Business School

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ABSTRACT Kolmogorov's refined similarity hypothesis (RSH) is extended to study the inertial-range scaling of a passive scalar advected by a rapidly changing incompressible velocity field in d dimensions. For zeta2>d, the non-negativity of the scalar dissipation rate constrains the 2nth order scaling exponents, zeta2n, 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>=2, the exponents are found to be zeta2n = 12 [d-zeta2-g\(n\)zeta2]2+4ng\(n\)zeta2\(d-zeta2\)-12 [d-zeta2-g\(n\)zeta2], where g\(n\) = \(2n-1\) /.