Energy budget analysis and neutral curve characteristics for the linear instability of Couette-Poiseuille flow

Srinivas Kirthy, K and Diwan, SS (2021) Energy budget analysis and neutral curve characteristics for the linear instability of Couette-Poiseuille flow. In: Physics of Fluids, 33 (3).

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Abstract

Here, we present some interesting new results on the linear modal stability of the Couette-Poiseuille flow (CPF), by numerically solving the Orr-Sommerfeld equation within the temporal framework. We provide a mechanistic explanation to the well-known result that the upper plate movement causes progressive stabilization of the CPF. The temporal energy budget reveals appearance of a region of negative energy production with plate movement, which is located near the plate that has a higher relative velocity in the direction of the bulk flow. This has a negative contribution to the integral production term, which, along with the expectation that energy dissipation is nominally constant (to leading order) at a given Reynolds number (Re), reduces the growth rate of kinetic energy, thereby causing flow stabilization with an increase in plate speed. Next, we compare the linear stability portrait of the CPF for positive and negative plate speeds and find that the upper and lower neutral branches in the frequency-Re plane cross over each other (to form a "loop") for a certain range of negative plate speeds. Interestingly, this behavior is not seen for positive plate speeds. At high Re and small plate speeds (positive/negative), we observe that the CPF supports an additional unstable mode manifested in the neutral curves as a bifurcation of the unstable region into primary and secondary regions. The secondary unstable mode is found to be sufficiently distinct in character from the primary mode. These results contribute to the contemporary efforts to better understand the stability of the CPF. © 2021 Author(s).

Item Type:	Journal Article
Publication:	Physics of Fluids
Publisher:	American Institute of Physics Inc.
Additional Information:	The copyright for this article belongs to American Institute of Physics Inc.
Keywords:	Energy dissipation; Growth rate; Kinetic energy; Kinetics; Reynolds number; Speed; Stabilization; Stream flow, Couette-Poiseuille flow; Energy productions; Flow Stabilization; Linear instabilities; Linear Stability; Orr-Sommerfeld equations; Positive/negative; Relative velocity, Budget control
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	24 Mar 2021 11:28
Last Modified:	24 Mar 2021 11:28
URI:	http://eprints.iisc.ac.in/id/eprint/68514

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