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Wave Turbulence (Lecture Notes in Physics) by Sergey Nazarenko

By Sergey Nazarenko

Wave Turbulence refers back to the statistical thought of weakly nonlinear dispersive waves. there's a extensive and becoming spectrum of actual purposes, starting from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. past the basics the e-book hence additionally covers new advancements comparable to the interplay of random waves with coherent constructions (vortices, solitons, wave breaks), inverse cascades resulting in condensation and the transitions among vulnerable and robust turbulence, turbulence intermittency in addition to finite procedure dimension results, akin to “frozen” turbulence, discrete wave resonances and avalanche-type power cascades. This e-book is an outgrow of numerous lectures classes held by way of the writer and, for that reason, written and based fairly as a graduate textual content than a monograph, with many routines and options provided alongside the way in which. the current compact description essentially addresses scholars and non-specialist researchers wishing to go into and paintings during this box.

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Tech. 4, 22–24 (1965)] 121. : Kolmogorov spectra in weak turbulence problems. N. ) Handbook of Plasma Physics, vol. 2, Basic Plasma Physics, pp. 3–36. North-Holland, Elsevier (1984) 122. : Energy spectrum for stochastic oscillations of a fluid surface. Dokl. Acad. Nauk SSSR 170, 1292–1295 (1966) (translation: Sov. Phys. Dokl. 11, 881–884 (1967)) 123. : Weak turbulence of capillary waves. Zh. Prikl. Mekh. Tekh. Phys. 4(5), 62 (1967) (in Russian: J. Appl. Mech. Tech. Phys. 4, 506) 124. : Wave turbulence in onedimensional models.

3 Stratified Turbulence For turbulence in a stratified fluid, like in the surface gravity wave example, one can assume that there is only one relevant dimensional parameter,—in this case the buoyancy frequency XN . CB-equating of the linear and nonlinear dynamical terms is equivalent to saying that XN will be the only dimensional parameter defining the energy spectrum. Taking into account that strong stratification leads to strong anisotropy with pancake-like structures, kV ) kH, we get ð1DÞ Ek $ X2N kVÀ3 : ð3:32Þ This spectrum was obtained by Dewan [32] and Billand and Chomaz [33].

Phys. Dokl. 32, 560 (1987) 130. : Canonical variables for Rossby waves and plasma drift waves. Phys. Lett. A 126(8–9), 497 (1988) 14 1 Introduction 131. : Spectrum of acoustic turbulence. Sov. Phys. Dokl. 15, 439 (1970) 132. : Sov. Phys. JETP 25, 718 (1967) 133. : Cosmological experiments in superfluid helium? Nature 317, 505 (1985) 134. : Acta. Phys. 1 Basic Facts about Hydrodynamic Turbulence The name ‘‘Wave Turbulence’’ may appear paradoxical to people unfamiliar with the subject, because traditionally turbulence is associated mostly with vortices, and the waves are only secondary.

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