VISCOUS LENGTHS IN HYDRODYNAMIC TURBULENCE ARE ANOMALOUS SCALING FUNCTIONS

It is shown that the idea that scaling behavior in turbulence is limit ed by one outer length L and one inner length eta is untenable. Every nth order correlation function of velocity differences F-n(R(1), R(2), ...) exhibits its own crossover length eta(n) to dissipative behavior as a function of R(1). This depends on n and on the remaining separati ons R(2)/R(3),.... One result is that when separations are of the same order R, this scales as eta(n)(R)similar to eta(R/L)(xn) with )=(zeta (n)-zeta(n+1)+zeta(3)-zeta(2))/(2-zeta(2)), zeta(n) the scaling expone nt of the nth order structure function. We derive an infinite set of s caling relations that bridge the exponents of correlations of gradient fields to the exponents zeta(n), including the ''bridge relation'' fo r the scaling exponent of dissipation fluctuations mu=2-zeta(6).