Energy and Enstrophy Transfer in Decaying Two-Dimensional Turbulence

Abstract

We present experimental data on the direct enstrophy cascade in decaying two-dimensional turbulence. Velocity and vorticity fields are obtained using particle tracking velocimetry. From those fields we directly compute the enstrophy and energy flux by using a filtering technique inspired by large-eddy simulations. This allows considerable insight into the physical processes of turbulence when compared with structure-function or spectral analysis. The direct cascade of enstrophy is weakly forward, with almost as much backscatter as down-scale enstrophy transfer, whereas the inverse energy cascade is strongly upscale with a modest amount of backscatter.

Polymers suppress the inverse transfers of energy and the enstrophy flux fluctuations in two-dimensional turbulence

“…Very recent experiments [18] show that the enstrophy cascade is only weakly forward (i.e., from large to small scales) with considerable "backscatter"; only at very small scales (comparable to the range where our measurements also show a negative flux) did this flux become negative. Our results seem to be in line with these measurements carried out using a different technique, namely particle image velocimetry.…”

Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence

“…lence enstrophy is expected to transfer in a direct cascade to smaller length scales, while energy is often observed in both experiments and numerical simulations to display an inverse cascade to larger length scales (see e.g. [5,6]). …”

Irreversibility of the two-dimensional enstrophy cascade

“…The inverse cascade of energy is characterized by a Kolmogorov-like spectrum with close-to-Gaussian statistics [9] and its time-reversal properties have been the subject of previous works [3,7]. In the direct cascade enstrophy is transferred at a rate η from the forcing scales f down to the small dissipative scales ν ∼ ν 1/2 /η 1/6 generating a power-law spectrum with an exponent close to the dimensional prediction −3 [10][11][12][13][14][15][16][17]. The ratio of these scales defines the Reynolds number as the ratio of the forcing and dissipative scales of the cascade as Re…”