Passive Scalar: Scaling Exponents and Realizability

An isotropic passive scalar field T advected by a rapidly varying velocity field is studied. The tail of the probability distribution P({theta},r) for the difference {theta} in T across an inertial-range distance r is found to be Gaussian. Scaling exponents of moments of {theta} increase as {radical}(n) or faster at large order n , if a mean dissipation conditioned on {theta} is a nondecreasing function of {vert_bar}{theta}{vert_bar} . The P({theta},r) computed numerically under the so-called linear ansatz is found to be realizable. Some classes of gentle modifications of the linear ansatz are not realizable. {copyright} {ital 1997} {ital The American Physical Society}