Structured input–output analysis of stably stratified plane Couette flow

Abstract

We employ a recently introduced structured input–output analysis (SIOA) approach to analyse streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds-number ( $Re$ ) low-bulk Richardson number ( $Ri_b$ ) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent–laminar layers commonly observed in the high- $Re$ high- $Ri_b$ intermittent regime. An SIOA across a range of $Ri_b$ and $Re$ values suggests that the classical Miles–Howard stability criterion ( $Ri_b\leq 1/4$ ) is associated with a change in the most amplified flow structures when the Prandtl number is close to one ( $Pr\approx 1$ ). However, for $Pr\ll 1$ , the most amplified flow structures are determined by the product $PrRi_b$ . For $Pr\gg 1$ , SIOA identifies another quasi-horizontal flow structure that we show is principally associated with density perturbations. We further demonstrate the dominance of this density-associated flow structure in the high $Pr$ limit by constructing analytical scaling arguments for the amplification in terms of $Re$ and $Pr$ under the assumptions of unstratified flow (with $Ri_b=0$ ) and streamwise invariance.