Weak Alfvenic turbulence in a periodic domain is considered as a mixed state of Alfven waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed and indeed none is fou
nd. If the 2D modes are not directly forced, k^{-2} and k^{-1} spectra are found for the Alfven waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagting Alfven waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved.
E.V. Kozik and B.V. Svistunov (KS) paper Symmetries and Interaction Coefficients of Kelvin waves, arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010, contains a comment on paper Symmetries and Interaction coefficients of Kelvin waves, V. V. Lebedev and V
. S. Lvov, arXiv:1005.4575, 25 May 2010. It relies mainly on the KS text Geometric Symmetries in Superfluid Vortex Dynamics}, arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a symmetry argument prevents linear in wavenumber infrared asymptotics of the interaction vertex and thereby implies locality of the Kelvin wave spectrum previously obtained by these authors. In the present note we reply to their arguments. We conclude that there is neither proof of locality nor any refutation of the possibility of linear asymptotic behavior of interaction vertices in the texts of KS.
Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on Wave Turbulence, (WT) i.e. on the statistical behavior of
broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: Discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave clusters consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate, or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.
It is proposed that critical balance - a scale-by-scale balance between the linear propagation and nonlinear interaction time scales - can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave
systems. Magnetohydrodynamic (MHD), rotating and stratified turbulence are considered under this assumption and, in particular, a novel and experimentally testable energy cascade scenario and a set of scalings of the spectra are proposed for low-Rossby-number rotating turbulence. It is argued that in neutral fluids, the critically balanced anisotropic cascade provides a natural path from strong anisotropy at large scales to isotropic Kolmogorov turbulence at very small scales. It is also argued that the kperp^{-2} spectra seen in recent numerical simulations of low-Rossby-number rotating turbulence may be analogous to the kperp^{-3/2} spectra of the numerical MHD turbulence in the sense that they could be explained by assuming that fluctuations are polarised (aligned) approximately as inertial waves (Alfven waves for MHD).
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent termi
nal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel, used to study e.g. rain initiation and particle distributions in the atmosphere. We solve the kinetic equation analytically to obtain steady state and self-similar solutions in time and in height, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.
