  We study 2d vortex sheets with unbounded support. First we show a version of
the Biot- Savart law related to a class of objects including such vortex
sheets. Next, we give a formula associating the kinetic energy of a very
general class of ows with certain moments of their vorticities. It allows us to
identify a class of vortex sheets of unbounded support being only ?-finite
measures (in particluar including measures \omega such that \omega(R2) =
\infty), but with locally finite kinetic energy. One of such examples are
celebrated Kaden approximations. We study them in details. In particular our
estimates allow us to show that the kinetic energy of Kaden approximations in
the neighbourhood of an origin is dissipated, actually we show that the energy
is pushed out of any ball centered in the origin of the Kaden spiral. The
latter result can be interpreted as an artificial viscosity in the center of a
spiral.
