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Abstract: Helicity is a quadratic invariant of the Euler equation in three dimensions.As the energy, when present helicity cascades to smaller scales where itdissipates. However, the role played by helicity in the energy cascade is stillunclear. In non-helical flows, the velocity and the vorticity tend to alignlocally creating patches with opposite signs of helicity. Also in helical flowshelicity changes sign rapidly in space. Not being a positive definite quantity,global studies considering its spectral scaling in the inertial range areinconclusive, except for cases where one sign of helicity is dominant. We usethe cancellation exponent to characterize the scaling laws followed by helicityfluctuations in numerical simulations of helical and non-helical turbulentflows, with different forcing functions and spanning a range of Reynoldsnumbers from approximately 670 to 6200. The exponent is a measure ofsign-singularity and can be related to the fractal dimension as well as to thefirst order helicity scaling exponent. The results are consistent with thegeometry of helical structures being filamentary. Further analysis indicatesthat statistical properties of helicity fluctuations do not depend on theglobal helicity of the flow.



Author: Paola Rodriguez Imazio, Pablo Daniel Mininni

Source: https://arxiv.org/







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