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Structure and scaling of extremely large velocity gradients in hydrodynamic turbulence.

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TUR - Mathematical aspects of turbulence: where do we stand?

Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients, which can be orders of magnitude larger than their typical value. With the help of direct numerical simulations of the Navier–Stokes equations at very high resolution, we characterize such extreme events over a broad range of turbulence intensities. The results suggest a power-law dependence of the properties of the extreme events as a function of the Taylor-based Reynolds number. This can be quantitatively interpreted with the help of the properties of the rate of strain conditioned on the vorticity, leading to a very good description of numerical results up to the highest Taylor Reynolds number studied (1,300).   The nonlocal relation between strain and vorticity appears as a major difficulty to provide a quantitative description of the flow properties. To investigate this non-locality, we decompose the strain-rate tensor into nonlocal and a local contributions, obtained by performing the Biot-Savart integral over a sphere of radius R. Our numerical results reveal that the local strain, surprisingly, counteracts the amplification of very intense vortices. This uncovered self-attenuation mechanism potentially provides a direction in establishing the regularity of the Navier-Stokes equations.

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

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