Intermittency of Burgers’ Turbulence

Disordered systems and Burgers’ turbulence

The problem of fully developped turbulence is to characterize the statistical properties of the velocity field of a stirred fluid described by Navier stokes equations. The simplest scaling approach, due to Kolmogorov in 1941, gives a reasonable starting point, but it must be corrected due to the failure of naive scaling giving ‘intermittency’ corrections which are presumably associated with the...

0 Aspects of the stochastic Burgers equation and their connection with turbulence

Aspects of the stochastic Burgers equation and their connection with turbulence. Summary. We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes...

Scaling and intermittency in Burgers turbulence.

Instanton theory of Burgers shocks and intermittency.

A Lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken Galilean invariance, the asymptotic form of the probability distribution function of negative velocity differences. The origin of Burgers intermittency is found to rely on the...

Ja n 19 99 Intermittency in turbulence

We derive from the Navier-Stokes equation an exact equation satisfied by the dissi-pation rate correlation function, < ǫ(x + r, t + τ)ǫ(x, t) >, which we study in the equal time limit. We exploit its mathematical similarity to the corresponding equation derived from the 1-dimensional stochastic Burgers equation to show that the main intermittency exponents are µ 1 = 2 − ζ 6 and µ 2 = 2 ˜ z 4 − ...

Statistics of turbulence in a generalized random-force-driven Burgers equation

The statistics of solutions to a family of one-dimensional random-force-driven advection-diffusion equations is studied using high resolution numerical simulations. The equation differs from the usual Burgers equation by the non-local form of the nonlinear interaction term mimicking the non-locality of the Navier–Stokes equation. It is shown that under an appropriate choice of random forcing th...