Vortex stretching origins of Richardson's turbulence cascade and Kolmogorov's scaling

What is it about?

The significance of vortex stretching and enstrophy intensification in turbulence physics was recognized as early as G. I. Taylor's pioneering work. Through direct calculations of Navier-Stokes vortex-tube interactions, we demonstrate that vortex stretching drives the cascade of energy from large to small scales, reproducing the Kolmogorov spectrum of turbulence. Moreover, we show that the Kolmogorov spectrum does not emerge directly from the cascade process itself but rather from the spectrum of quasi-singular vortex structures formed at the culmination of the energy cascade. These quasi-singular vorticity concentrations arise from the generation and subsequent stretching of emergent vortex structures, driven by Crow and helical vortex line instabilities during the stretching of larger-scale vortices. In addition, we establish that Kolmogorov spectra are compatible with diverse underlying vortex dynamics. For example, we observe Kolmogorov scaling in defect turbulence governed by the Schroedinger equation, where neither vortex-core dynamics nor vortex stretching occurs, emphasizing the broader applicability of Kolmogorov's scaling laws.

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Photo by Darwin Vegher on Unsplash

Photo by Darwin Vegher on Unsplash

Why is it important?

Turbulence is a universal phenomenon, found throughout the universe and in countless technological applications. This work offers a geometrical and structural perspective on its behavior, providing deeper insight into this fundamental physical process.

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