INTERMITTENCY AND ANOMALOUS SCALING OF PASSIVE SCALARS IN ANY SPACE DIMENSION

We establish exact inequalities for the structure-function scaling exp onents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity structure functions and, in a refined form, an intermittency exponent of the convective-range scalar flux. They ar e valid for three-dimensional Navier-Stokes turbulence and satisfied w ithin errors by present experimental data. The inequalities also hold for any ''synthetic'' turbulent velocity statistics with a finite corr elation in time. We show that for time-correlation exponents of the ve locity smaller than the ''local turnover'' exponent, the scalar spectr al exponent is strictly less than that in Kraichnan's [Phys. Rev. Lett . 72, 1016 (1994); Phys. Fluids 11, 945 (1968); J. Fluid Mech. 64, 737 (1974); 62, 305 (1974)] soluble ''rapidchange'' model with velocity d elta correlated in time. Our results include as a special case an expo nent inequality derived previously by Constantin and Procaccia [Nonlin earity 7, 1045 (1994)], but with a more direct proof. The inequalities in their simplest form follow from a Kolmogorov-type relation for the turbulent passive scalar valid in each space dimension d. Our improve d inequalities are based upon a rigorous version of the refined simila rity hypothesis for passive scalars. These are compared with the relat ions implied by ''fusion rules'' hypothesized for scalar gradients.