In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...

In this note we prove that the finite time blow-up of classical solutions of the 3-D homogeneous incompressible Euler equations is controlled by the Besov space, Ḃ0 ∞,1, norm of the two components of the vorticity. For the axisymmetric flows with swirl we deduce that the blow-up of solution is controlled by the same Besov space norm of the angular component of the vorticity. For the proof of th...

[1] We present an experimental and numerical study of a rotating fluid with a zonal flow produced from small-scale eddies, a common feature of many planetary systems. The apparatus consists of a water-filled annular tank with a sloped bottom. Flow is forced mechanically at small, nonaxisymmetric scales. Potential vorticity is materially conserved and well-mixed. This implies the existence of no...

In two dimensions, vorticity is materially conserved in an invisicid environment. Additionally, if the fluid is nondivergent, the velocity field can be determined from a solution to the Poisson equation relating velocity and vorticity. Vortex methods translate these well-known facts as well as the ability to capture the time evolution of Lagrangian particles into a method of representing the fl...

This paper presents a novel non-rigid registration method. The main contribution of the method is the modeling of the vorticity (respectively divergence) of the deformation field using vortex (respectively sink and source) particles. Two parameters are associated with a particle: the vorticity (or divergence) strength and the influence domain. This leads to a very compact representation of vort...

We suggest an algorithm for the calculation of large-amplitude traveling water waves in irrotational flows and in flows with constant and nonconstant vorticity, respectively. The algorithm is based on a quite general partial differential equation constrained optimization formulation, maximizing the wave amplitude subject to the PDE constraint that the Euler equations hold. Numerical examples il...

The effect of yaw angle on wake characteristics behind a yawed square cylinder was examined at a Reynolds number (Re) of 3600. Velocity and vorticity fluctuations were measured using a one-dimensional hot-wire vorticity probe. It is found that the large-scale structures contribute the most to the streamwise and transverse velocity variances, as well as Reynolds shear stress, despite the reducti...

The transport of the potential vorticity gradient ∇q along surfaces of constant potential temperature θ is investigated for the stratified Euler, Navier–Stokes and hydrostatic primitive equations of the oceans and atmosphere, in terms of the divergence-less flux vector B = ∇Q(q)×∇θ , for any smooth function Q of the potential vorticity q. The flux vector B is shown to satisfy a transport equati...

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-S...

We present a set of equations governing the motion of a body due to prescribed shape changes in an inviscid, planar fluid with nonzero vorticity. The derived equations, when neglecting vorticity, reduce to the model developed in [4] for swimming in potential flow, and are also consistent with the models developed in [2,5,15] for a rigid body interacting dynamically with point vortices. The effe...