scholarly journals Vorticity Statistics in the Two-Dimensional Enstrophy Cascade

1999 ◽  
Vol 83 (17) ◽  
pp. 3418-3421 ◽  
Author(s):  
Jérôme Paret ◽  
Marie-Caroline Jullien ◽  
Patrick Tabeling
Keyword(s):  
Two Dimensional ◽  
Enstrophy Cascade

Charney isotropy and equipartition in quasi-geostrophic turbulence

2010 ◽  
Vol 656 ◽  
pp. 448-457 ◽  
Author(s):  
ANDREAS VALLGREN ◽  
ERIK LINDBORG
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
Horizontal Velocity ◽  
Energy Cascade ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Wide Range ◽  
Geostrophic Turbulence ◽  
Decaying Turbulence ◽  
Enstrophy Cascade

High-resolution simulations of forced quasi-geostrophic (QG) turbulence reveal that Charney isotropy develops under a wide range of conditions, and constitutes a preferred state also in β-plane and freely decaying turbulence. There is a clear analogy between two-dimensional and QG turbulence, with a direct enstrophy cascade that is governed by the prediction of Kraichnan (J. Fluid Mech., vol. 47, 1971, p. 525) and an inverse energy cascade following the classic k−5/3 scaling. Furthermore, we find that Charney's prediction of equipartition between the potential and kinetic energy in each of the two horizontal velocity components is approximately fulfilled in the inertial ranges.

scholarly journals The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulence

2012 ◽  
Vol 694 ◽  
pp. 493-523 ◽  
Author(s):  
Eleftherios Gkioulekas
Keyword(s):  
Large Scale ◽  
Bottom Layer ◽  
Two Dimensional ◽  
Interlayer Interaction ◽  
Open Questions ◽  
Small Scales ◽  
Scale Range ◽  
Geostrophic Turbulence ◽  
Enstrophy Cascade ◽  
Potential Enstrophy

AbstractIn the Nastrom–Gage spectrum of atmospheric turbulence, we observe a${k}^{\ensuremath{-} 3} $energy spectrum that transitions into a${k}^{\ensuremath{-} 5/ 3} $spectrum, with increasing wavenumber$k$. The transition occurs near a transition wavenumber${k}_{t} $, located near the Rossby deformation wavenumber${k}_{R} $. The Tung–Orlando theory interprets this spectrum as a double downscale cascade of potential enstrophy and energy, from large scales to small scales, in which the downscale potential enstrophy cascade coexists with the downscale energy cascade over the same length scale range. We show that, in a temperature-forced two-layer quasi-geostrophic model, the rates with which potential enstrophy and energy are injected place the transition wavenumber${k}_{t} $near${k}_{R} $. We also show that, if the potential energy dominates the kinetic energy in the forcing range, then the Ekman term suppresses the upscale cascading potential enstrophy more than it suppresses the upscale cascading energy, a behaviour contrary to what occurs in two-dimensional turbulence. As a result, the ratio$\eta / \varepsilon $of injected potential enstrophy over injected energy, in the downscale direction, decreases, thereby tending to decrease the transition wavenumber${k}_{t} $further. Using a random Gaussian forcing model, we reach the same conclusion, under the modelling assumption that the asymmetric Ekman term predominantly suppresses the bottom layer forcing, thereby disregarding a possible entanglement between the Ekman term and the nonlinear interlayer interaction. Based on these results, we argue that the Tung–Orlando theory can account for the approximate coincidence between${k}_{t} $and${k}_{R} $. We also identify certain open questions that require further investigation via numerical simulations.

Physical Mechanism of the Two-Dimensional Enstrophy Cascade

2003 ◽  
Vol 91 (21) ◽  
Author(s):  
Shiyi Chen ◽  
Robert E. Ecke ◽  
Gregory L. Eyink ◽  
Xin Wang ◽  
Zuoli Xiao
Keyword(s):  
Physical Mechanism ◽  
Two Dimensional ◽  
Enstrophy Cascade

scholarly journals Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence

2017 ◽  
Vol 119 (18) ◽  
Author(s):  
Matthew T. Reeves ◽  
Thomas P. Billam ◽  
Xiaoquan Yu ◽  
Ashton S. Bradley
Keyword(s):  
Quantum Turbulence ◽  
Two Dimensional ◽  
Enstrophy Cascade

Coherent vortices and tracer cascades in two-dimensional turbulence

2007 ◽  
Vol 574 ◽  
pp. 429-448 ◽  
Author(s):  
ARMANDO BABIANO ◽  
ANTONELLO PROVENZALE
Keyword(s):  
Inertial Range ◽  
Two Dimensional ◽  
Passive Tracer ◽  
Simultaneous Presence ◽  
Inverse Cascade ◽  
Coherent Vortices ◽  
Small Scales ◽  
Elliptic Regions ◽  
Enstrophy Cascade

We study numerically the scale-to-scale transfers of enstrophy and passive-tracer variance in two-dimensional turbulence, and show that these transfers display significant differences in the inertial range of the enstrophy cascade. While passive-tracer variance always cascades towards small scales, enstrophy is characterized by the simultaneous presence of a direct cascade in hyperbolic regions and of an inverse cascade in elliptic regions. The inverse enstrophy cascade is particularly intense in clusters of small-scales elliptic patches and vorticity filaments in the turbulent background, and it is associated with gradient-decreasing processes. The inversion of the enstrophy cascade, already noticed by Ohkitani (Phys. Fluids A, vol. 3, 1991, p. 1598), appears to be the main difference between vorticity and passive-tracer dynamics in incompressible two-dimensional turbulence.

scholarly journals The direct enstrophy cascade of two-dimensional soap film flows

2014 ◽  
Vol 26 (5) ◽  
pp. 055105 ◽  
Author(s):  
M. K. Rivera ◽  
H. Aluie ◽  
R. E. Ecke
Keyword(s):  
Soap Film ◽  
Two Dimensional ◽  
Enstrophy Cascade ◽  
Film Flows
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