In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro’s paper is that solutions of the incompressible 2D Euler equations with compactly supported nonnegative initial vorticity in the exterior of a connected bounded region have vorticity support with diameter growing at most...

It is not unreasonable to expect that boreal forests which exist along 60 o N in the Eurasian and North American continents were created and are maintained by warm seasonal rainfall. As revealed from satellite observations and various precipitation sources, zonally elongated rainbelts appear along these forests. Previous studies show that a relationship may exist between the frontal zone along ...

We present a general Lagrangian formalism that allows the treatment of vorticity. We give solutions for the rotational perturbations up to the third-order in a flat background universe. We show how the primordial vorticity affects the evolution of the density fluctuation in high-density regions. The study of the galaxy formation based on gravitational instability has not revealed the origin of ...

We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998,...

Research into dynamic bushfire behaviour conducted over the last few years has shown that bushfires burning on lee-facing slopes can exhibit atypical forms of propagation under extreme weather conditions. For instance, recent numerical simulations have indicated that pyrogenic vorticity (the curl of the velocity field) is a key driver of rapid lateral fire spread as a consequence, this type of ...

The determination of the flow properties of a fluid containing a cylindrical inclusion with its long axis oriented parallel to the vorticity direction is a 2-dimensional problem which is treated as a special case in a calculation of the corresponding D-dimensional problem. The velocity and pressure are obtained from the solution of the equations of hydrodynamics where D-dimensional multipole po...

We investigate the stability of self-propelled particle flocks in the Taylor-Green vortex, a steady vortical flow. We consider a model in which particles align themselves to a combination of the orientation and the acceleration of particles within a critical radius. We identify two distinct regimes: If alignment with orientation is dominant, the particles tend to be expelled from regions of hig...

A three-dimensional vortex element method is developed to simulate the flow field of an incompressible transverse jet at high Reynolds number — in particular, to explore the response of large-scale vortical structures in the jet to actuation. Vorticity produced in the channel wall boundary layer interacts with the jet flow at the nozzle exit, producing both axial and azimuthal perturbations to ...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

Large fluctuations in complex systems from earthquakes to financial markets, though infrequent, are particularly important because of their disproportionate impact. Our ability to forecast them is quite poor at present. Large fluctuations occur also in intermittent features of turbulent flows. Some dynamical understanding of these features is possible because the governing equations are known a...