Progress in Turbulence II pp 37-40 | Cite as
An Exact Solution for the Forced Burgers Equation
Conference paper
Abstract
We derive the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. We present numerical results for fixed boundary conditions, and analyze the formation of shocks.
Keywords
Burger Equation Solvability Condition Joint Probability Distribution Spatial Coordinate Random Force
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.J.M. Burgers, The Nonlinear Diffusion Equation, D. Reidel, Dordrecht (1974).MATHGoogle Scholar
- 2.U. Frisch and J. Bec, Les Houches 2000: New Trends in Turbulence, M Lesieur, ed., Springer, Berlin (2001)Google Scholar
- 3.W.A. Woyczyński, Burgers-KPZ Turbulence, Springer, Berlin (1998)Google Scholar
- 4.E. Hopf, The partial differential equation ut + uux ⩵ uxx, Comm. Pure Appl. Math. 3 (1950), 201–230.MATHCrossRefMathSciNetGoogle Scholar
- 5.J.D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951), 225–236.MATHMathSciNetGoogle Scholar
- 6.A.M. Polyakov, Turbulence without pressure, Phys. Rev. E 52 (1995), 6183–6188.CrossRefMathSciNetGoogle Scholar
- 7.D.I. Pullin, P.G. Saffman, Vortex dynamics in turbulence, Anu. Rev. FluidMech. 30, 31 (1998)CrossRefMathSciNetGoogle Scholar
Copyright information
© Springer-Verlag 2007