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In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry. A surface with a constant value of the Stokes stream function encloses a streamtube, everywhere tangential to the flow velocity vectors. Further, the volume flux within this streamtube is constant, and all the streamlines of the flow are located on this surface. The velocity field associated with the Stokes stream function is solenoidal—it has zero divergence. This stream function is named in honor of George Gabriel Stokes. ==Cylindrical coordinates== Consider a cylindrical coordinate system ( ''ρ'' , ''φ'' , ''z'' ), with the ''z''–axis the line around which the incompressible flow is axisymmetrical, ''φ'' the azimuthal angle and ''ρ'' the distance to the ''z''–axis. Then the flow velocity components ''uρ'' and ''uz'' can be expressed in terms of the Stokes stream function by:〔Batchelor (1967), p. 78.〕 : The azimuthal velocity component ''uφ'' does not depend on the stream function. Due to the axisymmetry, all three velocity components ( ''uρ'' , ''uφ'' , ''uz'' ) only depend on ''ρ'' and ''z'' and not on the azimuth ''φ''. The volume flux, through the surface bounded by a constant value ''ψ'' of the Stokes stream function, is equal to ''2π ψ''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stokes stream function」の詳細全文を読む スポンサード リンク
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