Velocity fluctuations in a turbulent soap film: The third moment in two dimensions

Quasi-two-dimensional decaying turbulence is studied in a flowing soap film by measuring the moments of the probability density function P(δv(r)) for the longitudinal velocity differences δv(r) on a scale r. As in three-dimensional (3-D) turbulence, P becomes non-Gaussian with decreasing r. The third moment S₃(r) ≡ 〈(δv(r))³〉 is small and negative at small scales, but becomes positive at larger scales. The exact calculation of S₃(r) for 2-D homogeneous isotropic turbulence relates this change in sign to the development of the velocity correlation function as the turbulence decays.