We analyze the dynamics of a perfectly flexible string with a constant length and a vanishing inner friction. The local angular velocity of line elements in this seemingly simple mechanical system is shown to have many mathematical and physical properties in common with vorticity in the three-dimensional incompressible Euler equation. It is demonstrated that initially smooth vorticity fields lo...

Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant. A formulation of potential vorticity...

Neutral thermospheric wind pattern at high latitudes obtained from cross-track acceleration measurements of the CHAMP satellite above both polar regions are used to deduce statistical neutral wind vorticity distributions and were analyzed in their dependence on the Interplanetary Magnetic Field (IMF). The average pattern confirms the large duskside anticyclonic vortex seen in the average wind p...

The three-dimensionality of the velocity field in the wake of a circular cylinder has excited considerable interest and debate over the past decade. Presented here are experimental results that characterize the underlying vorticity field of such wakes. Using particle image velocimetry (PIV), instantaneous velocity fields were measured and from these the vorticity of the longitudinal vortices ly...

1. introduction heavy snow hazards, although have less frequency in comparison with extreme weather events such as freezing, but are major hazards in midlatitudes (smith, 2009, 196). heavy snow damages manmade structures, crops, casualties, even between urban and rural ways of blocking.(briant. 69, 2005. ohara et al, 2009, 1611). various definitions have been offered for heavy snow, those are c...

The relationship between tropical cyclogenesis and solar activity is addressed in this paper, analyzing the relationship between important parameters in the evolution of tropical cyclones as the CAPE, wind shear and relative vorticity, and the Dst geomagnetic index as a parameter of solar activity. The apparent relationship between all this phenomena has a different response depending on the ph...

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.