Statistical Fluctuations of Two Dimensional Turbulence

by Jun, Yonggun

The statistics of two-dimensional (2D) turbulence driven by electro-magnetic force are investigated in freely-suspended soap film. The turbulent flow is analyzed using the particle imaging velocimetry (PIV) method. In this thesis, three important features of 2D turbulence are mainly studied. First, the effects of addition of small amounts of polymers on 2D turbulent flows are carefully investigated. As the polymer concentration $phi$ increases, large scale velocity fluctuations are suddenly suppressed at a certain $phi$. This suppression is believed to happen due to the redistribution of saddle points of the flow. It implies that the saddle structures may play a role in energy-transfer to large scales. The thesis also presents 2D intermittency in inverse energy cascade regime. In this subrange, the energy transfers from injection scale $l_{inj}$ to large scales. Intermittency is recognized and analyzed by the structure function $S_{p}(l)$ of the velocity difference between two points, and log-normal model of the energy dissipation rate $varepsilon$. The analyses show signs of intermittency even though its intensity is weaker than that in three-dimensional (3D) turbulence. Finally, single-point(SP) velocity statistics are investigated, inspired by the theory proposed by Falkovich and Lebedev (FL). This theory reveals the connection between SP statistics and forcing statistics. For forced 2D turbulence, the SP velocity probability distribution function (PDF) deviates from Gaussian when turbulence intensity is sufficiently strong, which can be explained using FL theory. In the case of decaying turbulence, SP velocity PDF gradually evolves from super-Gaussian to sub-Gaussian as time increases.