  We perform a three-dimensional, short-wavelength stability analysis on the
numerically simulated two-dimensional flow past a circular cylinder for
Reynolds numbers in the range $50\le Re\le300$; here, $Re = U_{\infty}D/\nu$
with $U_\infty$, $D$ and $\nu$ being the free-stream velocity, the diameter of
the cylinder and the kinematic viscosity of the fluid, respectively. For a
given $Re$, inviscid local stability equations from the geometric optics
approach are solved on three distinct closed fluid particle trajectories
(denoted as orbits 1, 2 & 3) for purely transverse perturbations. The inviscid
instability on orbits 1 & 2, which are symmetric counterparts of one another,
is shown to undergo bifurcations at $Re\approx50$ and $Re\approx250$. Upon
incorporating finite-wavenumber, finite-Reynolds number effects to compute
corrected local instability growth rates, the inviscid instability on orbits 1
& 2 is shown to be suppressed for $Re\lesssim262$. Orbits 1 & 2 are thus shown
to exhibit a synchronous instability for $Re\gtrsim262$, which is remarkably
close to the critical Reynolds number for the mode-B secondary instability.
Further evidence for the connection between the local instability on orbits 1 &
2, and the mode-B secondary instability, is provided via a comparison of the
growth rate variation with span-wise wavenumber between the local and global
stability approaches. In summary, our results strongly suggest that the
three-dimensional short-wavelength instability on orbits 1 & 2 is a possible
mechanism for the emergence of the mode B secondary instability.
