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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 ...
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:
Within that region, the flow is no longer irrotational: the vorticity becomes non-zero, with direction roughly parallel to the vortex axis. The Rankine vortex is a model that assumes a rigid-body rotational flow where r is less than a fixed distance r 0 , and irrotational flow outside that core regions.
More simply, vortex lines move with the fluid. Also vortex lines and tubes must appear as a closed loop, extend to infinity or start/end at solid boundaries. Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have application in understanding: Generation of lift on an airfoil; Starting vortex; Horseshoe vortex
A vortex is a region where the fluid flows around an imaginary axis. For an irrotational vortex, the flow at every point is such that a small particle placed there undergoes pure translation and does not rotate. Velocity varies inversely with radius in this case.
A turbulent flow is a flow regime in fluid dynamics where fluid velocity varies significantly and irregularly in both position and time. [3] Furthermore, a coherent structure is defined as a turbulent flow whose vorticity expression, which is usually stochastic, contains orderly components that can be described as being instantaneously coherent over the spatial extent of the flow structure.
Animation of a Rankine vortex. Free-floating test particles reveal the velocity and vorticity pattern. The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an irrotational (potential or free ...
In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum. [1] Vortex stretching is associated with a particular term in the vorticity equation. For example ...