Constraints on inertial range scaling laws in forced two-dimensional Navier–Stokes turbulence

2007 ◽  
Vol 19 (10) ◽  
pp. 108109 ◽  
Author(s):  
Chuong V. Tran
Keyword(s):  
Scaling Laws ◽  
Inertial Range ◽  
Navier Stokes ◽  
Two Dimensional

scholarly journals On inertial-range scaling laws

1996 ◽  
Vol 306 ◽  
pp. 167-181 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Scaling Laws ◽  
State Energy ◽  
Three Dimensional ◽  
Inertial Range ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Unified Framework ◽  
Asymptotic Nature

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

scholarly journals On energetics and inertial-range scaling laws of two-dimensional magnetohydrodynamic turbulence

2012 ◽  
Vol 703 ◽  
pp. 238-254 ◽  
Author(s):  
Luke A. K. Blackbourn ◽  
Chuong V. Tran
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Energy Flux ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Inertial Range ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Direct Energy ◽  
Energy Equipartition

AbstractWe study two-dimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial-range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction due to Alfvén wave effects by the Iroshnikov–Kraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the Iroshnikov–Kraichnan theory to the present case, particularly its predictions of energy equipartition and ${k}^{\ensuremath{-} 3/ 2} $ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than ${k}^{\ensuremath{-} 3/ 2} $, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than ${k}^{\ensuremath{-} 3/ 2} $ for $r\approx 2$, even at moderate resolutions. Here $r\approx 2$ is the magnetic-to-kinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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