Estimating the turbulent kinetic energy dissipation rate from one-dimensional velocity measurements in time

Schröder, Marcel; Bätge, Tobias; Bodenschatz, Eberhard; Wilczek, Michael; Bagheri, Gholamhossein

The turbulent kinetic energy dissipation rate is one of the most important quantities characterizing turbulence. Experimental studies of a turbulent flow in terms of the energy dissipation rate often rely on one-dimensional measurements of the flow velocity fluctuations in time. In this work, we first use direct numerical simulation of stationary homogeneous isotropic turbulence at Taylor-scale Reynolds numbers inline-formula M1inlinescrollmathml normal 74 R italic λ normal 321 70pt12ptsvg-formulamathimgf57f0097def5657b86185f64c0d42568 amt-17-627-2024-ie00001.svg70pt12ptamt-17-627-2024-ie00001.png to evaluate different methods for inferring the energy dissipation rate from one-dimensional velocity time records. We systematically investigate the influence of the finite turbulence intensity and the misalignment between the mean flow direction and the measurement probe, and we derive analytical expressions for the errors associated with these parameters. We further investigate how statistical averaging for different time windows affects the results as a function of inline-formulaRλ. The results are then combined with Max Planck Variable Density Turbulence Tunnel hot-wire measurements at inline-formula M3inlinescrollmathml normal 147 R italic λ normal 5864 82pt12ptsvg-formulamathimgae37250181e5b26a5949962d95a13cc6 amt-17-627-2024-ie00002.svg82pt12ptamt-17-627-2024-ie00002.png to investigate flow conditions similar to those in the atmospheric boundary layer. Finally, practical guidelines for estimating the energy dissipation rate from one-dimensional atmospheric velocity records are given.

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Schröder, Marcel / Bätge, Tobias / Bodenschatz, Eberhard / et al: Estimating the turbulent kinetic energy dissipation rate from one-dimensional velocity measurements in time. 2024. Copernicus Publications.

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