REFINED SIMILARITY HYPOTHESIS FOR A RANDOMLY ADVECTED PASSIVE SCALAR

Kolmogorov's refined similarity hypothesis (RSH) is extended to study the inertial-range scaling of a passive scalar advected by a rapidly c hanging incompressible velocity field in d dimensions. For zeta(2) > d , the non-negativity of the scalar dissipation rate constrains the 2nt h order scaling exponents, zeta(2n), to be linear in n asymptotically. With the RSH formulated in terms of a stochastic variable theta, the molecular-diffusion terms are evaluated in general d dimensions. For d greater than or equal to 2, the exponents are found to be zeta(2n) = 1/2 root[d - zeta(2) - g(n)zeta(2)](2) + 4ng(n)zeta(2)(d - zeta(2)) - 1/2[d - zeta(2) - g(n)zeta(2)], where g(n) = (2n - 1)[theta(2n-2)][the ta(2)]/[theta(2n)]. [S0031-9007(97)04461-X].