Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Field Theory of Turbulence   We revisit the problem of stationary distribution of vorticity in
three-dimensional turbulence. Using Clebsch variables we construct an explicit
invariant measure on stationary solutions of Euler equations with the extra
condition of fixed energy flow/dissipation. The asymptotic solution for large
circulation around large loops is studied as a WKB limit (instanton). The
Clebsch fields are discontinuous across minimal surface bounded by the loop,
with normal vorticity staying continuous. There is also a singular tangential
vorticity component proportional to $\delta(z)$ where $z$ is the normal
direction. Resulting flow has nontrivial topology. This singular tangent
vorticity component drops from the flux but dominates the energy dissipation as
well as the Biot-Savart integral for velocity field. This leads us to a
modified equation for vorticity distribution along the minimal surface compared
to that assumed in a loop equations, where the singular terms were not noticed.
In addition to describing vorticity distribution over the minimal surface, this
approach provides formula for the circulation PDF, which was elusive in the
Loop Equations.

21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex