  Since Kolmogorov proposed his phenomenological theory of hydrodynamic
turbulence in 1941, the description of mechanism leading to the energy cascade
and anomalous scaling remains an open problem in fluid mechanics. Soon after,
in 1949 Onsager noticed that the scaling properties in inertial range imply
non-differentiability of the velocity field in the limit of vanishing
viscosity. This observation suggests that the turbulence mechanism may be
related to a finite-time singularity (blowup) of incompressible Euler
equations. However, the existence of such blowup is still an open problem too.
In this paper, we show that the blowup indeed represents the driving mechanism
of inertial range for a simplified (shell) model of turbulence. Here, blowups
generate coherent structures (instantons), which travel through the inertial
range in finite time and are described by universal self-similar statistics.
The anomaly (deviation of scaling exponents of velocity moments from the
Kolmogorov theory) is related analytically to the process of instanton creation
using the large deviation principle. The results are confirmed by numerical
simulations.
