We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide a wide range of examples including polynomial, exponential, trigonometric and hyperbolic vorticity functions.

The spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equatio...

We have reached our goal of implementing a computationally cheap algorithm for realtime rendering of realistic two-dimensional fire. The fire is simulated using computational fluid dynamics, vorticity confinement, and combustion modelling and visualized using black-body radiation. Small rotationally homogenous fires like torches and candles viewed in front are the best candidates when using thi...

We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated to vector fields with gradient given by a singular integral in order to define Lagrangian solutions, for which the vorticity is transported by the flow. We pr...

One of the important properties of boundary layer is, from the point of view of Strömungslehre, that it pumps vorticity into the flow field. Vorticity in fluid flows plays diverse roles and produces tremendous variety of flow phenomena. We consider four aspects of vorticity in fluid flows: (A) Kinematical aspect of a vortex sheet, (B) mechanical aspect of hydrodynamic impulse of a vortex system...

Abyssal Abyssal flows, flows, as as part part of of the the global global thermohaline thermohaline circulation, circulation, make make a a sig­ sig­ nificant nificant contribution contribution to to the the flux flux of of heat heat over over the the earth, earth, and and therefore therefore affect affect the the planet's planet's climate. climate. In In the the Atlantic, Atlantic, the the dee...

We investigated the three-dimensional vorticity dynamics of the flows generated by revolving wings using a volumetric 3-component velocimetry system. The threedimensional velocity and vorticity fields were represented with respect to the base axes of rotating Cartesian reference frames, and the second invariant of the velocity gradient was evaluated and used as a criterion to identify two core ...

This paper examines two-dimensional vortex motion in a shear-flow with nonuniform vorticity. Typically, a vortex travels to an extremum in the background vorticity distribution. In general, the rate of this migration increases with the magnitude of the background vorticity gradient; however, a retrograde vortex, which rotates against the local shear, moves orders of magnitude faster than a prog...

Interaction among potential vorticity perturbations and propagating internal gravity waves in a horizontally sheared zonal flow is investigated. In the strong stratification limit, an initial vorticity perturbation weakly excites two propagating gravity waves while the density component of the potential vorticity perturbation is significantly amplified, potentially leading to convective collaps...

The vorticity field in tokamak evolves to self organization and is concentrated in a narrow layer at the edge. The particle density and the current density have local maxima on the same layer, leading to destabilization of the rotation, breaking up of the layer and filamentation. We propose this as a basic model for the Edge Localized Modes. Large scale vorticity is injected in tokamak plasma v...