Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow
| dc.creator | Malik, M. | |
| dc.creator | Dey, J. | |
| dc.creator | Alam, Meheboob | |
| dc.date | 2008-04-01 | |
| dc.date.accessioned | 2026-07-07T09:29:37Z | |
| dc.date.available | 2026-07-07T09:29:37Z | |
| dc.description | Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow with {\it stratified} viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the critical Reynolds number ($Re$) is significantly smaller for the uniform shear flow than its non-uniform shear counterpart. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for ``mode I'' instability, whereas it occurs in the bulk of the flow domain for ``mode II''. For the non-modal analysis, it is shown that the maximum amplification of perturbation energy, $G_{\max}$, is significantly larger for the uniform shear case compared to its non-uniform counterpart. For $α=0$, the linear stability operator can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the $Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim {\it Re}^2$. A reduced inviscid model has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, it is shown that the {\it viscosity-stratification} of the underlying mean flow would lead to a delayed transition in compressible Couette flow. | |
| dc.identifier | https://arxiv.org/abs/0804.0069 | |
| dc.identifier | http://arxiv.org/abs/0804.0069 | |
| dc.identifier | Physical Review E, vol. 77, 036322 (2008, march) | |
| dc.identifier | doi:10.1103/PhysRevE.77.036322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157853 | |
| dc.subject | Fluid Dynamics | |
| dc.title | Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow | |
| dc.type | text |