Statistical analysis of the effects of helicity in inhomogeneous turbulence

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Abstract
Effects of helicity in three‐dimensional incompressible inhomogeneous turbulence are examined with the aid of a two‐scale direct‐interaction approximation (DIA). The turbulent helicity gives a measure of the reflectional asymmetry in a turbulent flow and its inhomogeneity contributes to the sustainment of large‐scale vorticity field in a three‐dimensional mean flow. The importance of helicity effects is discussed in the context of flows in a rotating system and swirling flows in a pipe. A three‐equation model with the turbulent helicity incorporated is proposed using the theoretical results. The validity of the model is confirmed quantitatively through the application to a decaying swirling flow in a pipe.