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E. Jurčišinová - One of the best experts on this subject based on the ideXlab platform.
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diffusion in anisotropic fully developed turbulence turbulent Prandtl Number
Physical Review E, 2016Co-Authors: E. Jurčišinová, M. JurčišinAbstract:Using the field theoretic renormalization group technique in the leading order of approximation of a perturbation theory the influence of the uniaxial small-scale anisotropy on the turbulent Prandtl Number in the framework of the model of a passively advected scalar field by the turbulent velocity field driven by the Navier-Stokes equation is investigated for spatial dimensions d>2. The influence of the presence of the uniaxial small-scale anisotropy in the model on the stability of the Kolmogorov scaling regime is briefly discussed. It is shown that with increasing of the value of the spatial dimension the region of stability of the scaling regime also increases. The regions of stability of the scaling regime are studied as functions of the anisotropy parameters for spatial dimensions d=3,4, and 5. The dependence of the turbulent Prandtl Number on the anisotropy parameters is studied in detail for the most interesting three-dimensional case. It is shown that the anisotropy of turbulent systems can have a rather significant impact on the value of the turbulent Prandtl Number, i.e., on the rate of the corresponding diffusion processes. In addition, the relevance of the so-called weak anisotropy limit results are briefly discussed, and it is shown that there exists a relatively large region of small absolute values of the anisotropy parameters where the results obtained in the framework of the weak anisotropy approximation are in very good agreement with results obtained in the framework of the model without any approximation. The dependence of the turbulent Prandtl Number on the anisotropy parameters is also briefly investigated for spatial dimensions d=4 and 5. It is shown that the dependence of the turbulent Prandtl Number on the anisotropy parameters is very similar for all studied cases (d=3,4, and 5), although the numerical values of the corresponding turbulent Prandtl Numbers are different.
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Turbulent Prandtl Number in the A model of passive vector admixture.
Physical Review E, 2016Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theoretic renormalization group technique in the second-order (two-loop) approximation the explicit expression for the turbulent vector Prandtl Number in the framework of the general A model of passively advected vector field by the turbulent velocity field driven by the stochastic Navier-Stokes equation is found as the function of the spatial dimension d>2. The behavior of the turbulent vector Prandtl Number as the function of the spatial dimension d is investigated in detail especially for three physically important special cases, namely, for the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence (A=1), for the passive admixture of a vector impurity by the Navier-Stokes turbulent flow (A=0), and for the model of linearized Navier-Stokes equation (A=-1). It is shown that the turbulent vector Prandtl Number in the framework of the A=-1 model is exactly determined already in the one-loop approximation, i.e., that all higher-loop corrections vanish. At the same time, it is shown that it does not depend on spatial dimension d and is equal to 1. On the other hand, it is shown that the turbulent magnetic Prandtl Number (A=1) and the turbulent vector Prandtl Number in the model of a vector impurity (A=0), which are essentially different at the one-loop level of approximation, become very close to each other when the two-loop corrections are taken into account. It is shown that their relative difference is less than 5% for all integer values of the spatial dimension d≥3. Obtained results demonstrate strong universality of diffusion processes of passively advected scalar and vector quantities in fully symmetric incompressible turbulent environments.
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Spatial parity violation and the turbulent magnetic Prandtl Number
Theoretical and Mathematical Physics, 2013Co-Authors: E. Jurčišinová, M. Jurčišin, R. Remecký, Peter ZalomAbstract:Using the field theory renormalization-group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl Number in the model of kinematic magnetohydrodynamic turbulence, where the magnetic field behaves as a passive vector quantity advected by the helical turbulent environment given by the stochastic Navier-Stokes equation. We show that the presence of helicity decreases the value of the turbulent magnetic Prandtl Number and that the two-loop helical contribution to the turbulent magnetic Prandtl Number is up to 4.2% of its nonhelical value. This result demonstrates the strong stability of the properties of diffusion processes of the magnetic field in turbulent environments with spatial parity violation compared with the corresponding systems without the helicity.
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Influence of helicity on the turbulent Prandtl Number: Two-loop approximation
Theoretical and Mathematical Physics, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theory renormalization group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent Prandtl Number in the model of a scalar field passively advected by the helical turbulent environment given by the stochastic Navier-Stokes equation with a self-similar Gaussian random stirring force δ-correlated in time with the correlator proportional to k4−d−2ɛ. We briefly discuss the influence of helicity on the stability of the corresponding scaling regime. We show that the presence of helicity increases the value of the turbulent Prandtl Number up to 50% of its nonhelical value.
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Turbulent magnetic Prandtl Number in kinematic magnetohydrodynamic turbulence: two-loop approximation.
Physical Review E, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:The turbulent magnetic Prandtl Number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl Number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl Number is the same as the two-loop turbulent Prandtl Number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl Number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.
M. Jurčišin - One of the best experts on this subject based on the ideXlab platform.
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diffusion in anisotropic fully developed turbulence turbulent Prandtl Number
Physical Review E, 2016Co-Authors: E. Jurčišinová, M. JurčišinAbstract:Using the field theoretic renormalization group technique in the leading order of approximation of a perturbation theory the influence of the uniaxial small-scale anisotropy on the turbulent Prandtl Number in the framework of the model of a passively advected scalar field by the turbulent velocity field driven by the Navier-Stokes equation is investigated for spatial dimensions d>2. The influence of the presence of the uniaxial small-scale anisotropy in the model on the stability of the Kolmogorov scaling regime is briefly discussed. It is shown that with increasing of the value of the spatial dimension the region of stability of the scaling regime also increases. The regions of stability of the scaling regime are studied as functions of the anisotropy parameters for spatial dimensions d=3,4, and 5. The dependence of the turbulent Prandtl Number on the anisotropy parameters is studied in detail for the most interesting three-dimensional case. It is shown that the anisotropy of turbulent systems can have a rather significant impact on the value of the turbulent Prandtl Number, i.e., on the rate of the corresponding diffusion processes. In addition, the relevance of the so-called weak anisotropy limit results are briefly discussed, and it is shown that there exists a relatively large region of small absolute values of the anisotropy parameters where the results obtained in the framework of the weak anisotropy approximation are in very good agreement with results obtained in the framework of the model without any approximation. The dependence of the turbulent Prandtl Number on the anisotropy parameters is also briefly investigated for spatial dimensions d=4 and 5. It is shown that the dependence of the turbulent Prandtl Number on the anisotropy parameters is very similar for all studied cases (d=3,4, and 5), although the numerical values of the corresponding turbulent Prandtl Numbers are different.
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Turbulent Prandtl Number in the A model of passive vector admixture.
Physical Review E, 2016Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theoretic renormalization group technique in the second-order (two-loop) approximation the explicit expression for the turbulent vector Prandtl Number in the framework of the general A model of passively advected vector field by the turbulent velocity field driven by the stochastic Navier-Stokes equation is found as the function of the spatial dimension d>2. The behavior of the turbulent vector Prandtl Number as the function of the spatial dimension d is investigated in detail especially for three physically important special cases, namely, for the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence (A=1), for the passive admixture of a vector impurity by the Navier-Stokes turbulent flow (A=0), and for the model of linearized Navier-Stokes equation (A=-1). It is shown that the turbulent vector Prandtl Number in the framework of the A=-1 model is exactly determined already in the one-loop approximation, i.e., that all higher-loop corrections vanish. At the same time, it is shown that it does not depend on spatial dimension d and is equal to 1. On the other hand, it is shown that the turbulent magnetic Prandtl Number (A=1) and the turbulent vector Prandtl Number in the model of a vector impurity (A=0), which are essentially different at the one-loop level of approximation, become very close to each other when the two-loop corrections are taken into account. It is shown that their relative difference is less than 5% for all integer values of the spatial dimension d≥3. Obtained results demonstrate strong universality of diffusion processes of passively advected scalar and vector quantities in fully symmetric incompressible turbulent environments.
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Spatial parity violation and the turbulent magnetic Prandtl Number
Theoretical and Mathematical Physics, 2013Co-Authors: E. Jurčišinová, M. Jurčišin, R. Remecký, Peter ZalomAbstract:Using the field theory renormalization-group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl Number in the model of kinematic magnetohydrodynamic turbulence, where the magnetic field behaves as a passive vector quantity advected by the helical turbulent environment given by the stochastic Navier-Stokes equation. We show that the presence of helicity decreases the value of the turbulent magnetic Prandtl Number and that the two-loop helical contribution to the turbulent magnetic Prandtl Number is up to 4.2% of its nonhelical value. This result demonstrates the strong stability of the properties of diffusion processes of the magnetic field in turbulent environments with spatial parity violation compared with the corresponding systems without the helicity.
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Influence of helicity on the turbulent Prandtl Number: Two-loop approximation
Theoretical and Mathematical Physics, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theory renormalization group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent Prandtl Number in the model of a scalar field passively advected by the helical turbulent environment given by the stochastic Navier-Stokes equation with a self-similar Gaussian random stirring force δ-correlated in time with the correlator proportional to k4−d−2ɛ. We briefly discuss the influence of helicity on the stability of the corresponding scaling regime. We show that the presence of helicity increases the value of the turbulent Prandtl Number up to 50% of its nonhelical value.
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Turbulent magnetic Prandtl Number in kinematic magnetohydrodynamic turbulence: two-loop approximation.
Physical Review E, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:The turbulent magnetic Prandtl Number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl Number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl Number is the same as the two-loop turbulent Prandtl Number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl Number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.
Xiaoming Wang - One of the best experts on this subject based on the ideXlab platform.
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Bound on vertical heat transport at large Prandtl Number
Physica D: Nonlinear Phenomena, 2008Co-Authors: Xiaoming WangAbstract:Abstract We prove a new upper bound on the vertical heat transport in Rayleigh–Benard convection of the form c Ra 1 3 ( ln Ra ) 2 3 under the assumption that the ratio of Prandtl Number over Rayleigh Number satisfies Pr Ra ≥ c 0 where the non-dimensional constant c 0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) Ra 1 3 bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl Number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl Number convection, J. Stat. Phys. 94 (1) (1999) 159–172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl Number Rayleigh–Benard convection, J. Fluid Mech. 560 (2006) 229–241]. It also improves a uniform (in Prandtl Number) Ra 1 2 bound for the Nusselt Number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049–1060] in the case of large Prandtl Number.
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Stationary Statistical Properties of Rayleigh-Bénard Convection at Large Prandtl Number
Communications on Pure and Applied Mathematics, 2008Co-Authors: Xiaoming WangAbstract:This is the third in a series of our study of Rayleigh-Benard convection at large Prandtl Number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Benard convection at large Prandtl Number are related to those of the infinite Prandtl Number model for convection that is formally derived from the Boussinesq system via setting the Prandtl Number to infinity. We study asymptotic behavior of stationary statistical solutions, or invariant measures, to the Boussinesq system for Rayleigh-Benard convection at large Prandtl Number. In particular, we show that the invariant measures of the Boussinesq system for Rayleigh-Benard convection converge to those of the infinite Prandtl Number model for convection as the Prandtl Number approaches infinity. We also show that the Nusselt Number for the Boussinesq system (a specific statistical property of the system) is asymptotically bounded by the Nusselt Number of the infinite Prandtl Number model for convection at large Prandtl Number. We discover that the Nusselt Numbers are saturated by ergodic invariant measures. Moreover, we derive a new upper bound on the Nusselt Number for the Boussinesq system at large Prandtl Number of the form
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Asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl Number†
Communications on Pure and Applied Mathematics, 2007Co-Authors: Xiaoming WangAbstract:We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Benard convection at large Prandtl Number. In particular, we show that the global attractors to the Boussinesq system for Rayleigh-Benard convection converge to that of the infinite-Prandtl-Number model for convection as the Prandtl Number approaches infinity. This offers partial justification of the infinite-Prandtl-Number model for convection as a valid simplified model for convection at large Prandtl Number even in the long-time regime. c 2006 Wiley Periodicals, Inc.
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Large Prandtl Number behavior of the Boussinesq system of Rayleigh-Bénard convection
Applied Mathematics Letters, 2004Co-Authors: Xiaoming WangAbstract:Abstract We establish the validity of the inifinite Prandtl Number model as an approximation of the Boussinesq system at large Prandtl Number on finite and infinite time interval, as well as in some statistical sense.
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Infinite Prandtl Number limit of Rayleigh-Bénard convection
Communications on Pure and Applied Mathematics, 2003Co-Authors: Xiaoming WangAbstract:We rigorously justify the infinite Prandtl Number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Benard convection as the Prandtl Number approaches infinity. This is a singular limit problem involving an initial layer. © 2003 Wiley Periodicals, Inc.
R. Remecký - One of the best experts on this subject based on the ideXlab platform.
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Turbulent Prandtl Number in the A model of passive vector admixture.
Physical Review E, 2016Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theoretic renormalization group technique in the second-order (two-loop) approximation the explicit expression for the turbulent vector Prandtl Number in the framework of the general A model of passively advected vector field by the turbulent velocity field driven by the stochastic Navier-Stokes equation is found as the function of the spatial dimension d>2. The behavior of the turbulent vector Prandtl Number as the function of the spatial dimension d is investigated in detail especially for three physically important special cases, namely, for the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence (A=1), for the passive admixture of a vector impurity by the Navier-Stokes turbulent flow (A=0), and for the model of linearized Navier-Stokes equation (A=-1). It is shown that the turbulent vector Prandtl Number in the framework of the A=-1 model is exactly determined already in the one-loop approximation, i.e., that all higher-loop corrections vanish. At the same time, it is shown that it does not depend on spatial dimension d and is equal to 1. On the other hand, it is shown that the turbulent magnetic Prandtl Number (A=1) and the turbulent vector Prandtl Number in the model of a vector impurity (A=0), which are essentially different at the one-loop level of approximation, become very close to each other when the two-loop corrections are taken into account. It is shown that their relative difference is less than 5% for all integer values of the spatial dimension d≥3. Obtained results demonstrate strong universality of diffusion processes of passively advected scalar and vector quantities in fully symmetric incompressible turbulent environments.
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Spatial parity violation and the turbulent magnetic Prandtl Number
Theoretical and Mathematical Physics, 2013Co-Authors: E. Jurčišinová, M. Jurčišin, R. Remecký, Peter ZalomAbstract:Using the field theory renormalization-group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl Number in the model of kinematic magnetohydrodynamic turbulence, where the magnetic field behaves as a passive vector quantity advected by the helical turbulent environment given by the stochastic Navier-Stokes equation. We show that the presence of helicity decreases the value of the turbulent magnetic Prandtl Number and that the two-loop helical contribution to the turbulent magnetic Prandtl Number is up to 4.2% of its nonhelical value. This result demonstrates the strong stability of the properties of diffusion processes of the magnetic field in turbulent environments with spatial parity violation compared with the corresponding systems without the helicity.
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Influence of helicity on the turbulent Prandtl Number: Two-loop approximation
Theoretical and Mathematical Physics, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:Using the field theory renormalization group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent Prandtl Number in the model of a scalar field passively advected by the helical turbulent environment given by the stochastic Navier-Stokes equation with a self-similar Gaussian random stirring force δ-correlated in time with the correlator proportional to k4−d−2ɛ. We briefly discuss the influence of helicity on the stability of the corresponding scaling regime. We show that the presence of helicity increases the value of the turbulent Prandtl Number up to 50% of its nonhelical value.
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Turbulent magnetic Prandtl Number in kinematic magnetohydrodynamic turbulence: two-loop approximation.
Physical Review E, 2011Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:The turbulent magnetic Prandtl Number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl Number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl Number is the same as the two-loop turbulent Prandtl Number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl Number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.
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Comment on "Two-loop calculation of the turbulent Prandtl Number".
Physical review. E Statistical nonlinear and soft matter physics, 2010Co-Authors: E. Jurčišinová, M. Jurčišin, R. RemeckýAbstract:We have revised the value of the turbulent Prandtl Number obtained in the model of a passive scalar advected by the velocity field driven by the stochastic Navier-Stokes equation which was calculated by L. Ts. Adzhemyan [Phys. Rev. E 71, 056311 (2005)] by using the field-theoretic renormalization group approach within the two-loop approximation in the corresponding perturbative theory. It is shown that the correct two-loop contribution to the turbulent Prandtl Number is essentially smaller than that calculated by Adzhemyan and, as a result, the final two-loop value of the turbulent Prandtl Number is Pr(t)=0.7051 instead of Pr(t)=0.7693. The source of discrepancy between our result and that obtained by Adzhemyan is identified and discussed.
Charles F Gammie - One of the best experts on this subject based on the ideXlab platform.
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the turbulent magnetic Prandtl Number of mhd turbulence in disks
The Astrophysical Journal, 2009Co-Authors: Xiaoyue Guan, Charles F GammieAbstract:The magnetic Prandtl Number PrM is the ratio of viscosity to resistivity. In astrophysical disks the diffusion of angular momentum (viscosity) and magnetic fields (resistivity) are controlled by turbulence. Phenomenological models of the evolution of large-scale poloidal magnetic fields in disks suggest that the turbulent magnetic Prandtl Number PrM,T controls the rate of escape of vertical field from the disk; for PrM,T ≤ R/H vertical field diffuses outward before it can be advected inward by accretion. Here we measure field diffusion and angular momentum transport due to MHD turbulence in a shearing box, and thus PrM,T, by studying the evolution of a sinusoidal perturbation in the magnetic field that is injected into a turbulent background. We show that the perturbation is always stable, decays approximately exponentially, has decay rate k 2, and that the implied PrM,T ~ 1.
