On Geometrical Alignment Properties of Two-Dimensional Forced Turbulence

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.

Section: Introductionmentioning

confidence: 83%

Section: Gradient-decreasing Processes and Inverse Energy Transfermentioning

confidence: 99%

Coherent vortices and tracer cascades in two-dimensional turbulence

Babiano¹,

Provenzale²

2007

“…In rotation-dominated regions (II > 0), P oscillates between positive and negative values. Physically, ∇ω rotates and alternates between amplification and damping, a condition which results in elliptic instability (Protas, Babiano & Kevlahan 1999). We expect the dynamic effect of P on ∇ω to be most significant in strong strain-dominated regions (II < 0), i.e.…”

Section: Vortex Merging: Unstratified Flowmentioning

confidence: 97%

The physics of vortex merger and the effects of ambient stable stratification

Brandt

Nomura

2007

The merging of a pair of symmetric, horizontally oriented vortices in unstratified and stably stratified viscous fluid is investigated. Two-dimensional numerical simulations are performed for a range of flow conditions. The merging process is resolved into four phases of development and key underlying physics are identified. In particular, the deformation of the vortices, explained in terms of the interaction of vorticity gradient, ∇ω, and rate of strain, S, leads to a tilt in ω contours in the vicinity of the center of rotation (a hyperbolic point). In the diffusive/deformation phase, diffusion of the vortices establishes the interaction between ∇ω and mutually induced S. During the convective/deformation phase, induced flow by filaments and, in stratified flow, baroclinically generated vorticity (BV), advects the vortices thereby modifying S, which, in general, may enhance or hinder the development of the tilt. The tilting and diffusion of ω near the center hyperbolic point causes ω from the core region to enter the exchange band where it is entrained. In the convective/entrainment phase, the vortex cores are thereby eroded and ultimately entrained into the exchange band, whose induced flow becomes dominant and transforms the flow into a single vortex. The critical aspect ratio, associated with the start of the convective/entrainment phase, is found to be the same for both the unstratified and stratified flows. In the final diffusive/axisymmetrization phase, the flow evolves towards axisymmetry by diffusion. In general, the effects of stratification depend on the ratio of the diffusive time scale (growth of cores) to the turnover time (establishment of BV), i.e. the Reynolds number. A crossover Reynolds number is found, above which convective merging is accelerated with respect to unstratified flow and below which it is delayed.

“…It is well known that the two-dimensional dynamics of a passive scalar is generically characterized by geometrical alignments of the scalar gradient with preferred directions prescribed by the flow (Okubo 1970;Weiss 1991;Protas, Babiano & Kevlahan 1999;Lapeyre, Klein & Hua 1999;Klein, Hua & Lapeyre 2000). It is therefore natural to try to distinguish active and passive scalars using their alignment properties in connection with a complex distribution of strain.…”

Section: Introductionmentioning

confidence: 99%

Comparing the two-dimensional cascades of vorticity and a passive scalar

Dubos

Babiano

2003

We compare two-dimensional vorticity and passive scalar cascades seen as a gradient enhancement process. Our criteria are based on conditional averages of the first and second Lagrangian derivatives of vorticity and passive scalar gradients in relation to the local flow geometry. In order to interpret these criteria, transient properties are derived for random vorticity and scalar fields, showing that the second-order Lagrangian derivatives of vorticity and passive scalar gradients may behave differently. Cascades obtained in numerical simulations of decaying and forced incompressible turbulence are analysed. First-order analysis reveals that the direct cascade in elliptic domains is more efficient than previously suspected. While several first-order diagnostics collapse to a single curve for vorticity and passive scalars, second-order diagnostics consistently show that the vorticity gradient exhibits faster temporal fluctuations than the passive scalar gradient, a property which we anticipate qualitatively in the study of random fields.