Structured input-output analysis of stably stratified plane Couette flow

Abstract

We employ a recently introduced structured input-output analysis (SIOA) approach 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 ($R{i}_b$) 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-$R{i}_b$ intermittent regime. An SIOA across a range of $R{i}_b$ and $Re$ values suggests that the classical Miles-Howard stability criterion ($R{i}_b\le 1/4$) is associated with a change in the most amplified flow structures when Prandtl number is close to one ($Pr\approx 1$). However, for $Pr\ll 1$, the most amplified flow structures are determined by the product $PrR{i}_b$. 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 $R{i}_b=0$) and streamwise invariance.

arXiv comment27 pages, 12 figures

References in corpus (12)

• A critical layer model for turbulent pipe flow
• Color of turbulence
• From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
• Self-organized criticality of turbulence in strongly stratified mixing layers
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part I: Numerical simulations of a stratified plane Couette flow
• The stability of stratified spatially periodic shear flows at low Péclet number
• The linear instability of the stratified plane Couette flow
• Disruption of SSP/VWI states by a stable stratification
• Streamwise-constant large-scale structures in Couette and Poiseuille flows
• Resolvent analysis of stratification effects on wall-bounded shear flows
• Layer formation and relaminarisation in plane Couette flow with spanwise stratification
• Stably stratified exact coherent structures in shear flow: the effect of Prandtl number

Cited by in corpus (1)

• Localized layers of turbulence in stratified horizontally sheared Poiseuille flow