2001/05/08 by Victor S. L’vov, Victor S. L'vov · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Fluid Dynamics and Turbulent Flows #Theoretical and Computational Physics #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.65.026309
published as Phys.Rev. E 65, 026309 (2002). · 11 pages, 8 figures (included), PRE, submitted
arxiv created 2001/05/08 · openalex publication_date 2002/01/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A variation principle is suggested to find self-similar solitary solutions (referred to as solitons) of shell model of turbulence. For the Sabra shell model the shape of the solitons is approximated by rational trial functions with relative accuracy of O(10(-3)). It is found how the soliton shape, propagation time t(n) (from a shell n to shells with n --> infinity), and the dynamical exponent z(0) (which governs the time rescaling of the solitons in different shells) depend on parameters of the model. For a finite interval of z the author discovered quasisolitons which approximate with high accuracy corresponding self-similar equations for an interval of times from -infinity to some time in the vicinity of the peak maximum or even after it. The conjecture is that the trajectories in the vicinity of the quasisolitons (with continuous spectra of z) provide an essential contribution to the multiscaling statistics of high-order correlation functions, referred to in the paper as an asymptotic multiscaling. This contribution may be even more important than that of the trajectories in the vicinity of the exact soliton with a fixed value z(0). Moreover there are no solitons in some regions of the parameters where quasisolitons provide a dominant contribution to the asymptotic multiscaling.