** Authors:**
Ayşe ERZAN

** Abstract: **
It has recently been proposed [1] that in
highly developed hydrodynamic turbulence the dissipation field has
an anomalous scaling behaviour independent of the velocity fields.
The anomalous scaling exponent is ``subcritical" so that the
Kolmogorov scaling behaviour of the velocity fields is retained in
the
limit of Re\to \infty. On the other hand, the formation of
vortex
tubes leading to local isotropy-breaking has been shown to give
rise
to anomalous scaling behaviour of the moments of the derivatives
of the velocity field, \partial_\alpha u_\beta,
in terms of which one is able to define an
"anisotropy factor" [2].
We argue that the formation of the locally two-dimensional
structures, namely the vortex tubes, is also what gives
rise to the anomalous behaviour of the dissipation field, since the
dissipation field itself is defined in terms of the velocity
gradients
as \epsilon \equiv
\langle \nu \vert \nabla u\vert ^2\rangle,
so that the ``anisotropy factor" [2] and \epsilon can be related
by
operator algebra. We also examine the lowest order term in the
expansion of \epsilon in
terms of the
nonlinearity in the Navier Stokes equations.
It is the logarithmic singularity
in this term that later sums, via ladder diagrams, up to a
correction to
the scaling behaviour.
We show how
vortex tubes and sheets may contribute.

** Keywords: **