Vortex Dynamics In 2-D Flow And Control

Vortex motion is the general pattern of fluid and the main content of vortex dynamics. As an important branch of fluid mechanics, vortex dynamics has a long history and good application value in engineering. The lifting line (or surface) theory is based on the vortex model, which consists of attached vortices and free vortices. Flow separation is directly related to generation and influx of vortices near the bound. Especially, the properties of random, coherent, quasi-order and intermittent in turbulence are the results of interaction of vortices with different sizes. Nevertheless, vortex motion, in general, is strong unsteady and nonlinear. These properties make the research more difficult. Ignoring the stretch of 3-D vortex, we focus on some problems of 2-D point vortex dynamics.After the detailed review on 2-D point vortex dynamics, the general results of vortices and Hamiltonian framework, as a theoretical basis of this paper, are introduced. Thereafter, some important problems of point vortex dynamics are discussed and studied systematically, which includes the motion patterns of many vortices, the influence of bound, the motion of passive particles and effect of viscosity(white noise) in point vortex system. Of course, an attempt to settle each problem thoroughly is impractical, so we choose the integrable or nearly integrable point vortex system as research objects. Firstly, we show the bound destroys the self-similar motion of vortices in the upper half plane. Subsequently, thickness of Random layer in vortex system is estimated by the approach of Kuznetsov and Zaslavsky, and the partition of flow field is also obtained by (local) Lyapunov exponent, as the measurement of stability of passive particle. At last,using Fokker-Planck equations to construct a mathematical model, the advection and diffusion of vortex patches are described. The investigation shows the strong advection in the collapse process is avoided by the exciting role of white noise (slight viscousity). These researches are very useful to comprehension of vorticity fleid, turbulence and directing flow control.