Coherent vortices and tracer cascades in two-dimensional turbulence

Abstract

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.

Vertical mixing and coherent anticyclones in the ocean: the role of stratification

“…4b) have slopes slightly steeper than k −3 for k > k f in the upper few hundred meters, consistent with the behaviour of 2-D turbulence and stratified quasigeostrophic turbulence in the direct enstrophy cascade (Babiano and Provenzale, 2007;Smith and Vallis, 2002). Note that the higher amount of surface baroclinic energy found in the SS case ( Fig.…”

Dynamics of wind‐forced coherent anticyclones in the open ocean

“…Different realizations with identical power spectra are linearly interpolated every 20 days. This forcing is a close approximation to that adopted in simulations of forced 2‐D or QG turbulence [ Elhmaidi et al , 1993; Babiano and Provenzale , 2007], and it implies weak surface buoyancy gradients. As a result, vorticity distribution in the flow resembles that of quasi‐geostrophic solutions and is less frontal than found in other recent idealized studies focused on surface frontal ocean dynamics [ Mahadevan and Tandon , 2006; Capet et al , 2008b, 2008c; Klein et al , 2008] where sQG provides a better approximation [ Capet et al , 2008a; M. J. Molemaker et al, Balanced and unbalanced routes to dissipation in an equilibrated Eady flow, submitted to Journal of Fluid Mechanics , 2009].…”

“…[13] Figure 3a shows the horizontal kinetic energy spectra at depths of 5, 20, 78 and 204 m. In the upper 100 m, the spectra for k > k f are slightly steeper than k À3 , consistent with the behavior of two-dimensional turbulence in the direct enstrophy cascade [e.g., Elhmaidi et al, 1993;Babiano and Provenzale, 2007], with simulations of shallow water turbulence [Cho and Polvani, 1996], and with forced dissipated homogeneous stratified quasi-geostrophic turbulence [Smith and Vallis, 2002]. Since L d is comparable to the forcing scale, an inverse energy cascade is not present.…”

Observed and Modeled Global Ocean Turbulence Regimes as Deduced from Surface Trajectory Data

“…Taylor (1921) first proposed the idea that the scales of turbulence could be regarded as infinitesimal compared to the scales of the mean flow, thus opening up the possibility for scale separation in dispersal studies. Studies along these lines have been undertaken in numerous works within the field of stochastic ocean modeling-compare references in Griffa (1996), as well as in studies of, for example, tracer cascades in 2D turbulence in fluids (Babiano and Provenzale 2007). Elhmaidi et al (1993), Pasquero et al (2001), and Rupolo et al (1996) discussed and evaluated the possibility of separating the near-surface ocean turbulence in two limiting cases according to the inherent dispersal properties of the flow, that is, the frozen turbulence and fixed-float regimes.…”