Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free Surface in 2D Potential Flow: Singularities, Invariants and Virtual
  Fluid   We study a 2D potential flow of an ideal fluid with a free surface with
decaying conditions at infinity. By using the conformal variables approach, we
study a particular solution of Euler equations having a pair of square--root
branch points in the conformal plane, and find that the analytic continuation
of the fluid complex potential and conformal map define a flow in the entire
complex plane, excluding a vertical cut between the branch points. The expanded
domain is called the ``virtual'' fluid, and it contains a vortex sheet whose
dynamics is equivalent to the equations of motion posed at the free surface.
The equations of fluid motion are analytically continued to both sides of the
vertical branch cut (the vortex sheet), and additional time--invariants
associated with the topology of conformal plane and Kelvin's theorem for
virtual fluid are discovered. We called them ``winding'' and virtual
circulation. This result can be generalized to a system of many cuts connecting
many branch points, and resulting in a pair of invariants for each pair of
branch points. We develop an asymptotic theory that shows how a solution
originating from a single vertical cut forms a singularity at the free surface
in infinite time, the rate of singularity approach is double-exponential, and
supercedes the previous result of the short branch cut theory with finite time
singularity formation.
  The present work offers a new look at fluid dynamics with free surface by
unifying the problem of motion of vortex sheets, and the problem of 2D water
waves. A particularly interesting question that arises in this context is
whether Kelvin--Helmholtz instability for virtual vortex sheet is related to
breaking of steep ocean waves.

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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys