Passive scalar: Sealing 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) far the difference theta in T across an inertial-range distance r is found to be Gaussian, Scaling exponents of moments of theta increase as root n or faster at large order n, if a mean dissipation conditioned on theta is a nondecreasing function of \theta\. 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.