In this work, the authors develop new methods for the accurate and efficient solution of the two-dimensional, incompressible Euler equations in the vorticity form. Here, the velocity is recovered directly from the Biot-Savart relation with vorticity, and the vorticity is evolved through its transport equation. Using a generalized Poisson summation formula, the full asymptotic error expansion is...

Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity "eld, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For su$ciently deep submergence of the cylinder, the orbital natu...

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 present results on the connection between the vorticity equation and the shape and evolution of the single-point vorticity probability density function. The statistical framework for these observations is based on the classical hierarchy of evolution equations for the probability density functions by Lundgren, Novikov, and Monin combined with conditional averaging of the unclosed terms. The ...

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 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.

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...

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...