Hilbert-Huang Transform Of Vorticity Statistics In Two-dimensional Turbulence And Preliminary Experiment Of Two-dimensional Turbulence

In the real world, turbulence is always three-dimensional (3D) motion. However, in some special cases, three-dimensional turbulence motion can be approximated as two-dimensional (2D) motion, that is the so-called Two-dimensional Turbulence. Although the2D turbulence manifests multi-scale similarity as3D turbulence does, but the energy transfers process is different from that in3D turbulence. The main work of this paper consists of two parts:the first part of work is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang transform, to a vorticity field obtained from a direct numerical simulation of the2D turbulence; in the second part of work, we designed and built an electromagnetically driven2D turbulence system and performed some preliminary investigative experiment of2D turbulence. The Hilbert-Huang Transform (HHT) was proposed by Prof. E Huang. In this paper, we successfully applied Hilbert-Huang Transform to the vorticity fields obtained from a2D high-resolution direct numerical simulation. A dual-cascade phenomenon is observed, i.e. the inverse energy cascade and the forward enstrophy cascade. In the inverse energy cascade, all conditional probability density function p(C|k) at given wavenumber k has an exponential tail. The shape of function p(C|k) does collapse with each other, indicating a nonintermittent cascade process. The measured scaling exponent(?)ωΙ(q) is linear with the statistical order q, i.e.,(?)ωΙ(q)=-q/3, confirming the nonintermittent cascade process. In the forward enstrophy cascade, the core part of p(C|k) is changing with wavenumber k, indicating an intermittent forward cascade. The measured scaling exponent(?)ωF(q) is nonlinear with q and can be described very well by a log-Poisson fitting:(?)ωF(q)=q/3+0.45(10.43q).The second part of work focused on the experiment research of2D turbulence. First, we explained how the electromagnetically driven2D turbulence system worked and provided some fundamental parameters of the experiment system. Then, we conducted some preliminary exploratory experiments by two different experimentaltechniques, i.e., Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry(PTV). We obtained velocity and vorticity fields of2D turbulence using PIVexperimental technique and then calculated energy spectrum which manifested thedouble cascade with a turning point that approximately corresponded to the injectedscale of our experiment. Through PTV experimental method, we successfullyobtained the trajectory of mass centroid of particle, i.e., translational movementinformation, and also the evolution of centroid axis of rod-like particle, i.e.,rotational movement information. And instantaneous particle velocities (and angularvelocities) are measured by low-pass fitting to the trajectories. In the end, we drewup the probability density function (PDF) of particle velocities and angular velocities.However, the curve of PDF was not smooth enough, which was caused by theinsufficient of experimental data sets, and much more experiments were needed to beperformed...