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The strength of a vortex line is constant along its length. Helmholtz's second theorem A vortex line cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path. Helmholtz's third theorem A fluid element that is initially irrotational remains irrotational. Helmholtz's theorems apply to inviscid flows.
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. The 'strength' of a vortex tube (also called vortex flux ) [ 10 ] is the integral of the vorticity across a cross-section of the tube, and is the same everywhere along the tube (because vorticity has zero ...
A plughole vortex. The fluid motion in a vortex creates a dynamic pressure (in addition to any hydrostatic pressure) that is lowest in the core region, closest to the axis, and increases as one moves away from it, in accordance with Bernoulli's principle. One can say that it is the gradient of this pressure that forces the fluid to follow a ...
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases.It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of water and other liquids in motion).
This article summarizes equations in the theory of fluid mechanics. Definitions. Flux F through a surface, dS is the differential vector area element, ...
Similarly, when a vortex of air is broadened, it in turn spins more slowly. When the air converges horizontally, the air speed increases to maintain potential vorticity, and the vertical extent increases to conserve mass. On the other hand, divergence causes the vortex to spread, slowing down the rate of spin.
A vortex beam of order l will be split into n = l + 1 lobes, roughly around the depth of focus of a tilted convex lens. Furthermore, the orientation of lobes (right and left diagonal), determine the positive and negative orbital angular momentum orders. [16] A vortex beam generates a lobe structure when interfered with a vortex of opposite sign.