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

<p>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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">74</mn><mo>≤</mo><msub><mi>R</mi><mi mathvariant="italic">λ</mi></msub><mo>≤</mo><mn mathvariant="normal">321</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="70pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="f57f0097def5657b86185f64c0d42568"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-17-627-2024-ie00001.svg" width="70pt" height="12pt" src="amt-17-627-2024-ie00001.png"/></svg:svg></span></span> 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 <span class="inline-formula"><i>R</i>_<i>λ</i></span>. The results are then combined with Max Planck Variable Density Turbulence Tunnel hot-wire measurements at <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">147</mn><mo>≤</mo><msub><mi>R</mi><mi mathvariant="italic">λ</mi></msub><mo>≤</mo><mn mathvariant="normal">5864</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="82pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="ae37250181e5b26a5949962d95a13cc6"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-17-627-2024-ie00002.svg" width="82pt" height="12pt" src="amt-17-627-2024-ie00002.png"/></svg:svg></span></span> 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.</p>