Squire's theorem

In fluid dynamics, Squire's theorem states that of all the perturbations that may be applied to a shear flow (i.e. a velocity field of the form U = ( U ( z ) , 0 , 0 ) ), the perturbations which are least stable are two-dimensional, i.e. of the form u ′ = ( u ′ ( x , z , t ) , 0 , w ′ ( x , z , t ) ) . This applies to incompressible flows which are governed by the Navier–Stokes equations.

Squire's theorem allows many simplifications to be made in stability theory. If we want to decide whether a flow is unstable or not, it suffices to look at two-dimensional perturbations. These are governed by the Orr–Sommerfeld equation for viscous flow, and by Rayleigh's equation for inviscid flow.