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On helical multiscale characterisation of homogeneous turbulence

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Topological Dynamics in the Physical and Biological Sciences

The helical properties of five prototypical homogeneous turbulent flows are investigated: statistically steady forced isotropic turbulence, decaying isotropic turbulence, decaying rotating turbulence, growing sheared turbulence, and growing rotating sheared turbulence with a rotation ratio f/S = +0.5. The five turbulent flows were originally studied using direct numerical simulations. An orthogonal wavelet decomposition is used to study the scale-dependent properties of the cases. For comparison, a solenoidal uncorrelated Gaussian random field is included in the analysis as a sixth case. It was found that flows with growing turbulent kinetic energy and turbulent motion at large scales show a maximum in the velocity helicity probability distribution functions (PDFs) at zero, corresponding to a trend to local two-dimensionalization of the flow with vorticity and velocity being perpendicular. Flows with decaying turbulent kinetic energy and turbulent motion at small scales, how ever, show maxima of the velocity helicity PDFs at plus and minus one, indicating a preference for helical motion with alignment or anti-alignment of vorticity and velocity. The PDFs of vorticity helicity always assume maxima at plus and minus for all flows. Joint PDFs of relative velocity helicity and relative vorticity helicity show that the quantities tend to have the same sign for all flows including the random field, indicating that vorticity helicity dissipates velocity helicity.

This talk is part of the Isaac Newton Institute Seminar Series series.

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