This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120◦ or a horizontal tange...

We show that the vorticity appearing in stationary vacuum spacetimes is always related to the existence of a flow of super–energy on the plane orthogonal to the vorticity vector. This result, toghether with the previously established link between vorticity and super–energy in radiative (Bondi–Sachs) spacetimes strength further the case for this latter quantity as the cause of frame dragging.

We study a two-phase sample of superfluid 3He where vorticity exists in one phase (3He-A) but cannot penetrate across the interfacial boundary to a second coherent phase (3He-B). We calculate the bending of the vorticity into a surface vortex sheet on the interface and solve the internal structure of this new type of vortex sheet. The compression of the vorticity from three to two dimensions en...

We prove that for a large class of vorticity functions the crest of a corresponding travelling water wave is necessarily a point of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure in the flow is everywhere larger than the atmospheric pressure. A related a priori estimate for waves with nonnegative vorticity is also given.

The effect of constant background vorticity on the pressure beneath steady long gravity waves at the surface of a fluid is investigated. Using an asymptotic expansion for the streamfunction, we derive a model equation and a formula for the pressure in a flow with constant vorticity. The model equation was previously found by Benjamin (1962), [3], and is given in terms of the vorticity ω0, and t...

In incompressible Euler flows, vorticity is intensified by line stretching, a process that can come either from the action of shear, or from advection with curvature. Focusing on the latter process, we derive some estimates on the maximal growth of vorticity in axisymmetric flow without swirl, given that vorticity support volume or kinetic energy is fixed. This leads to consideration of locally...

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 authors employ data from the NOAA Wind Profiler Network to present a scale-discriminating vorticity budget for a mesoscale convective vortex (MCV) that was generated by a mesoscale convective system (MCS) in Oklahoma and Kansas on 1 August 1996. A spatial bandpass filter was used to divide observed wind into mesoscale and synoptic components. Then the authors sought sources and sinks of vor...

Two aspects of vorticity associated with cold pools are addressed. First, tilting of horizontal vortex tubes by the updraft at a gust front has been proposed as a means of getting near-ground rotation and hence a tornado. Theory and a numerical simulation are used to show that this mechanism will not work because warm air parcels approaching the gust front decelerate in strong adverse pressure ...