Recent experimental discovery of extended self-similarity (ESS) was one of
the most interesting developments. enabling precise determination of the sc
aling exponents of fully developed turbulence. A sufficient condition for e
xtended self-similarity in a general dynamical system is derived in this pa
per. It is also shown that if the pressure-gradient contributions are expre
ssed in terms of velocity differences in the mean-field approximation [V. Y
akhot, Phys. Rev. E 63, 026307 (2001)], then the ESS is a consequence of th
e Navier-Stokes equations.