  Coherent small-amplitude unsteadiness of the shock wave and the separation
region over a canonical double cone flow, termed in literature as
oscillation-type unsteadiness, is experimentally studied at Mach 6. The double
cone model is defined by three non-dimensional geometric parameters: fore- and
aft-cone angles ($\theta_1$ and $\theta_2$), and ratio of the conical slant
lengths ($\Lambda$). Previous studies of oscillations have been qualitative in
nature, and mostly restricted to a special case of the cone model with fixed
$\theta_1 = 0^\circ$ and $\theta_2 = 90^\circ$ (referred to as the
spike-cylinder model), where $\Lambda$ becomes the sole governing parameter. In
the present effort we investigate the self-sustained flow oscillations in the
$\theta_1$-$\Lambda$ parameter space for fixed $\theta_2 = 90^\circ$ using
time-resolved schlieren visualization. The experiments reveal two distinct
sub-types of oscillations, characterized by the motion (or lack thereof) of the
separation point on the fore-cone surface. The global time scale associated
with flow oscillation is extracted using spectral proper orthogonal
decomposition. The non-dimensional frequency (Strouhal number) of oscillation
is seen to exhibit distinct scaling for the two oscillation sub-types. The
relationship observed between the local flow properties, instability of the
shear layer, and geometric constraints on the flow suggests that an
aeroacoustic feedback mechanism sustains the oscillations. Based on this
insight, a simple model with no empiricism is developed for the Strouhal
number. The model predictions are found to match well with experimental
measurements. The model provides helpful physical insight into the nature of
the self-sustained flow oscillations over a double cone at high-speeds.
