Vorticity and passive-scalar dynamics in two-dimensional turbulence

Babiano, A.; Basdevant, C.; Legras, Bernard; Sadourny, R.

doi:10.1017/s0022112087002684

Cited by 158 publications

(100 citation statements)

References 23 publications

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“…We have indeed found in our numerical 2D simulations that, for times longer than an initial enstrophy time scale, the two gradients have an identical orientation in most of the domain. This is also confirmed by Babiano et al [1] who have noted that isolines of tracer and vorticity have similar orientations. Therefore, the present results are valid for both gradients.…”

Section: Resultssupporting

confidence: 82%

Alignment of tracer gradient vectors in 2D turbulence

Klein

Hua

Lapeyre

2000

Physica D: Nonlinear Phenomena

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This numerical study examines the stirring properties of a 2D flow field with a specific focus on the alignment dynamics of tracer gradient vectors. In accordance with the study of Hua and Klein [Physica D 113 (1998) 98], our approach involves the full second order Lagrangian dynamics and in particular the second order in time equation for the tracer gradient norm. If the physical space is partitioned into strain-dominated regions and "effective" rotation-dominated regions (following a criterion defined by Lapeyre et al. [Phys. Fluids 11 (1999) 3729]), the new result of this study concerns the "effective" rotation-dominated regions: it is found, from numerical simulations of 2D turbulence, that the tracer gradient vector statistically aligns with one of the eigenvector of a tensor that comes out from the second order equation and is related to the pressure Hessian. The consequence is that, in those regions, the observed exponential growth or decay of the tracer gradient vector can be predicted contrary to previous results which implied zero growth and only a rotation of this vector. This result strongly emphasizes the important role of the time evolution of the strain rate amplitude which, with the rotation of the strain tensor, significantly contributes to the alignment dynamics. Both effects are related to the anisotropic part of the pressure Hessian, which emphasizes the non-locality of the mechanisms involved. These results are reminiscent of those recently obtained by Nomura and Post [J. Fluid Mech. 377 (1998) 65] for 3D turbulence.

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Section: Resultssupporting

confidence: 82%

Alignment of tracer gradient vectors in 2D turbulence

Klein

Hua

Lapeyre

2000

Physica D: Nonlinear Phenomena

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“…The degree of correlation in two-dimensional turbulence between passive scalars and vorticity does not appear to be the subject of consensus. Babiano et al (1987) claim there is no correlation. However the simulations of Holloway & Kristmannsson (1984) and Holloway, Riser & Ramsden (1986) suggest that tracer is being concentrated in vortex cores and strained between the cores.…”

Section: Hydrodynamics Of Forced Vortex Flowsmentioning

confidence: 93%

Vortex dynamos

Smith

Tobias

2004

J. Fluid Mech.

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We investigate the kinematic dynamo properties of interacting vortex tubes. These flows are of great importance in geophysical and astrophysical fluid dynamics: for al a r g er a n g eo fs ystems, turbulence is dominated by such coherent structures. We obtain a dynamically consistent 2 1 2 -dimensional velocity field of the form (u(x, y, t),v(x, y, t),w(x, y, t)) by solving the z-independent Navier-Stokes equations in the presence of helical forcing. This system naturally forms vortex tubes via an inverse cascade. It has chaotic Lagrangian properties and is therefore a candidate for fast dynamo action. The kinematic dynamo properties of the flow are calculated by determining the growth rate of a small-scale seed field. The growth rate is found to have a complicated dependence on Reynolds number Re and magnetic Reynolds number Rm, but the flow continues to act as a dynamo for large Re and Rm. Moreover the dynamo is still efficient even in the limit Re ≫ Rm,p r o v i ding Rm is large enough, because of the formation of coherent structures.

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“…In decaying 2D turbulence, it has been shown that at sufficiently large times, when the coherent structures are well-formed, some aspects of the system evolution may be modelled in terms of a limited number of interacting point vortices [3,5]. In forced turbulence, the turbulent field among the coherent structures is not as passive as in decaying flows; new coherent structures are continuously formed in the background field and a statistically stationary state may be obtained [4,6].…”

Section: Introductionmentioning

confidence: 99%