Energy and velocity of a forming vortex ring

Energy and velocity of a forming vortex ring

It is known that vortex rings formed by large stroke ratios ~in a piston/cylinder arrangement! pinch off from their generating jets at a fairly constant universal time scale. In this paper we show that the hypothesis that at the pinch off the translational velocity of the ring equals the jet flow velocity near the ring is equivalent to the recently proposed idea based on a variational principle...

Velocity, energy, and helicity of vortex knots and unknots.

In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w given by the ratio of the number of meridian...

Vortex ring

By rigorous mathematical method, we construct traveling wave solutions with a stationary or traveling vortex ring to the Gross-Pitaevskii equation iût = ε 2 4 û + ( Ṽ − |û| ) û, û ∈ H(R), where the unknown function û is defined as û : R × R → C, ε is a small positive parameter and Ṽ is a smooth potential.

A formulation for calculating the translational velocity of a vortex ring or pair.

Cephalopods, among other marine animals, use jet propulsion for swimming. A simple actuator is designed to loosely mimic pulsatile jet formation in squid and jellyfish. The actuator is comprised of a cavity with an oscillating diaphragm and an exit orifice. Periodic oscillation of the diaphragm results in the formation of an array of vortex rings and eventually could generate a periodic pulsati...

Evolution of a Curved Vortex Filament into a Vortex Ring