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 ...

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 ...

[1] The modification of near‐surface near‐inertial oscillations (NIOs) by the geostrophic vorticity is studied globally from an observational standpoint. Surface drifter are used to estimate NIO characteristics. Despite its spatial resolution limits, altimetry is used to estimate the geostrophic vorticity. Three characteristics of NIOs are considered: the relative frequency shift with respect t...

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...

The mechanism for the generation of vorticity at a viscous free surface is described This is a free surface analogue of Lighthill s strategy for determining the vorticity ux at solid boundaries In this method the zero shear stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity vorticity description of the ow A vortex sheet along t...

The mechanism for the generation of vorticity at a viscous free surface is described. This is a free-surface analogue of Lighthill’s strategy for determining the vorticity flux at solid boundaries. In this method the zero-shear-stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity– vorticity description of the flow. A vortex sheet...

We derive the dispersion relation for water waves with surface tension and having a piecewise constant vorticity distribution. More precisely, we consider here two scenarios; the first one is that of a flow with constant non-zero vorticity adjacent to the flat bed while above this layer of vorticity we assume the flow to be irrotational. The second type of flow has a layer of non-vanishing vort...

Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching...