  We argue on the basis of empirical data that Kolmogorov's refined similarity
hypothesis (RSH) needs to be modified for transverse velocity increments, and
propose an alternative. In this new form, transverse velocity increments bear
the same relation to locally averaged enstrophy (squared vorticity) as
longitudinal velocity increments bear in RSH to locally averaged dissipation.
We support this hypothesis by analyzing high-resolution numerical simulation
data for isotropic turbulence. RSH and its proposed modification for transverse
velocity increments (RSHT) appear to represent two independent scaling groups.
