Single-point velocity statistics of forced and decaying two-dimensional turbulence

The single-point (SP) velocity statistics are investigated in forced and decaying two-dimensional turbulence in a flowing soap film. It is shown that the probability distribution functions (PDF) in both cases deviate from a Gaussian distribution, which is normally anticipated in turbulent fluid flows. In the forced turbulence case, the tail of the SP velocity PDF decays faster than Gaussian (termed the sub-Gaussian) and can be correlated with the forcing statistics on small scales. In the decaying-turbulence case, the SP velocity PDF evolves from a sub-Gaussian to a super-Gaussian behavior as a function of time. However, in all times, the locally averaged vorticity remains normally distributed. While our forced turbulence data may be explained by a recent theory proposed by Falkovich et al., the decaying-turbulence data remain unexplained.