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      Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids

      , , ,
      Journal of Fluid Mechanics
      Cambridge University Press (CUP)

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          Hydrodynamic stability without eigenvalues.

          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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            Three‐dimensional optimal perturbations in viscous shear flow

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              Mechanics and Prediction of Turbulent Drag Reduction with Polymer Additives

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                Author and article information

                Journal
                applab
                Journal of Fluid Mechanics
                J. Fluid Mech.
                Cambridge University Press (CUP)
                0022-1120
                1469-7645
                December 25 2013
                November 25 2013
                December 2013
                : 737
                : 249-279
                Article
                10.1017/jfm.2013.572
                be56290a-062b-4c20-a4c3-506d36ba2d5b
                © 2013
                History

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