  We consider self-similar solutions describing intermittent bursts in shell
models of turbulence, and study their relationship with blowup phenomena in
continuous hydrodynamic models. First, we show that these solutions are very
close to self-similar solution for the Fourier transformed inviscid Burgers
equation corresponding to shock formation from smooth initial data. Then, the
result is generalized to hyperbolic conservation laws in one space dimension
describing compressible flows. It is shown that the renormalized wave profile
tends to a universal function, which is independent both of initial conditions
and of a specific form of the conservation law. This phenomenon can be viewed
as a new manifestation of the renormalization group theory. Finally, we discuss
possibilities for application of the developed theory for detecting and
describing a blowup in incompressible flows.
