Dynamic multiscaling in stochastically forced Burgers turbulence
Abstract
We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced onedimensional Burgers equation. We introduce the concept of $\textit{interval collapse times}$ $\tau_{\rm col}$, the time taken for an interval of length $\ell$, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponent of the order$p$ moment of $\tau_{\rm col}$, we show that (a) there is $\textit{not one but an infinity of characteristic time scales}$ and (b) the probability distribution function of $\tau_{\rm col}$ is nonGaussian and has a powerlaw tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamicmultiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to dimensions $d >1 $, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08969
 Bibcode:
 2022arXiv220508969D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Fluid Dynamics