  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 $\RE\to \infty$.
