Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field.
The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.
Jurcisinová
E
E
Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovakia.
Jurcisin
M
M
Remecký
R
R
D016880:Anisotropy; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012212:Rheology / Q000379:methods*; D013269:Stochastic Processes