2022/02/17 by Kirthy K. Srinivas, Srinivas, Kirthy K., Sourabh S. Diwan +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2202.08467
openalex publication_date 2022/02/17 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Here we report some interesting new features of the spatio-temporal instability of the incompressible plane Couette-Poiseuille flow (CPF). First of all, this flow represents the first instance of a "non-inflectional" absolute instability, within constant-viscosity formulation, which is triggered when one of the plates moves opposite to the bulk motion. More strikingly, with further increase in the negative plate motion, the absolute instability (\textrmAI) transitions to an "upstream" convective instability (\textrmCI-), wherein an unstable wave packet moves opposite to the direction of the bulk flow. Thus, the CPF exhibits a unique \textrmCI+ → \textrmAI → \textrmCI- transition, for a given Reynolds number (Re), where \textrmCI+ denotes the commonly-observed case of a "downstream" convective instability. This type of transition has not been reported for other known examples of absolutely unstable flows. We compute the leading and trailing edge velocities for an amplifying wave packet and find that, for the plane Poiseuille flow, both these velocities approach zero as Re → ∞. As a result, at high Re, even the slightest of negative plate motions is sufficient to trigger \textrmAI and subsequently \textrmCI-, as observed for the CPF. The wave-packet dispersion first increases with Re, followed by a decrease, which points to a peculiar "dual" role of viscosity in sustaining \textrmAI in the CPF, namely, viscosity promotes sustenance of \textrmAI at moderate Reynolds numbers but suppresses it at low and high Reynolds numbers. These results can be well understood within the Ginzburg-Landau framework, and therefore can be expected to have a wider applicability.