Transient growth: A factor in bypass transition

Transient growth arises through the coupling between slightly damped, highly oblique (nearly streamwise) T–S and Squire modes leading to algebraic growth followed by exponential decay in a region that is subcritical with respect to the T–S neutral curve. A weak transient growth can also occur for two dimensional or axisymmetric modes since the Orr–Sommerfeld operator and its compressible counterpart are not self-adjoint, therefore their eigenfunctions are not strictly orthogonal. So transient growth is a candidate mechanism for many examples of bypass transition. The original transient growth theories were all temporal. However spatial growth formulations are now emerging including their extension to compressible flow with pressure gradient and heat transfer. The relevance to bypass transition is examined through several examples including Poiseuille pipe flow, the hypersonic blunt body paradox and distributed roughness effects.