Understanding the physical mechanisms of how the flow field and its structure affect the transport of mass or heat in turbulent flow is important for controlling turbulent transport. A possible approach is to relate helicity density and normalized helicity to transport, since helicity has been shown to identify and differentiate primary and secondary vortices [1]. Defined as the dot product of the velocity,
u, and vorticity,
ω [2], high values of helicity indicate high speed and high vorticity and a small angle between the two vectors. There have been several studies focusing on the effect of helicity on the energy cascade and the relation between helicity and dissipation or intermittency and coherent flow structures [3,4]. Some studies argued that when helicity increases, the dissipation decreases, or the regions which are helical have low dissipation. However, other reports applied on different flow configurations demonstrated that relative helicity was not associated with low dissipation or coherent structures [5]. Speziale proved the theorical suggestion that there was no relation between helicity and dissipation when the Lamb vector was decomposed into irrotational and solenoidal parts [6]. Therefore, the role of helicity in turbulence has been debated [7]. In this study, we employed Direct Numerical Simulation in combination with Lagrangian Scalar Tracking method for particles in Couette and channel flow with viscous Reynolds number Re
Ï„=300. The trajectories of particles at different Schmidt numbers, Sc, were calculated in these flow fields with the goal of elucidating the correlation between helicity and helicity density to dissipation for transport in anisotropic turbulence. The Couette flow was applied to show the interaction between helicity and large- scale flow structures. The correlation between helicity and dissipation has been characterized through calculations of the Joint Probability Density Function, auto-correlations and Pearson cross-correlations between helicity density and dissipation along the trajectories of particles released in the flow field at various distances form the wall of the channel. Particles that exhibited the highest helicity and particles that were transported the farthest in the direction normal to the channel walls were isolated to determine the flow conditions that they experienced during their dispersion in the flow field. In general, this presentation will be focused on the relation between helicity and dissipation at different types of flow and different Sc numbers. While helicity and dissipation do not appear to be correlated, the normalized helicity appears to be related to effective turbulent transport.
ACKNOWLEDGEMENTS
The support of NSF under grant 1803014 is gratefully acknowledged as the use of computing facilities at the University of Oklahoma Supercomputing Center for Education and Research (OSCER) and at XSEDE (under allocation CTS-090025).
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