Unstable modes versus non-normal modes in supercritical channel flows

We propose a measure to quantify the relative importance of unstable and non-normal modes in supercritical channel flows. The effect of non-normal modes is quantified by measuring the response of the flow to body force excitations. In the supercritical regime, unstable modes in channel flows grow relatively slowly, and we show that when compared over long but finite times, non-normal modes dominate the dynamics by orders of magnitude. Our analysis method is based on computing so-called exponentially discounted input-output system gains. It is well known that non-normal modes in the form of elongated streamwise structures prevail over Tollmien-Schlichting (TS) modes in subcritical channel flows. Our method of analysis shows that effectively, this is also the situation in the supercritical regime.