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J Honkonen

Publications and source records attributed to J Honkonen.

12 recordsLinked to original sources
PubMed2005

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. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to correlation functions have not been found.

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PubMed2005

Two-loop calculation of the turbulent Prandtl number.

The turbulent Prandtl number has been calculated in the two-loop approximation of the epsilon expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of the earlier one-loop result with the experiment. This situation is drastically different from other available nontrivial two-loop results, which exhibit corrections of the magnitude of the one-loop term. The reason is traced to the mutual cancellation of additional divergences appearing in two dimensions, which have had a major effect on the results of previous calculations of other quantities.

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PubMed2005

Improved epsilon expansion for three-dimensional turbulence: two-loop renormalization near two dimensions.

An improved epsilon expansion in the d -dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order, which incorporates the effect of pole singularities at d--> 2 in coefficients of the epsilon expansion of universal quantities. For a proper account of the effect of these singularities, two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions. By direct calculation, it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two-loop order. On the other hand, a two-loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the ultraviolet (UV) renormalization theory. The latter renormalization prescription is used for the two-loop renormalization-group analysis amended with partial resummation of the pole singularities near two dimensions, leading to a significant improvement of the agreement with experimental results for the Kolmogorov constant.

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PubMed2005

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.

The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.

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PubMed2002

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

The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy spectrum of the velocity is chosen in the form E(k) proportional, variant k(1-2 epsilon ), and the correlation time at the wave number k scales as k(-2+eta). Inertial-range anomalous scaling for the structure functions and other correlation functions emerges as a consequence of the existence in the model of composite operators with negative scaling dimensions, identified with anomalous exponents. For eta> epsilon, these exponents are the same as in the rapid-change limit of the model; for eta< epsilon, they are the same as in the limit of a time-independent (quenched) velocity field. For epsilon =eta (local turnover exponent), the anomalous exponents are nonuniversal through the dependence on a dimensionless parameter, the ratio of the velocity correlation time, and the scalar turnover time. The nonuniversality reveals itself, however, only in the second order of the epsilon expansion and the exponents are derived to order epsilon (2), including anisotropic contributions. It is shown that, for moderate order of the structure function n, and the space dimensionality d, finite correlation time enhances the intermittency in comparison with both the limits: the rapid-change and quenched ones. The situation changes when n and/or d become large enough: the correction to the rapid-change limit due to the finite correlation time is positive (that is, the anomalous scaling is suppressed), it is maximal for the quenched limit and monotonically decreases as the correlation time tends to zero.

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PubMed2001

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. It is shown that in spite of the additional divergences, the kinetic fixed point associated with the Kolmogorov scaling regime remains stable for all space dimensions d > or =2 for rapidly enough falling off correlations of the magnetic forcing. A scaling regime driven by thermal fluctuations of the velocity field has been identified and analyzed. The absence of a scaling regime near two dimensions driven by the fluctuations of the magnetic field has been confirmed. A renormalization scheme has been put forward and numerically investigated to interpolate between the epsilon expansion and the double expansion.

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PubMed2001

Anomalous scaling in two models of passive scalar advection: effects of anisotropy and compressibility.

The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian, delta correlated in time, and scales with a positive exponent epsilon. Explicit inertial-range expressions for the scalar correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal anomalous exponents (dependent only on epsilon and alpha, the compressibility parameter). The complete set of anomalous exponents for the pair correlation functions is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(epsilon(2)) using the renormalization group. As in the incompressible case, the exponents exhibit a hierarchy related to the degree of anisotropy: the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. As the degree of compressibility increases, the corrections become closer to the leading terms. The small-scale anisotropy reveals itself in the odd ratios of correlation functions: the skewness factor slowly decreases going down to small scales for the incompressible case, but starts to increase if alpha is large enough. The higher odd dimensionless ratios (hyperskewness, etc.) increase, thus signaling persistent small-scale anisotropy; this effect becomes more pronounced for larger values of alpha.

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PubMed2000

Velocity-fluctuation-induced anomalous kinetics of the A+A--> reaction

The effect of a random velocity field on the kinetics of the single-species annihilation reaction A+A--> is analyzed near two dimensions with the aid of the perturbative renormalization group. The previously found asymptotic behavior induced by density fluctuations only in the diffusion-limited reaction is shown to be unstable to any velocity fluctuations (including thermal fluctuations near equilibrium) in spatial dimensions d</=d(c)=2. Four different stable long-time asymptotic regimes induced by the combined effect of velocity and density fluctuations are identified and the corresponding decay rates calculated in the leading order.

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PubMed2000

Asymptotic properties of Levy flights in quenched random fields

Long-time asymptotic behavior of the probability distribution function of Levy flights in quenched random fields is analyzed with the use of field-theoretic renormalization group. This problem has been recently studied with the aid of a dynamic renormalization group based on the momentum-shell integration method [H.C. Fogedby, Phys. Rev. E 58, 1690 (1998)]. While a great deal of the results of the quoted paper are confirmed by the present analysis, it is also shown that random field with long-range spatial correlations gives rise to asymptotic behavior with the dynamic critical exponent z less than the step index f of the Levy flights, for a finite range of values of f contrary to the conjecture that always z=f. In particular, in divergenceless random field z=d/2+1-alpha<f, when alpha<1+d/2-f and d<2+2alpha, and correlations fall off as r(-d+2alpha). The physical content of a new critical dimension proposed in the aforementioned paper in connection with the anomalous scaling of the diffusion coefficient is also discussed.

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PubMed2000

Manifestation of anisotropy persistence in the hierarchies of magnetohydrodynamical scaling exponents

An example of a turbulent system where the failure of the hypothesis of small-scale isotropy restoration is detectable both in the "flattening" of the inertial-range scaling exponent hierarchy and in the behavior of odd-order dimensionless ratios, e.g., skewness and hyperskewness, is presented. Specifically, within the kinematic approximation in magnetohydrodynamical turbulence, we show that for compressible flows, the isotropic contribution to the scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, the skewness factor now diverges as the Peclet number goes to infinity, a further indication of small-scale anisotropy.

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