Asymptotic Theory for the Probability Density Functions in Burgers Turbulence
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynolds number (inviscid) limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the dissipative anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than {vert_bar}{xi}{vert_bar}{sup {minus}3} . A further argument confirms the prediction of E {ital et al.}thinspthinsp[Phys.thinspthinspRev.thinspthinspLett.thinspthinsp{bold 78}, 1904 (1997)] that it should decay as {vert_bar}{xi}{vert_bar}{sup {minus}7/2} . {copyright} {ital 1999} {ital The American Physical Society}
- OSTI ID:
- 692514
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 13 Vol. 83; ISSN 0031-9007; ISSN PRLTAO
- Country of Publication:
- United States
- Language:
- English
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