Title:
1D Burgers Turbulence as a model case for the Kolmogorov Theory
Abstract:
The Kolmogorov 1941 theory (K41) is, in a way, the starting point for
all models of turbulence. In particular, K41 and corrections to it
provide estimates of small-scale quantities such as increments and
energy spectrum for a 3D turbulent flow. However, because of the
well-known difficulties involved in studying 3D turbulent flows, there
are no rigorous results confirming or infirming those predictions. Here,
we consider a well-known simplified model for 3D turbulence: Burgulence,
or turbulence for the 1D Burgers equation. In the space-periodic case
with a stochastic white in time and smooth in space forcing term, we
give sharp estimates for small-scale quantities such as increments and
energy spectrum.