Abstract
The three-dimensional linear instability of parallel shear flows is investigated through simple geometrical constructions based on the classical Squire transformation. It is shown that if a profile is unstable for a finite Reynolds number and some value of (total) horizontal wavenumber, this profile is also unstable for all larger Reynolds numbers and the same wavenumber. In particular, the direction of the unstable mode tends toward the perpendicular as the Reynolds number increases, thus providing the viscous/shear balance required for resistive instability. The example of plane Poiseuille flow is discussed in detail, and the results compared with classical viscous and inviscid stability criteria.
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