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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| Published in | Physics of fluids (1994) Vol. 31; no. 8 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Melville
American Institute of Physics
01.08.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1070-6631 1089-7666 |
| DOI | 10.1063/1.5109059 |
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| Abstract | 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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| AbstractList | 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°. |
| Author | Lee, Harry Doering, Charles R. |
| Author_xml | – sequence: 1 givenname: Harry surname: Lee fullname: Lee, Harry organization: Department of Mathematics, University of Michigan – sequence: 3 givenname: Charles R. surname: Doering fullname: Doering, Charles R. organization: Center for the Study of Complex Systems, Department of Mathematics, and Department of Physics, University of Michigan |
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| Cites_doi | 10.1093/qjmam/28.3.341 10.1017/jfm.2015.613 10.1007/s00209-008-0361-2 10.1063/1.870443 10.1016/j.physleta.2013.09.009 10.1063/1.4919930 10.1007/bf01450040 10.1103/physrevlett.69.1648 10.1103/physreve.56.3000 10.1016/j.physleta.2017.12.023 10.1016/j.apm.2007.06.036 10.1017/s0022112002003361 10.1007/bf00266474 10.1103/physreve.92.043012 10.1063/1.3319824 10.1103/physreve.49.4087 10.1103/physreve.51.3192 10.1017/jfm.2017.863 10.1063/1.4919095 10.1017/s0022112070000599 |
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| SubjectTerms | Energy dissipation Fluid dynamics Laminar flow Physics Shear flow Suction Upper bounds |
| Title | Improved upper bounds on the energy dissipation rate for shear flow with injection and suction |
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