Dissipation and Topological Features Conditioned by Velocity Level-Crossings in Wall Turbulence
The dissipation statistics conditioned by fixed amplitudes of the velocity field are analyzed through direct numerical simulations data of a turbulent channel flow up to the Karman number \( R{e}_{\tau }=1100 \) . The largest contribution to the dissipati
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Dissipation and Topological Features Conditioned by Velocity Level-Crossings in Wall Turbulence Sedat Tardu
25.1 Introduction Palm statistics are the statistics of a given quantity under the condition that another stochastic process crosses a fixed level. A relatively easy flow quantity to understand connected to the level-crossing statistics in wall turbulence is the local instantaneous production P D uv @U . Here, u and v are, respectively, the fluctuating streamwise @y
is the mean shear. The conditional level-crossing and wall normal velocity and @U @y statistics p are determined when, for example, u crosses a fixed amplitude `u u , where u D uu is the root mean square of streamwise velocity fluctuations. Figure 25.1 adapted from Tardu and Bauer [14] shows the distribution of the production P`u conditioned by the u crossings and scaled by the local mean P versus the threshold `u at the edge of the viscous sublayer, at a distance scaled by the viscosity and the shear (friction) velocity of yC D 5. The profiles are compared with the simplest reference P`
model assuming joint normality between u and v in which case Pui D `2ui although it is known that u and v deviate strongly from normality next to the wall. Note P first that the P`u profiles are significantly asymmetric with respect to the threshold `u and are obviously far being Gaussian. Strong contributions of the ejections or P of the quadrant QII events (v > 0, u < 0) make P`u over Gaussian at the `u < 0 side, pointing at the preponderance of the interaction of intense u 0. The striking feature of the results presented in Fig. 25.1 is that, at the `u > 0 crossings, the mean production is curiously negative within the range 0 < `u < 1:5 and stays weak at larger thresholds compared to the`u < 0 side. The only categories G
S. Tardu () Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Université Grenoble Alpes, B.P. 53 X, 38041 Grenoble, Cédex 9, France e-mail: [email protected] © Springer International Publishing Switzerland 2017 A. Pollard et al. (eds.), Whither Turbulence and Big Data in the 21st Century, DOI 10.1007/978-3-319-41217-7_25
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Fig. 25.1 Production conditioned by up and down crossings of the streamwise velocity u at `u u levels, at the edge of the viscous sublayer at the distanceyC D 5 from the wall and at four different Reynolds numbers
of events that can induce noise contamination and render P`u negative when u > 0 are the QI interactions .u > 0; v > 0/. The QI events induce incoherence at the edge of the viscous sublayer and render blurred the sweeps marked by the u-crossings. Enhancing this incoherence and weakening the effect of `u < 0 events can reduce significantly the production process in its early stage and lead to appreciable drag reduction. Note that such information can hardly be obtained from the classical conditional statistics such as the quadrant analysis. It has been argued for a while that the zero-crossings of fluctuating velocity signals should largely contribute to t
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