TY - JOUR
T1 - Vorticity statistics in the direct cascade of two-dimensional turbulence
AU - Falkovich, Gregory
AU - Lebedev, Vladimir
N1 - Minerva Foundation and Israel Science Foundation; Russian Foundation for Basic Research [09-02-01346-a]We thank I. Kololokolov and S. Korshunov for useful discussions. The work of G. F. is supported by grants from the Minerva Foundation and Israel Science Foundation. The work of V.L. is supported by the Russian Foundation for Basic Research (Grant No. 09-02-01346-a).
PY - 2011/4/11
Y1 - 2011/4/11
N2 - For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When is the vorticity coarse-grained over a scale R, the probability density function (PDF), P, has a universal asymptotic behavior lnP~-rms at rms=[Hln(L/R)]1/3, where H is the enstrophy flux and L is the pumping length. Therefore, the PDF has exponential tails and is self-similar, that is, it can be presented as a function of a single argument, rms, in distinction from other known direct cascades.
AB - For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When is the vorticity coarse-grained over a scale R, the probability density function (PDF), P, has a universal asymptotic behavior lnP~-rms at rms=[Hln(L/R)]1/3, where H is the enstrophy flux and L is the pumping length. Therefore, the PDF has exponential tails and is self-similar, that is, it can be presented as a function of a single argument, rms, in distinction from other known direct cascades.
UR - http://www.scopus.com/inward/record.url?scp=79961095580&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.83.045301
DO - 10.1103/PhysRevE.83.045301
M3 - مقالة
SN - 1539-3755
VL - 83
JO - Physical Review E
JF - Physical Review E
IS - 4
M1 - 045301
ER -