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👉 Toroid (geometry) in the context of Solid torus

In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle. It is homeomorphic to the Cartesian product $S^{1}\times D^{2}$ of the disk and the circle, endowed with the product topology.

A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, which has the same visual appearance: the torus is the two-dimensional space on the boundary of a toroid, while the solid torus includes also the compact interior space enclosed by the torus.

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Toroid (geometry) in the context of Vortex ring

A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid; that is, a region where the fluid mostly spins around an imaginary axis line that forms a closed loop. The dominant flow in a vortex ring is said to be toroidal, more precisely poloidal.

Vortex rings are plentiful in turbulent flows of liquids and gases, but are rarely noticed unless the motion of the fluid is revealed by suspended particles—as in the smoke rings which are often produced intentionally or accidentally by smokers. Fiery vortex rings are also a commonly produced trick by fire eaters. Visible vortex rings can also be formed by the firing of certain artillery, in mushroom clouds, in microbursts, and rarely in volcanic eruptions.

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Toroid (geometry) in the context of "Solid torus"

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👉 Toroid (geometry) in the context of Solid torus

Toroid (geometry) in the context of Vortex ring