Nonlinear input-output analysis of transitional shear flows using small-signal finite-gain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi mathvariant="script">L</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> stabili

Input-output analysis has been widely used to predict the transition to turbulence in wall-bounded shear flows, but it typically does not capture the full nonlinear effects. This work analyzes nonlinear input-output stability of transitional shear flows using the Small-Signal Finite-Gain (SSFG) stability theorem. This SSFG stability can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. The nonlinear input-output gain obtained from the SSFG stability theorem is higher than the linear input-output gain. The permissible forcing amplitude identified from the SSFG stability theorem is consistent with that obtained by bisection search.