Intermittency in 2D soap film turbulence

Abstract

The Reynolds number dependency of intermittency for 2D turbulence is studied in a flowing soap film. The Reynolds number used here is the Taylor microscale Reynolds number R_{\lambda}, which ranges from 20 to 800. Strong intermittency is found for both the inverse energy and direct enstrophy cascades as measured by (a) the pdf of velocity differences P(\delta u(r)) at inertial scales r, (b) the kurtosis of P(\partial_x u), and (c) the scaling of the so-called intermittency exponent \mu, which is zero if intermittency is absent. Measures (b) and (c) are quantitative, while (a) is qualitative. These measurements are in disagreement with some previous results but not all. The velocity derivatives are nongaussian at all R_{\lambda} but show signs of becoming gaussian as R_{\lambda} increases beyond the largest values that could be reached. The kurtosis of P(\delta u(r)) at various r indicates that the intermittency is scale dependent. The structure function scaling exponents also deviate strongly from the Kraichnan prediction. For the enstrophy cascade, the intermittancy decreases as a power law in R_{\lambda}. This study suggests the need for a new look at the statistics of 2D turbulence.Comment: 15 pages, 11 figure

One-dimensional hydrodynamic model generating a turbulent cascade

“…However the logarithmic local slope, [ln S 2 (r + ∆r) − ln S 2 (r)]/[ln(r + ∆r) − ln r] (∆r being the grid size), does not converge to a unique constant value in the IR as we decrease ν. One possibility is that the power-law exponent of S 2 (r) in the IR depends on ν (similar dependence was found for the velocity structure function of the 2D enstrophy-cascade turbulence [23]). Another possibility is that the dominant part of S 2 (r) is not a pure power law but with a correction.…”

“…Concerning the energy spectrum, the difference from the KLB k −3 scaling is more measurable in the gCLMG turbulence than in the 2D turbulence. The spectrum of the latter is occasionally fitted with the power law k −3.3 [16,17,[23][24][25]. Regarding the vorticity structure functions of the 2D turbulence, the result obtained in the laboratory experiment [26] showed that those of even orders up to 10 in the IR have power-law exponents indistinguishable from zero.…”

The collisionality dependence of intermittency level in drift-wave turbulence in the stellarator TJ-K

“…24,32,33 ). For a variable g(r) defined in space, the structure function of order q for points spaced L apart in the field is calculated from…”

“…This observation allows a more accurate estimate of ζ q to be made, and therefore a more accurate estimate of the scaling of the power-law relation, and the intermittent properties of the data. The intermittency level may be estimated by calculating the deviation of the 6th order structure function scaling exponent ζ 6 from the non-intermittent prediction of ζ 6 /ζ 3 = 2 24,32 . This is sometimes called the intermittency exponent 24,32 , and it appears in the log-normal model of intermittency.…”

“…The intermittency level may be estimated by calculating the deviation of the 6th order structure function scaling exponent ζ 6 from the non-intermittent prediction of ζ 6 /ζ 3 = 2 24,32 . This is sometimes called the intermittency exponent 24,32 , and it appears in the log-normal model of intermittency. Using this as a measure for intermittency in our case makes additional sense since it makes use of the highest available experimental structure function order, which deviates the most from the non-intermittent prediction.…”