A space-time variational approach to hydrodynamic stability theory
We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of s...
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| Format: | Article |
| Language: | en_US |
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Royal Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/97699 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1811087772460515328 |
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| author | Yano, Masayuki Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Yano, Masayuki Patera, Anthony T. |
| author_sort | Yano, Masayuki |
| collection | MIT |
| description | We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel. |
| first_indexed | 2024-09-23T13:51:44Z |
| format | Article |
| id | mit-1721.1/97699 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:51:44Z |
| publishDate | 2015 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | mit-1721.1/976992022-09-28T16:41:37Z A space-time variational approach to hydrodynamic stability theory Yano, Masayuki Patera, Anthony T. Massachusetts Institute of Technology. Department of Mechanical Engineering Yano, Masayuki Patera, Anthony T. We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel. United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613) United States. Office of Naval Research (Grant N00014-11-1-0713) 2015-07-07T16:26:26Z 2015-07-07T16:26:26Z 2013-05 2013-01 Article http://purl.org/eprint/type/JournalArticle 1364-5021 1471-2946 http://hdl.handle.net/1721.1/97699 Yano, M., and A. T. Patera. “A Space-Time Variational Approach to Hydrodynamic Stability Theory.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2155 (April 24, 2013): 20130036–20130036. https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1098/rspa.2013.0036 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Royal Society MIT web domain |
| spellingShingle | Yano, Masayuki Patera, Anthony T. A space-time variational approach to hydrodynamic stability theory |
| title | A space-time variational approach to hydrodynamic stability theory |
| title_full | A space-time variational approach to hydrodynamic stability theory |
| title_fullStr | A space-time variational approach to hydrodynamic stability theory |
| title_full_unstemmed | A space-time variational approach to hydrodynamic stability theory |
| title_short | A space-time variational approach to hydrodynamic stability theory |
| title_sort | space time variational approach to hydrodynamic stability theory |
| url | http://hdl.handle.net/1721.1/97699 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 |
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