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Competing Physical Processes in Turbulent Fluid Dynamics

Susan Kurien

When there are two globally conserved quantities in a turbulent fluid, the dynamics of one can be influenced significantly by the dynamics of the other. This is a familiar feature in two-dimensional turbulence where conservation both of kinetic energy and of a quantity known as the enstrophy forces a net kinetic energy transfer towards large scales and a net enstrophy transfer towards the small scales. In three-dimensional turbulence, both kinetic energy and $helicity$ are quadratic invariants. Helicity is the measure of parity-breaking (helical or twisting) motions in the fluid. The kinetic energy transfer processes have been thought to dominate the dynamics at all scales with the helicity being carried along passively. We showed that helicity possesses a timescale for transfer which can affect the energy transfer rate. Consequently, our understanding of two key features of turbulent fluid dynamics might need to be revised. First we show that the commonly observed pile-up or `bottleneck' feature of kinetic energy in the small-scales may be reasonably explained by the slowing down of the energy transfer to these scales by helical effects. And second, that the presence of a competing timescale due to helicity transfer introduces a dissipation length scale that is larger than the current standard for resolved simulations of turbulence. The latter result can be used to significantly reduce the computational resources required to compute and analyze very large simulations of fluid turbulence.