Structured input-output analysis of stably stratified plane Couette flow

We extend a recently developed structured input-output analysis (SIOA) to analyze streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds number (Re) low-bulk Richardson number (Ri) intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths of oblique turbulent bands that have been difficult to study due to the need for large channel extents to capture their full spatial extent. SIOA also identifies the quasi-horizontal flow structures resembling turbulent-laminar layers observed in the high-Re number high-Ri intermittent regime. We exploit SIOA to show that the classical Miles-Howard stability criterion (Ri≤1/4) appears to be associated with a change in the most amplified flow structures for Pr∼1. However, for Pr <<1, the most amplified flow structures are determined by the product Pr Ri. For Pr >>1, SIOA identifies another quasi-horizontal flow structure that we show is associated with density perturbations. The dominance of this density-associated flow structure in the high Pr limit is further demonstrated by the analytical scaling of amplification over Re and Pr under Ri=0 and streamwise constant assumptions.