Biomedical subjects

V Yakhot

Publications and source records attributed to V Yakhot.

At least 19 recordsLinked to original sources

PubMed2001

Mean-field approximation and extended self-similarity in turbulence.

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. A sufficient condition for extended self-similarity in a general dynamical system is derived in this paper. It is also shown that if the pressure-gradient contributions are expressed in terms of velocity differences in the mean-field approximation [V. Yakhot, Phys. Rev. E 63, 026307 (2001)], then the ESS is a consequence of the Navier-Stokes equations.

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PubMed2001

Symmetry breaking, anomalous scaling, and large-scale flow generation in a convection cell.

We consider a convection process in thin loops of different geometries. At Ra=Ra(')(cr) a first transition leading to the generation of corner vortices is observed. At higher Ra (Ra>Ra(cr)) a coherent large-scale flow, which persists for a very long time, sets up. The mean velocity nu mass flux m, and the Nusselt number Nu in this flow scale with Ra as nu proportional to m proportional to Ra0.45 and Nu proportional to Ra0.9, respectively, in a wide range of r=(Ra-Ra(cr))/Ra(cr) variation. The "normal" scaling nu proportional to sqrt[Ra] is detected as r-->0 and its range shrinks with decrease of the aspect ratio. The time evolution of the coherent flow is well described by the Landau amplitude equation with the appropriate selection of the Ra-dependent Landau constants. Analysis of the aspect ratio influence on the range of validity of anomalous scaling, observed in this paper, indicates the important role played by both thermal boundary conditions and geometry of the system.

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PubMed2001

Mean-field approximation and a small parameter in turbulence theory.

Numerical and physical experiments on two-dimensional (2D) turbulence show that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space dimensionality d=d(c), at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At d 0 and r/L-->0 in three-dimensional flows in close agreement with experimental data. In addition, some exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.

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PubMed1999

Two-dimensional turbulence in the inverse cascade range.

Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "normal" Kolmogorov scaling <(deltav)(2n)> proportional r(2n/3) and obey Gaussian statistics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explaining these observations is presented in this paper. The derived self-consistent expression for the pressure gradient contributions leads to the conclusion that small-scale transverse velocity differences are governed by a linear Langevin-like equation, stirred by a nonlocal, universal, solution-dependent Gaussian random force. This explains the experimentally observed Gaussian statistics of transverse velocity differences and their Kolmogorov scaling. The solution for the PDF of longitudinal velocity differences is based on the numerical smallness of the energy flux in two-dimensional turbulence. The theory makes a few quantitative predictions that can be tested experimentally.

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PubMed1996