Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence

Predictions of the spatial representation of instantaneous wall-bounded flows, via coherent structure-based models, are highly sensitive to the geometry of the representative structures employed by them. In this study, we propose a methodology to extract the three-dimensional (3-D) geometry of the statistically significant eddies from multi-point wall-turbulence datasets, for direct implementation into these models to improve their predictions. The methodology is employed here for reconstructing a 3-D statistical picture of the inertial wall coherent turbulence for all canonical wall-bounded flows, across a decade of friction Reynolds number ($Re_{\tau}$). These structures are responsible for the $Re_{\tau}$-dependence of the skin-friction drag and also facilitate the inner-outer interactions, making them key targets of structure-based models. The empirical analysis brings out the geometric self-similarity of the large-scale wall-coherent motions and also suggests the hairpin packet as the representative flow structure for all wall-bounded flows, thereby aligning with the framework on which the attached eddy model (AEM) is based. The same framework is extended here to also model the very-large-scaled motions, with a consideration of their differences in internal versus external flows. Implementation of the empirically-obtained geometric scalings for these large structures into the AEM is shown to enhance the instantaneous flow predictions for all three velocity components. Finally, an active flow control system driven by the same geometric scalings is conceptualized, towards favourably altering the influence of the wall coherent motions on the skin-friction drag.Comment: 16 pages, 11 figures, accepted for publication in the International Journal of Heat and Fluid Flo

Response of the temporal turbulent boundary layer to decaying free-stream turbulence

The turbulent boundary layer developing under a turbulence-laden free stream is numerically investigated using the temporal boundary layer framework. This study focuses on the interaction between the fully turbulent boundary layer and decaying free-stream turbulence. Previous experiments and simulations of this physical problem have considered a spatially evolving boundary layer beset by free-stream turbulence. The state of the boundary layer at any given downstream position in fact reflects the accumulated history of the co-evolution of boundary layer and free-stream turbulence. The central aim of the present work is to isolate the effect of local free-stream disturbances existing at the same time as the ‘downstream’ boundary layer. The temporal framework used here helps expose when and how disturbances directly above the boundary layer actively impart change upon it. The bulk of our simulations were completed by seeding the free stream above boundary layers that were ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. Moreover, this strategy allowed us to test various combinations of the turbulence intensity and large-eddy length scale of the free-stream turbulence with respect to the corresponding scales of the boundary layer. The relative large-eddy turnover time scale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades to a negligible level. If the large-eddy turnover time scale of the free-stream turbulence is much smaller than that of the boundary layer, the interaction will be ‘weak’, as the free-stream disturbances will markedly decay before the boundary layer is able be altered significantly as a result of the free-stream disturbances. For a ‘strong’ interaction, the injected free-stream turbulence causes increased spreading of the boundary layer away from the wall, permitting large incursions of free-stream fluid deep within it

Response of the temporal turbulent boundary layer to decaying free-stream turbulence

The turbulent boundary layer developing under a turbulence-laden free stream isnumerically investigated using the temporal boundary layer framework. This studyfocuses on the interaction between the fully turbulent boundary layer and decayingfree-stream turbulence. Previous experiments and simulations of this physical problemhave considered a spatially evolving boundary layer beset by free-stream turbulence.The state of the boundary layer at any given downstream position in fact reflectsthe accumulated history of the co-evolution of boundary layer and free-streamturbulence. The central aim of the present work is to isolate the effect of localfree-stream disturbances existing at the same time as the ‘downstream’ boundarylayer. The temporal framework used here helps expose when and how disturbancesdirectly above the boundary layer actively impart change upon it. The bulk of oursimulations were completed by seeding the free stream above boundary layers thatwere ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulencefrom a precursor simulation. Moreover, this strategy allowed us to test variouscombinations of the turbulence intensity and large-eddy length scale of the free-streamturbulence with respect to the corresponding scales of the boundary layer. The relativelarge-eddy turnover time scale between the free-stream turbulence and the boundarylayer emerges as an important parameter in predicting if the free-stream turbulenceand boundary layer interaction will be ‘strong’ or ‘weak’ before the free-streamturbulence eventually fades to a negligible level. If the large-eddy turnover time scaleof the free-stream turbulence is much smaller than that of the boundary layer, theinteraction will be ‘weak’, as the free-stream disturbances will markedly decay beforethe boundary layer is able be altered significantly as a result of the free-streamdisturbances. For a ‘strong’ interaction, the injected free-stream turbulence causesincreased spreading of the boundary layer away from the wall, permitting largeincursions of free-stream fluid deep within it