  In some linearly unstable flows, secondary instability is found to have a
much larger wavelength than that of the primary unstable modes, so that it
cannot be recovered with a classical Floquet analysis. In this work, we apply a
new formulation for capturing secondary instabilities coupling multiple length
scales of the primary mode. This formulation, based on two-dimensional
stability analysis coupled with a Bloch waves formalism originally described in
Schmid et al. (2017), allows to consider high-dimensional systems resulting
from several repetitions of a periodic unit, by solving an eigenproblem of much
smaller size. Collective instabilities coupling multiple periodic units can be
thus retrieved. The method is applied on the secondary stability of a swept
boundary-layer flow subject to stationary cross-flow vortices, and compared
with Floquet analysis. Two multi-modal instabilities are recovered: for
streamwise wavenumber $\alpha_v$ close to zero, approximately twelve sub-units
are involved in large-wavelength oscillations; whereas a staggered pattern,
characteristic of subharmonic instabilities, is observed for $\alpha_v =
0.087$.
