Multi-Zone Shell Model for Turbulent Wall Bounded Flows
| dc.creator | L'vov, Victor S. | |
| dc.creator | Pomyalov, Anna | |
| dc.creator | Tiberkevich, Vasil | |
| dc.date | 2003-05-12 | |
| dc.date.accessioned | 2026-07-07T05:34:44Z | |
| dc.date.available | 2026-07-07T05:34:44Z | |
| dc.description | We 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, $S_1\simeq S/2$, and areas of the next $j$-zones, $S_j$, decrease towards the wall like $S_j\propto 2^{-j}$. 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 $s_j\sim 2^{-j}$ 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 $\RE\to \infty$. | |
| dc.description | 27 pages, 17 figs, included, PRE, submitted | |
| dc.identifier | https://arxiv.org/abs/nlin/0305019 | |
| dc.identifier | http://arxiv.org/abs/nlin/0305019 | |
| dc.identifier | Phys. Rev. E, v. 68, 046308 (2003) | |
| dc.identifier | doi:10.1103/PhysRevE.68.046308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80479 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Multi-Zone Shell Model for Turbulent Wall Bounded Flows | |
| dc.type | text |