%0 Journal Article %1 citeulike:6859056 %A Farrell, Brian F. %A Ioannou, Petros J. %D 1996 %I American Meteorological Society %J J. Atmos. Sci. %K 86a10-meteorology-and-atmospheric-physics 76e06-hydrodynamic-stability-convection 35b35-pdes-stability 76b60-atmospheric-waves 34c11-growth-boundedness 47f05-partial-differential-operators 47a12-numerical-range-numerical-radius %N 14 %P 2025--2040 %R 10.1175/1520-0469(1996)053\%3C2025:gstpia\%3E2.0.co;2 %T Generalized Stability Theory. Part I: Autonomous Operators %U http://dx.doi.org/10.1175/1520-0469(1996)053\%3C2025:gstpia\%3E2.0.co;2 %V 53 %X Abstract Classical stability theory is extended to include transient growth processes. The central role of the nonnormality of the linearized dynamical system in the stability problem is emphasized, and a generalized stability theory is constructed that is applicable to the transient as well as the asymptotic stability of time-independent flows. Simple dynamical systems are used as examples including an illustrative nonnormal two-dimensional operator, the Eady model of baroclinic instability, and a model of convective instability in baroclinic flow.

@article{citeulike:6859056, abstract = {{Abstract Classical stability theory is extended to include transient growth processes. The central role of the nonnormality of the linearized dynamical system in the stability problem is emphasized, and a generalized stability theory is constructed that is applicable to the transient as well as the asymptotic stability of time-independent flows. Simple dynamical systems are used as examples including an illustrative nonnormal two-dimensional operator, the Eady model of baroclinic instability, and a model of convective instability in baroclinic flow.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Farrell, Brian F. and Ioannou, Petros J.}, biburl = {https://www.bibsonomy.org/bibtex/263bf121daee7dc296684e103bdd589a1/gdmcbain}, citeulike-article-id = {6859056}, citeulike-attachment-1 = {farrell_96_generalized_1002735.pdf; /pdf/user/gdmcbain/article/6859056/1002735/farrell_96_generalized_1002735.pdf; 6a34d317ed713dda4dd171c6d25a71533e22cf93}, citeulike-linkout-0 = {http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2}, citeulike-linkout-1 = {http://dx.doi.org/10.1175/1520-0469(1996)053\%3C2025:gstpia\%3E2.0.co;2}, day = 1, doi = {10.1175/1520-0469(1996)053\%3C2025:gstpia\%3E2.0.co;2}, file = {farrell_96_generalized_1002735.pdf}, interhash = {87e7a05403d7c3354e4a2a0ad06569d2}, intrahash = {63bf121daee7dc296684e103bdd589a1}, journal = {J. Atmos. Sci.}, keywords = {86a10-meteorology-and-atmospheric-physics 76e06-hydrodynamic-stability-convection 35b35-pdes-stability 76b60-atmospheric-waves 34c11-growth-boundedness 47f05-partial-differential-operators 47a12-numerical-range-numerical-radius}, month = jul, number = 14, pages = {2025--2040}, posted-at = {2015-01-27 05:55:23}, priority = {2}, publisher = {American Meteorological Society}, timestamp = {2021-05-06T06:18:50.000+0200}, title = {Generalized Stability Theory. Part {I}: Autonomous Operators}, url = {http://dx.doi.org/10.1175/1520-0469(1996)053\%3C2025:gstpia\%3E2.0.co;2}, volume = 53, year = 1996 }