In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow (Moffatt 1969). Let be the velocity field and the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible (), or it is compressible with a barotropic relation between pressure and density on which Let is defined by and , where , where and

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  • In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow (Moffatt 1969). Let be the velocity field and the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible (), or it is compressible with a barotropic relation between pressure and density ; and (iii) any body forces acting on the fluid are conservative. Under these conditions, any closed surface on which is, like vorticity, transported with the flow. Let be the volume inside such a surface. Then the helicity in is defined by For a localised vorticity distribution in an unbounded fluid, can be taken to be the whole space, and is then the total helicity of the flow. is invariant precisely because the vortex lines are frozen in the flow and their linkage and/or knottedness is therefore conserved, as recognized by Lord Kelvin (1868). Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow. Helicity is the only known integral invariant of the Euler equations, apart from energy, momentum and angular momentum. For two linked unknotted vortex tubes having circulations and , and no internal twist, the helicity is given by , where is the Gauss linking number of the two tubes, and the plus or minus is chosen according as the linkage is right- or left-handed.For a single knotted vortex tube with circulation , then, as shown by Moffatt & Ricca (1992), the helicity is given by , where and are the writhe and twist of the tube; the sum is known to be invariant under continuous deformation of the tube. The invariance of helicity provides an essential cornerstone of the subject topological fluid dynamics and magnetohydrodynamics, which is concerned with global properties of flows and their topological characteristics. (en)
  • En dynamique des fluides, l’hélicité est une mesure de l’effet d’entraînement qu’aura une rotation locale sur une parcelle de fluide. C’est une quantité utilisée pour déduire la turbulence du fluide et qui est particulièrement employée en météorologie pour estimer le potentiel tornadique. L’hélicité est une grandeur conservée si le fluide obéit aux équations de Navier-Stokes pour un fluide parfait et incompressible. (fr)
  • En mecánica de fluidos, la helicidad es una magnitud física asociada al flujo que mide en cada punto del mismo la proyección de la vorticidad sobre la velocidad, dado que la combinación de un giro con una traslación perpendicular a él genera una hélice de ahí proviene el nombre. (es)
  • In fluidodinamica, l' elicità idrodinamica è, sotto appropriate condizioni, un'invariante delle equazioni di Eulero del flusso dei fluidi, che ha interpretazione topologica come misura del link o della nodosità delle linee di vortice di un flusso. (it)
  • 流体力学において、ヘリシティー(英: helicity)はコルクスクリュー様の回転運動が起こる程度を表す。乱流を理論的に記述するために有用な概念である。 (ja)
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  • En dynamique des fluides, l’hélicité est une mesure de l’effet d’entraînement qu’aura une rotation locale sur une parcelle de fluide. C’est une quantité utilisée pour déduire la turbulence du fluide et qui est particulièrement employée en météorologie pour estimer le potentiel tornadique. L’hélicité est une grandeur conservée si le fluide obéit aux équations de Navier-Stokes pour un fluide parfait et incompressible. (fr)
  • En mecánica de fluidos, la helicidad es una magnitud física asociada al flujo que mide en cada punto del mismo la proyección de la vorticidad sobre la velocidad, dado que la combinación de un giro con una traslación perpendicular a él genera una hélice de ahí proviene el nombre. (es)
  • In fluidodinamica, l' elicità idrodinamica è, sotto appropriate condizioni, un'invariante delle equazioni di Eulero del flusso dei fluidi, che ha interpretazione topologica come misura del link o della nodosità delle linee di vortice di un flusso. (it)
  • 流体力学において、ヘリシティー(英: helicity)はコルクスクリュー様の回転運動が起こる程度を表す。乱流を理論的に記述するために有用な概念である。 (ja)
  • In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow (Moffatt 1969). Let be the velocity field and the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible (), or it is compressible with a barotropic relation between pressure and density on which Let is defined by and , where , where and (en)
rdfs:label
  • Hydrodynamical helicity (en)
  • Helicidad (mecánica de fluidos) (es)
  • Hélicité (dynamique des fluides) (fr)
  • Elicità idrodinamica (it)
  • ヘリシティー (流体) (ja)
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