NONCONSERVATIVE DYNAMICS OF VORTICAL STRUCTURES - A STATISTICAL-MECHANICAL PERSPECTIVE

Of great interest currently in turbulent fluids are processes which do not conserve local vorticity, such as viscous decay and production and cut-and-reconnection of vortex lines. Here we examine these processes from two complementary, novel points of view. Both involve the discretization of vortex lines as well as explicit description of the inherent stochasticity. The first is a quantized or particle approach and focusses on the crucial role played by viscous decay and production in determining flow statistics. The second is a continuum or field approach and goes further to elucidate the real-space structures and instabilities in the flow. In both approaches, statistical-mechanical treatment of a nonlinear system enables us to offer some insight into these nonconservative processes.