The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)]...
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)] is applied to high Rayleigh number convection in a Bénard cell. Quantitative interpretation of recent experimental data [B. Castaing et al. (private communication)] is presented. The predicted intermittency exponent following from comparison of the theory with experiment is 0.175<μ<0.275. A crucial experimental test of the renormalization group theory of turbulence is proposed.
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key as...
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key assumption in the present approach is that the central fluctuating temperature field actively interacts with the turbulent velocity field, and this interaction leads to a velocity inertial subrange that deviates significantly from Kolmogorov’s freely cascading inertial range.
We perform deep variational free energy calculations to investigate the dense hydrogen system at 1200 K and high pressures. In this computational framework, neural networks are used to model the free energy through th...
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Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described ...
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described initially by two circular patches is studied in detail. The numerical evidence indicates that when the minimum distance between the two patches is initially less than the radius of the patches a singularity forms in finite time on the boundary curves of the patches. The singularity appears to be a jump discontinuity in the tangent vector of the boundary curve.
We prove that the gradient descent training of a two-layer neural network on empirical or population risk may not decrease population risk at an order faster than t−4/(d−2) under mean field scaling. The loss functiona...
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A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
The expression for turbulent Prandtl number obtained from the renormalization group procedure is used to describe the process of heat transfer in turbulent pipe flow. The results are in a good agreement with experimen...
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The expression for turbulent Prandtl number obtained from the renormalization group procedure is used to describe the process of heat transfer in turbulent pipe flow. The results are in a good agreement with experimental data over the entire range of experimentally accessible Prandtl numbers, 10 -2 < σ 0 < 10 6 . L'expression du nombre de Prandtl turbulent obtenue à partir d'une procédure de groupe de renormalisation est utilisée pour décrire le mécanisme du transfert thermique dans l'écoulement turbulent dans un tube. Les résultats sont en bon accord avec des données expérimentales dans le domaine des nombres de Prandtl 10 −2 < σ 0 < 10 6 accessibles expérimentalement. Zur Beschreibung des Wärmeübergangs bei turbulenter Rohrströmung wird der Ausdruck für die turbulente Prandtl-Zahl verwendet, den man aus der Renormalisations-Gruppen-Prozedur erhält. Die Ergebnisse stimmen mit experimentellen Daten im gesamten Bereich der experimentell verfügbaren Prandtl-Zahlen, 10 −2 < σ 0 < 10 6 , gut überein. Для oпиcaния тeплoпePeнoca пPи тuPбuлeнтнoм тeчeнии B тPuбe иcпoльэueтcя выPaжeниe для тuPбuлeнтнoгo чиcлa ПPaндтля, пoлuчeннoe мeтoдoм PeнoPмaлиэaциoннoй гPuппы. Peзuльтaты нaчoдятcя B чoPoшeм cooтвeтcтвии C экcпePнмeнтaльными дaнными для вceгo диaпaэoнa знaчeннй чиcлa ПPaндтля, 10 −2 < σ 0 <10 6 .
The dynamics of vortex structures in turbulence have been investigated statistically in pseudospectral numerical simulations of moderate Reynolds number turbulence. Coherent features of vortex stretching dynamics, as ...
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The dynamics of vortex structures in turbulence have been investigated statistically in pseudospectral numerical simulations of moderate Reynolds number turbulence. Coherent features of vortex stretching dynamics, as manifested in the alignment of the vorticity vector with a principal axis of the rate of strain, are investigated with an emphasis on their time development in turbulence decay from a random gaussian field. In addition, we have observed a tendency in developed turbulence for velocity vectors to lie in the plane formed by the two principal stretching directions. These phenomena provide a mechanism for depletion of nonlinearity in turbulence. The spatial and temporal coherence of vortex structures has been further studied using recently developed techniques which combine dynamical visualisation with statistical sampling analysis.
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective...
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.
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