= Fjørtoft theorem
{c}
= Fjørtoft's theorem
{c}
{synonym}
For a smooth inviscid parallel shear profile with an exponentially growing mode, let $U_s$ be its velocity at an inflection point. The real and imaginary parts of the integrated <Rayleigh equation for inviscid shear flow> imply $\int U''(U-U_s)|\psi|^2/|U-c|^2=-\int(|\psi'|^2+k^2|\psi|^2)<0$. Consequently $U''(U-U_s)<0$ somewhere in the channel. This strengthens <Rayleigh's inflection-point theorem> but is still only a necessary condition, not a sufficient instability criterion.
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