Helicity in Laminar and Turbulent Flow

The quantity h(x, t) = u" o~ is the helicity density of the flow. Both h and ~ are pseudoscalar quantities, i.e. they change sign under change from a right-handed to a left-handed frame of reference (parity transformation). It is important therefore to specify the frame that is used; we shall always use a right-handed Cartesian (or orthogonal curvilinear) frame unless otherwise stated. The simplest (prototype) helical flow u = U+1⁄2f~ x where U and f~ are constants. Then curl

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