We revisit Squire's classical theorem, in which he showed that 2D modes are the more unstable ones, i.e., occur at a smaller Reynolds number, compared to 3D modes. Since this only applies to temporal modes, we extend it to spatiotemporal modes. This results in a new class of subcritical modes, where the 3D modes may occur at a smaller Reynolds number than the corresponding 2D modes. Three special features of the new modes become apparent: (i) they exhibit reflection symmetry breaking in the spanwise ($z$) direction; (ii) the spanwise complex wave number $\beta$ is proportional to the streamwise wave number $\alpha$ ($x$ direction), but with an imaginary prefactor. Hence, real and imaginary parts of $\alpha$ swap their roles for $\beta$, i.e., linking the wave propagation of one direction to the growth in the other direction; and (iii) ${\beta }_r$ constitutes a wave number and therefore refers to an associated wavelength in the $z$ direction. As a consequence, a finite box width in the $z$ direction controls the critical 3D Reynolds number, and, in turn, certain perturbations in slender boxes may not be permitted. We have further analyzed the second part of Squire's theorem, i.e., that the homogeneous Squire equation admits no temporally unstable modes, and this is also lost with the new spatiotemporal modes. Finally, it is emphasized that the use of a single new mode of the above-mentioned type is not meaningful, since its spatial part leads to a diverging perturbation energy. Nevertheless, specific combinations of these modes, such as in Briggs' theory, may lead to new subcritical transitions.

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• Flow instability
• Transition to turbulence