Vorticity

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  • Vorticity
definition
  • Measure of the rotational spin about an axis at some point within a fluid (or wind field). 
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Abstract from DBPedia
    In continuum mechanics, the 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. Conceptually, vorticity could be determined by marking the part of continuum 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 is a pseudovector field ω→, defined as the curl (rotational) of the flow velocity u→ vector. The definition 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 (line integral of the velocity) along a closed path by the (classical) Stokes' theorem. 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→ ∙ (dA n→) where ω→ is the vorticity at the center of C. Many phenomena, such as the blowing out of a candle by a puff of air, are more readily explained in terms of vorticity rather than the basic concepts of pressure and velocity. This applies, in particular, to the formation and motion of vortex rings.

    渦度(うずど、かど)は、流れの回転するありさまを表現する量である。渦度はベクトル量(さらに言えば擬ベクトル)であり、流れの速度ベクトルのなすベクトル場の回転である。 渦度ベクトル Ω は流速ベクトル v = (vx, vy, vz) により、以下のように表される。 渦度ベクトルを流線のようにつなげた曲線を渦線という。流れの中のある閉曲線上の各点を通る渦線によってできる曲面を渦管という。断面積を無限小にした渦管を渦糸という。渦糸が閉曲線になっている場合、これを渦輪という。

    (Source: http://dbpedia.org/resource/Vorticity)

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