On the Large Time Asymptoticsof Decaying Burgers Turbulence
Abstract
The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and velocity differences are computed exactly, together with the "timelike" structure functions . The analysis of the answers reveals both well known features of Burgers turbulence, such as the presence of dissipative anomaly, the extreme anomalous scaling of the velocity structure functions and self similarity of the statistics of the velocity field, and new features such as the extreme anomalous scaling of the "timelike" structure functions and the nonexistence of a global inertial scale due to multiscaling of the Burgers velocity field. We also observe that all the results can be recovered using the one point probability distribution function of the shock strength and discuss the implications of this fact for Burgers turbulence in general.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/s002200000214
 arXiv:
 arXiv:chaodyn/9909027
 Bibcode:
 2000CMaPh.212..415T
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 LATEX, 25 pages, The present paper is an extension of the talk delivered at the workshop on intermittency in turbulent systems, Newton Institute, Cambridge, UK, June 1999