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arXiv · 2504.13298

Whither the Zeroth Law of Turbulence?

Kartik P. Iyer·Theodore D. Drivas·Gregory L. Eyink·Katepalli R. Sreenivasan
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Abstract

Experimental and numerical studies of incompressible turbulence suggest that the mean dissipation rate of kinetic energy remains constant as the Reynolds number tends to infinity (or the non-dimensional viscosity tends to zero). This anomalous behavior is central to many theories of high-Reynolds-number turbulence and for this reason has been termed the "zeroth law". Here we report a sequence of direct numerical simulations of incompressible Navier-Stokes in a box with periodic boundary conditions, which indicate that the anomaly vanishes at a rate that agrees with the scaling of third-moment of absolute velocity increments. Our results suggest that turbulence without boundaries may not develop strong enough singularities to sustain the zeroth law.

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Kartik P. Iyer, Theodore D. Drivas, Gregory L. Eyink, Katepalli R. Sreenivasan. 2025-04-17. Whither the Zeroth Law of Turbulence?. https://arxiv.org/abs/2504.13298

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