Instantons in Burgers equation

The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent. The results agree with the one found recently by Polyakov, who used the operator product conjecture. If this conjecture is true, then our WKB asymptotics of the Wyld functional integral is exact to all orders of perturbation expansion around the instanton solution. We explicitly checked this in the first order. We also generalized our solution for the arbitrary dimention of Burgers (=KPZ) equation. As a result we find the angular dependence of the velocity difference PDF.

field equations: instanton
model: turbulence
WKB approximation: higher-order
correlation function
Burgers equation

References(6)

Figures(0)

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Alexander A. Migdal
(
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)

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•
e-Print:
- hep-th/9310088
•
DOI:
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Turbulence without pressure

Alexander M. Polyakov
(
- Princeton U.
)

- Phys.Rev.E 52 (1995) 6, 6183-6188
•
e-Print:
- hep-th/9506189
•
DOI:
- 10.1103/PhysRevE.52.6183

Turbulence without pressure

Alexander M. Polyakov
(
- Princeton U.
)

- Phys.Rev.E 52 (1995) 6, 6183-6188
•
e-Print:
- hep-th/9506189
•
DOI:
- 10.1103/PhysRevE.52.6183

Formulation of the theory of turbulence in an incompressible fluid

H.W Wyld

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DOI:
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- Phys.Rev.E 51 2739

- Phys.Rev.E 52 5681