Individually decaying nonorthogonal modes can interfere constructively and produce temporary energy growth. This mechanism is absent for an orthogonal eigenbasis of a normal evolution operator.
The Orr mechanism amplifies a leading two-dimensional shear disturbance as the background flow swings its wavefronts toward alignment. Conserved perturbation vorticity implies velocity amplitude proportional to the inverse wavevector magnitude. This produces algebraic or transient energy amplification without an exponentially growing normal mode. Viscosity limits the benefit of choosing an initially tightly wound disturbance.
// Target: gravitational-instability-of-an-astrophysical-disk.bigb
A streamwise-independent cross-stream disturbance in an inviscid parallel shear flow has time-independent wall-normal velocity. It advects the base streamwise momentum, producing the displayed linear growth of streamwise velocity and quadratic growth of perturbation kinetic energy. This is algebraic amplification, not an exponentially unstable normal mode; it exemplifies transient growth from non-normal modes.
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