Webinaire Hassan M. Nagib

Utilizing the three-pronged approach of experimental measurements, computational results (DNS), and matched asymptotic analysis (MAE), we have reexamined the three canonical wall-bounded turbulent flows of pipe, channel, and pressure gradient boundary layers (FPG, ZPG and APG). Detailed and systematic study confirmed the non-universality of the Kármán constant (κ) reported in 2008 by Nagib, H. M. and Chauhan, K. A. in Variations of Von Kármán Coefficient in Canonical Flows, Phys. Fluids 20, 101518. Recently, a new matching approach also revealed an inner-outer overlap consisting of a superposition of log-law and a linear term, as detailed in a paper by Monkewitz, P. A. and Nagib, H. M., The Hunt for the Kármán “Constant” Revisited, J. Fluid Mechanics, Vol. 967, A15, 2023. A similar linear term was suggested by Afzal and Yajnik, J. Fluid Mech. (1973 and 1970), Lee and Moser (2015), J. Fluid Mech, 774, pp. 395-414, and Luchini (2017) Phys. Rev. Lett. 118, 224501. In our results, we find that the coefficients of both terms are dependent on the pressure gradient of the flow. A new and robust method is devised to simultaneously determine the coefficients of the log and linear terms, and the constant term in pressure driven flows at currently accessible Reynolds numbers, and yields κ values that are consistent with the κ values deduced from the Reynolds number dependence of centerline velocities. After many decades of experience with “canonical” wall-bounded turbulent flows, we recognize fully developed pipe flow as the ideal flow to compare computations and experiments. With collaborators at several universities, we have conducted experiments, with Re_τ up to 33,000, and DNS for pipe flow at Re_τ = 550 and 1,000, with several resolutions, and extended Eddy Turnover Times (ETT) of up to 200. New criteria for resolution and an existing criterion for convergence of DNS are being developed and confirmed, respectively. We find that higher resolution DNS and longer computational times are required for wall-bounded turbulence, compared to values commonly used. Finally, the impact of the new combined log-law and linear term on textbooks, lecture notes, RANS codes, and turbulence models will be highlighted.