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29 March 2020
  » arxiv » nlin.CD/0305019

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Multi-Zone Shell Model for Turbulent Wall Bounded Flows
Victor S. L’vov ; Anna Pomyalov ; Vasil Tiberkevich ;
Date 12 May 2003
Journal Phys. Rev. E, v. 68, 046308 (2003) DOI: 10.1103/PhysRevE.68.046308
Subject Chaotic Dynamics | nlin.CD
AbstractWe suggested a emph{Multi-Zone Shell} (MZS) model for wall-bounded flows accounting for the space inhomogeneity in a "piecewise approximation", in which cross-section area of the flow, $S$, is subdivided into "$j$-zones". The area of the first zone, responsible for the core of the flow, $S_1simeq S/2$, and areas of the next $j$-zones, $S_j$, decrease towards the wall like $S_jpropto 2^{-j}$. In each $j$-zone the statistics of turbulence is assumed to be space homogeneous and is described by the set of "shell velocities" $u_{nj}(t)$ for turbulent fluctuations of the scale $propto 2^{-n}$. The MZS-model includes a new set of complex variables, $V_j(t)$, $j=1,2,... infty$, describing the amplitudes of the near wall coherent structures of the scale $s_jsim 2^{-j}$ and responsible for the mean velocity profile. Suggested MZS-equations of motion for $u_{nj}(t)$ and $V_j(t)$ preserve the actual conservations laws (energy, mechanical and angular momenta), respect the existing symmetries (including Galilean and scale invariance) and account for the type of the non-linearity in the Navier-Stokes equation, dimensional reasoning, etc. The MZS-model qualitatively describes important characteristics of the wall bounded turbulence, e.g., evolution of the mean velocity profile with increasing Reynolds number, $RE$, from the laminar profile towards the universal logarithmic profile near the flat-plane boundary layer as $RE o infty$.
Source arXiv, nlin.CD/0305019
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