  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.
