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

Abstract

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. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that, although the separate composite operators which define them strongly depend on the helicity parameter, the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown.

Influence of helicity on the turbulent Prandtl number: Two-loop approximation

“…Our aim is to find the explicit dependence of the turbulent Prandtl number on the parameter that controls the presence of helicity in the turbulent system. We try to show that the presence of helicity can rather strongly influence the diffusion processes in fully developed turbulence in agreement with earlier results obtained in [11], where a possible strong influence of the helicity on the diffusion coefficient was shown.…”

“…In the nonhelical case (ρ = 0), the expansions of the renormalization constants Z i are known up to the second order in g (two-loop approximation); the explicit forms of the coefficients z (i) 11 , z (i) 21 , and z (i) 22 , i = 1, 2 were obtained in [7], [8], [13]. The simplest one-loop result for z…”

Anisotropic Turbulent Advection of a Passive Vector Field: Effects of the Finite Correlation Time

“…As well, this model can be viewed as a d-dimensional generalization of the strongly anisotropic velocity ensemble introduced in [5] in connection with the turbulent diffusion problem and further studied and generalized in a number of papers [6][7][8]. Following [9], we included into the stochastic advection-diffusion equation [see equation (2) below] an additional arbitrary dimensionless parameter A 0 , which unifies different physical situations: the kinematic MHD model, the linearized NS equation and the passive admixture with complex internal structure of the particles.…”

Influence of helicity on the turbulent Prandtl number: Two-loop approximation

“…Цель статьи -найти явную зависимость турбулентного числа Прандтля от параметра, который управляет наличием спиральности в турбулент-ной системе. Мы постараемся показать, что наличие спиральности может довольно сильно влиять на процессы диффузии в полностью развитой турбулентности, что согласуется с более ранними результатами, полученными в работе [11], где было показано, что возможно сильное влияние спиральности на коэффициент диффузии.…”