vorticity

**vorticity**

### English Definitions:

#### vorticity (Noun)

A property of a fluid related to local angular rotation

#### Vorticity

In fluid dynamics, the vorticity is a pseudovector field that describes the local spinning motion of a fluid near some point, as would be seen by an observer located at that point and traveling along with the fluid. Conceptually, the vorticity could be determined by marking the particles of the fluid in a small neighborhood of the point in question, and watching their relative displacements as they move along the flow. The vorticity vector would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. This quantity must not be confused with the angular velocity of the particles relative to some other point. More precisely, the vorticity of a flow is a pseudovector field ω→, equal to the curl of its velocity field v→. It can be expressed by the vector analysis formula: where ∇→ is the del operator. The vorticity of a two-dimensional flow is always perpendicular to the plane of the flow, and therefore can be considered a scalar field. The vorticity is related to the flow's circulation along a closed path by the Stokes equation. Namely, for any infinitesimal surface element C with normal direction n→ and area dA, the circulation dΓ along the perimeter of C is the dot product ω→ ∙ where ω→ is the vorticity at the center of C.

#### Vorticity

In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings.Mathematically, the vorticity ω → {\displaystyle {\vec {\omega }}} is the curl of the flow velocity u → {\displaystyle {\vec {u}}} :

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"vorticity." *Kamus.net.* STANDS4 LLC, 2023. Web. 4 Dec. 2023. <https://www.kamus.net/english/vorticity>.

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