Abstract
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 |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2572-2575 |
| Number of pages | 4 |
| Journal | Physical Review Letters |
| Volume | 83 |
| Issue number | 13 |
| State | Published - Sep 27 1999 |
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Asymptotic theory for the probability density functions in burgers turbulence. / Weinan, E.; Vanden Eijnden, Eric.
In: Physical Review Letters, Vol. 83, No. 13, 27.09.1999, p. 2572-2575.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic theory for the probability density functions in burgers turbulence
AU - Weinan, E.
AU - Vanden Eijnden, Eric
PY - 1999/9/27
Y1 - 1999/9/27
N2 - 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 |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.
AB - 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 |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.
UR - http://www.scopus.com/inward/record.url?scp=29444442507&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29444442507&partnerID=8YFLogxK
M3 - Article
VL - 83
SP - 2572
EP - 2575
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 13
ER -