Some novel ideas in turbulence studies.
Practical aspect: Mixing and segregation in random flows.
Fundamental aspect: Strong fluctuations, symmetries and anomalies.
Imperial College, December 2005
Passive scalar decay
Small spherical spot released in a smooth flow with
→ singular (fractal) SRB Measure
An anomalous scaling corresponds to slower divergence of particles to get more weight.
Statistical integrals of motion (zero modes) of the backward-in-time evolution compensate
the increase in the distances by the mass decrease inside the volume.
Spatially smooth flow
Equivalent in 1d to Anderson localization:
localization length = Lyapunov exponent
All known cases of anomalies (symmetry remains
broken when symmetry breaking factor goes to zero)
can be traced to conserved quantities.
Anomalous scaling is due to statistical conservation laws.