10 −11 10 4 10 4 10 100 200 Frequency (Hz) 100 500 Frequency (Hz) Fig.