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Quasilinear theory of the 2D Euler equation

Pierre-Henri Chavanis
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Abstract

We develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive a H-theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.

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Pierre-Henri Chavanis. 2000-08-03. Quasilinear theory of the 2D Euler equation. https://doi.org/10.1103/physrevlett.84.5512

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