Exact solutions of equations of rotationally symmetric motion of an ideal incompressible liquid
E. Yu. Meshcheryakova
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 397-405
Abstract
A partially invariant solution of the
Euler equations is considered, where the
vertical component of velocity is a
function of the vertical coordinate and
time, whereas the remaining components
of velocity and pressure are independent
of the polar angle in a cylindrical
coordinate system. Using the
classification of equations obtained by
analysis of an overdetermined system, we
consider two hyperbolic systems: the
first one describes the motion of a
cylindrical layer of an ideal
incompressible liquid under a punch, and
the second system allows obtaining
solutions in a half-cylinder with
singularities at the axis of symmetry. A
class of new exact solutions is
obtained, which describe vortex motion
of an ideal incompressible liquid,
including the motion with singularities
(sources of vortices) located along the
axis of symmetry.
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