THE ANOMALOUS DIFFUSION OF THE SELF-INTERACTING PASSIVE SCALAR IN THETURBULENT ENVIRONMENT

Two variants of the statistical model of diffusing self-interacting pa ssive scalar theta(x, t) driven by the incompressible Navier-Stokes tu rbulence were studied by means of the field-theoretical renormalizatio n group technique and epsilon-expansion scheme, where epsilon denotes the parameter of the forcing spectrum. Dual integral d(d)xdt[theta(x, t)](2) and triple integral d(d)xdt[theta(x, t)](3) interaction terms o f the action represent two different mechanisms of the self-interactio n matching two alternative values of the critical dimension: d(c) = 4 and d(c) = 6. The major part of the calculations was carried out in th e one loop order, nevertheless, the inclusion of the specific two loop contributions represents the important step of the analysis of some r enormalization group functions. In the basic model variant the effecti ve action is renormalizable for the supercritical dimensions d > d(c). This theory exhibits the presence of the asymptotical regime, which i s stable for the inertial-conductive range of wave numbers. It was als o shown that stability of this regime remains preserved for a variety of the parametric paths connecting domain epsilon > 0, d > d(c) with e psilon < 2, d = 3. In the second model variant, the effective action i s constructed to be renormalizable at dimensions d > d(c) and to justi fy the realizability of the continuation from epsilon > 0, d > d(c) to epsilon < 2, d = 3. This variant of the model was analyzed using ''do uble expansion'' method with the expansion parameters (d - d(c))/2 and epsilon. The negative correction zeta (zeta similar or equal to 0.039 for d = 3) to the universal Richardson exponent 4/3 is the physical c onsequence stemming from the calculations.