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

Cracco, M., Davies, C. and Phillips, T. N. 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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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: 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: 11 Dec 2020 02:30

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