  The strength and trajectory of a leading edge vortex (LEV) formed by a
pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using
the $Q$-criterion method, which is calculated from the 2D velocity field
obtained from PIV measurements. The relative angle of attack at mid-stroke,
${\alpha_{T/4}} $, proves to be an effective method of combining heave
amplitude ($h_0/c$), pitch amplitude ($\theta_0$), and reduced frequency
($f^*$) into a single variable that predicts the maximum value of $Q$ over a
wide range of operating conditions. Once the LEV separates from the foil, it
travels downstream and rapidly weakens and diffuses. The downstream trajectory
of the LEV has two characteristic shapes. At low values of ${\alpha_{T/4}}$, it
travels straight downstream after separating from the foil, while at higher
values of ${\alpha_{T/4}} $, an accompanying Trailing Edge Vortex (TEV) forms
and the induced velocity generates a cross-stream component to the vortex
trajectories. This behavior is accurately predicted using a potential flow
model for the LEV and TEV. Supervised machine learning algorithms, namely
Support Vector Regression and Gaussian Process Regression, are used to create
regression models that predicts the vortex strength, shape and trajectory
during growth and after separation. The regression model successfully captures
the features of two vortex regimes observed at different values of
${\alpha_{T/4}} $. However, the predicted LEV trajectories are somewhat
smoother than observed in the experiments. The strengths of the vortex is often
under-predicted. Both of these shortcomings may be attributed to the relatively
small size of the training data set.
