Improved upper bounds on the energy dissipation rate for shear flow with injection and suction

Improved upper bounds on viscous energy dissipation rates of wall-driven shear flow subject to uniform injection and suction rates are computationally determined. The so-called “background” variational formulation is implemented via a time-stepping numerical scheme to determine optimal estimates. Sh...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 31; no. 8
Main Authors Lee, Harry, Doering, Charles R.
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.08.2019
Subjects
Energy dissipation
Fluid dynamics
Laminar flow
Physics
Shear flow
Suction
Upper bounds
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ISSN1070-6631
1089-7666
DOI10.1063/1.5109059

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Summary:Improved upper bounds on viscous energy dissipation rates of wall-driven shear flow subject to uniform injection and suction rates are computationally determined. The so-called “background” variational formulation is implemented via a time-stepping numerical scheme to determine optimal estimates. Shear flow Reynolds numbers range from 50 to 40 000 with injection angles up to 2°. The computed upper bounds for preselected angles of injection at high Reynolds numbers significantly improve the rigorously estimated ones. Our results suggest that the steady laminar flow is nonlinearly stable for angles of injection greater than 2°.
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ISSN:1070-6631
1089-7666
DOI:10.1063/1.5109059