Structured input-output analysis of stably stratified plane Couette flow

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) <= 1/4) is associated with a change in the most amplified flow structures when the Prandtl number is close to one (Pr approximate to 1). However, for Pr << 1, the most amplified flow structures are determined by the product PrRi(b). For Pr >> 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.