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      Spectral Properties of Dynamical Systems, Model Reduction and Decompositions

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      Journal: Nonlinear Dynamics
      Publisher: Springer Nature

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          Hydrodynamic stability without eigenvalues.

          L N Trefethen, A E Trefethen, S Reddy … (1993)
          Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 10(5) by a linear mechanism even though all the eigenmodes decay monotonically. The methods suggested here apply also to other problems in the mathematical sciences that involve nonorthogonal eigenfunctions.
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            Turbulence, Coherent Structures, Dynamical Systems and Symmetry

            Philip Holmes, John Lumley, Gal Berkooz (1996)
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              Three‐dimensional optimal perturbations in viscous shear flow

              Kathryn Butler, Brian F. Farrell (1992)
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                Author and article information

                Journal
                Title: Nonlinear Dynamics
                Abbreviated Title: Nonlinear Dyn
                Publisher: Springer Nature
                ISSN (Print): 0924-090X
                ISSN (Electronic): 1573-269X
                Publication date Created: August 2005
                Publication date (Print): August 2005
                Volume: 41
                Issue: 1-3
                Pages: 309-325
                Article
                DOI: 10.1007/s11071-005-2824-x
                SO-VID: caf4bdce-c71f-475c-85b6-cdf2c794da03
                Copyright © © 2005
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