  A physics-based data-driven computational framework for the quantitative
analysis of vortex kinematics and vortex-induced loads in vortex-dominated
problems is presented. Such flows are characterized by the dominant influence
of a small number of vortex structures, but the complexity of these flows makes
it difficult to conduct a quantitative analysis of this influence at the level
of individual vortices. The method presented here combines machine
learning-inspired clustering methods with a rigorous mathematical partitioning
of aerodynamic loads to enable detailed quantitative analysis of vortex
kinematics and vortex-induced aerodynamic loads. We demonstrate the utility of
this approach by applying it to an ensemble of 165 distinct Navier-Stokes
simulations of flow past a sinusoidally pitching airfoil. Insights enabled by
the current methodology include the identification of a period-doubling route
to chaos in this flow, and the precise quantification of the role that
leading-edge vortices play in driving aeroelastic pitch oscillations.
