The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.

Human Tracking Method Based on Maximally Stable Extremal Regions with Multi-Cameras

With respect to the human tracking with multi-cameras in the video surveillance system, a human tracking method based on MSER (Maximally Stable Extremal Regions) was established. The approach transforms the human tracking into elliptic region matching. The method does elliptic region fitting to each MSER, and then selects the elliptic regions which meet some constraints. These selected elliptic regions are normalized to unity circular regions. The right matched elliptic regions are gotten by rotational invariant vectors calculation, histogram density estimation and weighted average distance calculation. Experimental results show that the approach can effectively realize the human tracking with multi-cameras.

On non-elliptic regions and solvability of balance equations for atmosphere dynamics

To eliminate the fast gravitational waves of great amplitude, which are not observed in the real atmosphere, the initial fields for numerical schemes of atmosphere forecasting and modeling systems are usually adjusted dynamically by applying balance relations. In this study we consider different forms of the balance equations and for each of them we detect the nonelliptic regions in the gridded atmosphere data of the Southern Hemisphere. The performed analysis reveals the geographical, vertical and zonally averaged distributions of nonelliptic regions with the most concentration in the tropical zone. The area of these regions is essentially smaller and less intensive for more complete and physically justified balance relations. The obtained results confirm the Kasaharas assumption that ellipticity conditions are violated in the actual atmospheric fields essentially due to approximations made under deriving the balance equations.

Coherent vortices and tracer cascades in two-dimensional turbulence

We study numerically the scale-to-scale transfers of enstrophy and passive-tracer variance in two-dimensional turbulence, and show that these transfers display significant differences in the inertial range of the enstrophy cascade. While passive-tracer variance always cascades towards small scales, enstrophy is characterized by the simultaneous presence of a direct cascade in hyperbolic regions and of an inverse cascade in elliptic regions. The inverse enstrophy cascade is particularly intense in clusters of small-scales elliptic patches and vorticity filaments in the turbulent background, and it is associated with gradient-decreasing processes. The inversion of the enstrophy cascade, already noticed by Ohkitani (Phys. Fluids A, vol. 3, 1991, p. 1598), appears to be the main difference between vorticity and passive-tracer dynamics in incompressible two-dimensional turbulence.