The Centroid-Deformation Decomposition for Buoyant Vortex Patch Motion

The Equations of Motion for Thermally Driven, Buoyant Flows

In this paper a set of approximate equations is derived which is applicable to very nonadiabati c, nondissipative, buoyant flows of a perfect gas. The flows are assumed to be generated by a heat source in which the heat is added slowly. The study is motivated by the occurrence of such f] ows in fires. There, the time scale associated with the fire growth and resultant f]uid moti on is usually l...

The vortex patch problem for the surface quasi-geostrophic equation.

In this article, the analog of the Euler vortex patch problem for the surface quasi-geostrophic equation is considered.

Buoyant plumes and vortex rings in an autocatalytic chemical reaction.

Buoyant plumes, evolving free of boundary constraints, may develop well-defined mushroom-shaped heads. In conventional plumes, overturning flow in the head entrains less buoyant fluid from the surroundings as the head rises, robbing the plume of its driving force. We consider here a new type of plume in which the source of buoyancy is an autocatalytic chemical reaction. The reaction occurs at a...

Regularity of the velocity field for Euler vortex patch evolution

Motion of Particles under Pseudo-Deformation

In this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{A}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. We also observe that the effective force $mathbf{F}_e$ on that particle due to pseudo-force $mathbf{A}(t)$, is given by $ mathbf{F}_e= mathbf{F} mat...