Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.Comment: 7 page

Kinetic theory of point vortices: diffusion coefficient and systematic drift

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator technics, we derive a Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath of ``field'' vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization of point vortices at negative temperatures. A description that goes beyond the thermal bath approximation is attempted. A new kinetic equation is obtained which respects all conservation laws of the point vortex system and satisfies a H-theorem. Close to equilibrium this equation reduces to the ordinary Fokker-Planck equation.Comment: 50 pages. To appear in Phys. Rev.

Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting

We present a new visualization method for 2d flows which allows us to combine multiple data values in an image for simultaneous viewing. We utilize concepts from oil painting, art, and design as introduced in [1] to examine problems within fluid mechanics. We use a combination of discrete and continuous visual elements arranged in multiple layers to visually represent the data. The representations are inspired by the brush strokes artists apply in layers to create an oil painting. We display commonly visualized quantities such as velocity and vorticity together with three additional mathematically derived quantities: the rate of strain tensor (defined in section 4), and the turbulent charge and turbulent current (defined in section 5). We describe the motivation for simultaneously examining these quantities and use the motivation to guide our choice of visual representation for each particular quantity. We present visualizations of three flow examples and observations concerning some o..