Intermittency in two-dimensional turbulence with drag

Abstract

We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wavenumber spectrum drops with a power law faster than in the case without drag, and the vorticity field becomes intermittent, as shown by the anomalous scaling of the vorticity structure functions. Using previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wavenumber spectrum and the scaling exponents of the vorticity structure functions ζ2q. We also study, both by numerical experiment and theoretical analysis, the multifractal structure of the viscous enstrophy dissipation in terms of its Rényi dimension spectrum Dq and singularity spectrum f (α). We derive a relation between Dq and ζ2q, and discuss its relevance to a version of the refined similarity hypothesis. In addition, we obtain and compare theoretically and numerically derived results for the dependence on separation r of the probability distribution of δ r ω, the difference between the vorticity at two points separated by a distance r. Our numerical simulations are done on a 4096 × 4096 grid.

Local transfer and spectra of a diffusive field advected by large-scale incompressible flows

“…However, this is far from conclusive as the viscousconvective ranges accessible to modern computers are still quite limited. Furthermore, a number of studies [16,[24][25][26] have either argued for or found spectra shallower than the Batchelor spectrum. For these reasons, as well as the phenomenological nature of the Obukhov-Corrsin and Batchelor theories, further theoretical consideration and numerical analysis (with higher resolutions whenever possible) continue to be desirable.…”

Intermittency in the enstrophy cascade of two-dimensional fully developed turbulence: Universal features

“…Direct numerical simulations (DNS) of freely-decaying 2D FDT (McWilliams [22], Benzi et al [23], Brachet et al [24] and [25], Kida [26], Ohkitani [27], Schneider and Farge [28]) and forced-dissipative 2D FDT (Basdevant et al [29], Legras et al [30] and Tsang et al [31]) showed intermittency caused by the presence of coherent structures. These structures inhibit the local inertial transfer of enstrophy via phase correlations across many length scales and produce energy spectra which are steeper than the Kraichnan-Batchelor spectrum E(k) ∼ k −3 for the enstrophy cascade.…”

“…In addition to coherent structures, another cause of intermittency in the 2D enstrophy cascade can be contamination from the 3D effects in any real flow situation. In the geophysical context, it can be caused by the Ekman drag ( [31]) which simulates the frictional planetary boundary layer (Pedlosky [33]). The Ekman drag acts also as a sink at low wave numbers to take out the 'condensate' from the inverse energy cascade.…”

Controlling the dual cascade of two-dimensional turbulence

“…In two dimensions, the effects of linear damping which is active in all scales (as opposed to Rayleigh friction which is active only at the largest scales) has been studied in recent years (Boffetta et al 2002;Tsang et al 2005;Tsang & Young 2009). It should be noted that both linear forcing and linear damping are active over all scales, including the energy and enstrophy inertial ranges.…”