Benchmark solution for the stability of plane Couette flow with net throughflow

Abstract This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stab...

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Autores principales:	B. M. Shankar, I. S. Shivakumara
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/5a1d7cb6a78543d584b3c2d484979753
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spelling	oai:doaj.org-article:5a1d7cb6a78543d584b3c2d4849797532021-12-02T15:00:19ZBenchmark solution for the stability of plane Couette flow with net throughflow10.1038/s41598-021-90552-52045-2322https://doaj.org/article/5a1d7cb6a78543d584b3c2d4849797532021-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-90552-5https://doaj.org/toc/2045-2322Abstract This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.B. M. ShankarI. S. ShivakumaraNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q B. M. Shankar I. S. Shivakumara Benchmark solution for the stability of plane Couette flow with net throughflow
description	Abstract This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.
format	article
author	B. M. Shankar I. S. Shivakumara
author_facet	B. M. Shankar I. S. Shivakumara
author_sort	B. M. Shankar
title	Benchmark solution for the stability of plane Couette flow with net throughflow
title_short	Benchmark solution for the stability of plane Couette flow with net throughflow
title_full	Benchmark solution for the stability of plane Couette flow with net throughflow
title_fullStr	Benchmark solution for the stability of plane Couette flow with net throughflow
title_full_unstemmed	Benchmark solution for the stability of plane Couette flow with net throughflow
title_sort	benchmark solution for the stability of plane couette flow with net throughflow
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/5a1d7cb6a78543d584b3c2d484979753
work_keys_str_mv	AT bmshankar benchmarksolutionforthestabilityofplanecouetteflowwithnetthroughflow AT isshivakumara benchmarksolutionforthestabilityofplanecouetteflowwithnetthroughflow
_version_	1718389202388779008

Benchmark solution for the stability of plane Couette flow with net throughflow

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