Linear stability of the flow of a second order fluid past a wedge

Cracco, M., Davies, C. ORCID: https://orcid.org/0000-0002-5592-9541 and Phillips, T. N. ORCID: https://orcid.org/0000-0001-6455-1205 2020. Linear stability of the flow of a second order fluid past a wedge. Physics of Fluids 32 , 084102. 10.1063/5.0018300

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Abstract

The linear stability analysis of Rivlin–Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Mathematics
Publisher:	American Institute of Physics (AIP)
ISSN:	1070-6631
Funders:	EPSRC
Date of First Compliant Deposit:	14 July 2020
Date of Acceptance:	14 July 2020
Last Modified:	01 Aug 2024 10:15
URI:	https://orca.cardiff.ac.uk/id/eprint/133440

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