Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: two-loop approximation.

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator-product expansion within the two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents epsilon-eta, where epsilon characterizes the energy spectrum of the velocity field in the inertial range E proportional to k(1-2epsilon), and eta is related to the correlation time at the wave number k, which is scaled as k(-2+eta). The restrictions given by nonzero helicity on the regions with stable fixed points that correspond to the scaling regimes are analyzed in detail.

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy.

Inertial-range scaling behavior of high-order (up to order N=51 ) two-point correlation functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. Exponents of the power-like asymptotic behavior of the correlation functions have been calculated in the one-loop approximation. These exponents are shown to depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed.

Turbulence with pressure: anomalous scaling of a passive vector field.

The field theoretic renormalization group (RG) and the operator-product expansion are applied to the model of a transverse (divergence-free) vector quantity, passively advected by the "synthetic" turbulent flow with a finite (and not small) correlation time. The vector field is described by the stochastic advection-diffusion equation with the most general form of the inertial nonlinearity; it contains as special cases the kinematic dynamo model, linearized Navier-Stokes (NS) equation, the special model without the stretching term that possesses additional symmetries and has a close formal resemblance with the stochastic NS equation. The statistics of the advecting velocity field is Gaussian, with the energy spectrum E(k) proportional to k(1-epsilon) and the dispersion law omega proportional to k(-2+eta), k being the momentum (wave number).

Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence.

A statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the kinetic energy spectrum have been calculated in the leading order in the Mach number expansion. Furthermore, in this approximation the validity of the Kolmogorov hypothesis on the independence of the dissipation length of velocity correlation functions in the inertial range has been proved.

Stochastic magnetohydrodynamic turbulence in space dimensions d > or =2.

Interplay of kinematic and magnetic forcing in a model of a conducting fluid with randomly driven magnetohydrodynamic equations has been studied in space dimensions d > or =2 by means of the renormalization group. A perturbative expansion scheme, parameters of which are the deviation of the spatial dimension from two and the deviation of the exponent of the powerlike correlation function of random forcing from its critical value, has been used in one-loop approximation. Additional divergences have been taken into account that arise at two dimensions and have been inconsistently treated in earlier investigations of the model.