Simulation of cascade processes in turbulent flows

Desnianskii, V. N.; Новиков, Е. А.

doi:10.1016/0021-8928(74)90041-0

Cited by 57 publications

(43 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The shell models were suggested by Kolmogorov's school to describe the spectral energy transfer (Gledzer 1973;Desnianskii and Novikov 1974). After numerous refinements they became an effective tool for description of the spectral properties of the small-scale turbulence (see for review Bohr et al 1998).…”

Section: Higher Statistical Moments and Intermittencymentioning

confidence: 99%

Current Status of Turbulent Dynamo Theory

2012

View full text Add to dashboard Cite

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

show abstract

Section: Higher Statistical Moments and Intermittencymentioning

confidence: 99%

Current Status of Turbulent Dynamo Theory

2012

View full text Add to dashboard Cite

show abstract

“…Before developing a turbulence model we must identify these elementary "objects" and catalog their elementary interactions. For instance the cascade models (Desnjanski Novikov 1974, Kraichnan 1974, Frisch & Sulem 1975, Bell & Nelkin 1978, Gledzer et al 1981 assume that wavenumber octaves are the elementary objects needed to describe homogeneous turbulence and that their interactions consist of exchanging energy with the neighboring octaves. The first step toward modeling turbulence is to find an appropriate segmentation of the energy density in x-l phase space (Figure 1) and define some kind of phase-space "atoms" among which energy, or any other dynamically relevant quantity, is distributed and exchanged by the turbulent flow dynamics.…”

Section: Energy Decompositionmentioning

confidence: 99%

Wavelet Transforms and Their Applications to Turbulence

Farge¹

1992

Annu. Rev. Fluid Mech.

2,449

802

View full text Add to dashboard Cite

“…10). Shell models have been proposed and used in various physical contexts from basic fluid turbulence [11] to magnetohydrodynamic turbulence [12], to convective turbulence [13], to drift wave turbulence in plasmas [14], to rotating turbulence [15] to superfluid turbulence in Helium II [16] etc. More generally, such reduced models have been important historically, either for numerical reasons or for providing a theoretical insight into the phenomenology of turbulence [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence

et al. 2016

View full text Add to dashboard Cite

A detailed systematic derivation of a logarithmically discretized model for two dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with non-local interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seems to dominate over the dual cascade, which is a common problem of two dimensional shell models.

show abstract

Simulation of cascade processes in turbulent flows

Cited by 57 publications

References 4 publications

Current Status of Turbulent Dynamo Theory

Current Status of Turbulent Dynamo Theory

Wavelet Transforms and Their Applications to Turbulence

Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence

Contact Info

Product

Resources

About