Consistency between the attached-eddy model and the inner-outer interaction model: a study of streamwise wall-shear stress fluctuations in a turbulent channel flow

The inner-outer interaction model (Marusic, Mathis \& Hutchins, Science, vol. 329, 2010, 193-196) and the attached-eddy model (Townsend, Cambridge University Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wall-bounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting to the inner-outer interaction model, the streamwise wall-shear stress fluctuations generated by attached eddies in a turbulent channel flow are isolated. Direct comparison between the statistics from these two models demonstrates that they are consistent to and complement each other. Meanwhile, we further show that the superpositions of attached eddies follow an additive process strictly by verifying the validity of the strong and extended self similarity. Moreover, we propose a Gaussian model to characterize the instantaneous distribution of streamwise wall-shear stress, resulting from the attached-eddy superpositions. These findings are important for developing an advanced reduced-order wall model.

Compressible Velocity Transformations for Various Noncanonical Wall-Bounded Turbulent Flows

This work assesses several popular transformations for the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of high-enthalpy boundary layers with dissociation and vibrational excitation, supercritical channel and boundary-layer flows, and adiabatic boundary layers with pressure gradients. The transformations considered include the van Driest [Van Driest, J. Aeronaut. Sci., 18(1951):145-216], Zhang et al. [Zhang et al., Phys. Rev. Lett., 109(2012):054502], Trettel-Larsson [Trettel and Larsson, Phys. Fluids, 28(2016):026102], data-driven [Volpiani et al., Phys. Rev. Fluids, 5(2020):052602], and total-stress-based [Griffin et al., Proc. Natl. Acad. Sci. U.S.A., 118(2021):e2111144118] transformations. The Trettel-Larsson transformation collapses velocity profiles of high-enthalpy temporal boundary layers but not the spatial boundary layers considered. For supercritical channel flows, the Trettel-Larsson transformation also performs well over the entire inner layer. None of the transformations above works for supercritical boundary layers. For all the considered methods, the transformed velocity profiles of boundary layers with weak pressure gradients coincide well with the universal incompressible law of the wall. In summary, all these popular methods fail to deliver uniform performance for non-canonical compressible wall-bounded flows in the logarithmic region, and a more sophisticated version, which accounts for these different physics, is needed. The data-driven and total-stress-based transformations perform well in the viscous sublayer for all the considered flows.