Universal Scaling Exponents in Shell Models of Turbulence: Viscous Effects Are Finite-Sized Corrections to Scaling

The paper describes a technology for the automated compilation of equations for shell models of turbulence in the computer algebra system Maple. A general form of equations for the coefficients of nonlinear interactions is given, which will ensure that the required combination of quadratic invariants and power-law solutions is fulfilled in the model. Described the codes for the Maple system allowing to generate and solve systems of equations for the coefficients. The proposed technology allows you to quickly and accurately generate classes of shell models with the desired properties.

Download Full-text

A Two-Fluid Picture of Intermittency in Shell-Models of Turbulence

Fluid Mechanics and Its Applications - Advances in Turbulence VII ◽

10.1007/978-94-011-5118-4_54 ◽

1998 ◽

pp. 219-222 ◽

Cited By ~ 1

Author(s):

J. L. Gilson ◽

I. Daumont ◽

T. Dombre

Keyword(s):

Shell Models ◽

Shell Models Of Turbulence ◽

Two Fluid

Download Full-text

Application of computer algebra for the construction of shell models of turbulence

E3S Web of Conferences ◽

10.1051/e3sconf/201912702004 ◽

2019 ◽

Vol 127 ◽

pp. 02004

Author(s):

Liubov Feshchenko ◽

Gleb Vodinchar

Keyword(s):

Conservation Laws ◽

Computer Algebra ◽

Nonlinear Interaction ◽

Stationary Solutions ◽

Symbolic Calculation ◽

Shell Models ◽

Model Equations ◽

Shell Models Of Turbulence

The technique for automatic constructing of shell models of turbulence has been developed. The compilation of a model equations and its exactly solution is implemented using computer algebra (symbolic calculation) systems. The technique allows one to vary the scaling nonlocality of nonlinear interaction, form of expressions for conservation laws in models, and the form of stationary solutions with power distributions to scales.

Download Full-text

Continuous representation for shell models of turbulence

Nonlinearity ◽

10.1088/0951-7715/28/7/2497 ◽

2015 ◽

Vol 28 (7) ◽

pp. 2497-2514 ◽

Cited By ~ 5

Author(s):

Alexei A Mailybaev

Keyword(s):

Continuous Representation ◽

Shell Models ◽

Shell Models Of Turbulence

Download Full-text

Crossover scaling: A renormalization group approach

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0018 ◽

1994 ◽

Vol 444 (1921) ◽

pp. 287-296 ◽

Cited By ~ 7

Keyword(s):

Fixed Point ◽

Renormalization Group ◽

Correlation Length ◽

Degrees Of Freedom ◽

Scaling Laws ◽

Anisotropy Parameter ◽

Corrections To Scaling ◽

Group Approach ◽

Scaling Exponents ◽

Renormalization Group Approach

We derive a theory of crossover scaling based on a scaling variable g ξ g , where g is the anisotropy parameter inducing the crossover and ξ g is the correlation length in the presence of g . Our considerations are field theoretic and based on a renormalization group with a g dependent differential generator that interpolates between qualitatively different degrees of freedom. ξ g is a nonlinear scaling field for this renormalization group and interpolates between ( T – T c ( g )) – v 0 and ( T – T c ( g )) – v ∞ ( v 0 and v ∞ being the isotropic and anisotropic exponents respectively). By expanding about a ‘floating’ fixed point we can make corrections to scaling small throughout the crossover. In this formulation effective scaling exponents obey standard scaling laws, e. g. γ eff = v eff (2 – ɳ eff ). We discuss its advantages giving for various crossovers explicit supporting perturbative calculations of the susceptibility, which is found to conform to the general form derived from the g dependent renormalization group.

Download Full-text

MEASURING HURST EXPONENTS WITH THE FIRST RETURN METHOD

Fractals ◽

10.1142/s0218348x94000740 ◽

1994 ◽

Vol 02 (04) ◽

pp. 527-533 ◽

Cited By ~ 28

Author(s):

ALEX HANSEN ◽

THOR ENGØY ◽

KNUT JØRGEN MÅLØY

Keyword(s):

Fourier Analysis ◽

Efficient Method ◽

Hurst Exponent ◽

Corrections To Scaling ◽

Scaling Exponents ◽

Return Method ◽

Hurst Exponents

The First Return method has proven to be an efficient method for determining the Hurst exponent, H, of self-affine surfaces. We discuss its foundations and some corrections to scaling which must be taken into account for an adequate estimation of H. Using this method, we analyze a set of artificially generated curves with known Hurst exponent and compare the result with Fourier analysis. We also discuss the case where the surface to be analyzed has a curved bias with a maximum or minimum. In this case, the relation between the scaling exponents associated with the first-return histograms and the Hurst exponent H is different from the unbiased case.

Download Full-text