  Optimal extraction of information from gravitational-wave observations of
binary black-hole coalescences requires detailed knowledge of the waveforms.
Current approaches for representing waveform information are based on
spin-weighted spherical harmonic decomposition. Higher-order harmonic modes
carrying a few percent of the total power output near merger can supply
information critical to determining intrinsic and extrinsic parameters of the
binary. One obstacle to constructing a full multi-mode template of merger
waveforms is the apparently complicated behavior of some of these modes;
instead of settling down to a simple quasinormal frequency with decaying
amplitude, some $|m| \neq \ell$ modes show periodic bumps characteristic of
mode-mixing. We analyze the strongest of these modes -- the anomalous $(3,2)$
harmonic mode -- measured in a set of binary black-hole merger waveform
simulations, and show that to leading order, they are due to a mismatch between
the spherical harmonic basis used for extraction in 3D numerical relativity
simulations, and the spheroidal harmonics adapted to the perturbation theory of
Kerr black holes. Other causes of mode-mixing arising from gauge ambiguities
and physical properties of the quasinormal ringdown modes are also considered
and found to be small for the waveforms studied here.
