# Burgers Turbulence

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Modeling turbulent flow is one of the most difficult problems in fluid dynamics. Solutions to the Navier–Stokes equations, the full set of partial differential equations that represent fluid flow, are unstable for turbulent fluids. A highly simplified version of the Navier–Stokes equations, yet one that contains that same type of nonlinearity, is the one-dimensional inviscid (i.e., zero viscosity) Burgers equation, given by

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Contributed by: Garrett Neske (March 2011)

Open content licensed under CC BY-NC-SA

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References:

J. M. Burgers, "Mathematical Examples Illustrating Relations Occurring in the Theory of Turbulent Fluid Motion," *Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Natuurkunde. Tweede Sectie*, 17, 1939 pp. 1–53.

U. Frisch and J. Bec, "Burgulence," in *New Trends in Turbulence*, M. Lesieur, A. Yaglom, and F. David, eds., Berlin: Springer-Verlag, 2001.

W. E and E. Vanden Eijnden, "Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit," *Communications on Pure and Applied Mathematics.*, 53, 2000 pp. 852–901.

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