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10
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0005677679
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Finite amplitude effects in an unstable laminar boundary layer
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(1964)
Phys. Fluids
, vol.7
, pp. 319
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Benney, D.J.1
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13
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0002938389
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On the origin of streaks in turbulent shear flows
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Turbulent Shear Flows 8: selected papers from the 8th International Symposium on Turbulent Shear Flows, Munich, Germany, September 9–11 1991 edited by F. Durst, R. Friedrich, B.E. Launder, F.W. Schmidt, U. Schumann, and J.H. Whitelaw (Springer-Verlag, Berlin 1993 (http://web.mit.edu/waleffe/www/SSP.html or anonymous ftp at ftp-math-papers.mit.edu.)
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Waleffe, F.1
Kim, J.2
Hamilton, J.3
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24
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0001164514
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Chaos transition despite linear stability
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The Gebhardt and Grossmann model is somewhat more physical, in that it addresses the modification of the mean, and the reduction of non-normality. However, this is done using the unphysical global norm of the solution ‖u‖ also, and that extra nonlinearity is not quadratic and does not conserve energy. There is little evidence in the NSE for the significance of their other nonlinear terms that “recycle inputs into outputs†as in the BDT model (see Ref. 13).
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(1994)
Phys. Rev. E
, vol.50
, pp. 3705
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Gebhardt, T.1
Grossmann, S.2
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26
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21844493361
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Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process
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http://web.mit.edu/waleffe/www/SSP.html or anonymous ftp at ftp-math-papers.mit.edu..
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(1995)
Stud. Appl. Math
, vol.95
, pp. 319
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Waleffe, F.1
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30
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85034924886
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The R-scaling of ε is related to “slow time scales†in weakly nonlinear stability theory. The time-derivative term scales as [formula omitted] while the viscous term scales as [formula omitted] Hence a slow time scale of [formula omitted] as in the generic Landau equation, is equivalent to the scaling [formula omitted] A slow time scale of [formula omitted] typical of resonant triads, is equivalent to [formula omitted] Benney and Gustavsson[formula omitted] sought to establish a mechanism with [formula omitted] and Waleffe et al.[formula omitted] proposed a mechanism with [formula omitted] both weakly nonlinear theories were based on linear transients and correspond, respectively, to [formula omitted] and [formula omitted] scalings.
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31
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85034916656
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Actually, an explicit Navier-Stokes process that might lead to the [formula omitted] scaling was proposed by Waleffe et al.[formula omitted] but evidence was also presented that at transitional R some nonlinear effects bypass the transients. If the process proposed there is indeed active, it must dominate at sufficiently large R and lead to the [formula omitted] scaling.
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33
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0025474481
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Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity
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(1990)
J. Fluid Mech
, vol.217
, pp. 519
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Nagata, M.1
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34
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85034930111
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Similarly in the NSE, the primary transient growth occurs through the redistribution of streamwise momentum u by the wall-normal velocity υ according to [formula omitted] This u-perturbation is thus perfectly (and negatively) correlated with υ and reduces the mean shear, as can be seen by considering the mean equation (7), which for Couette flow in statistically steady state can be integrated once to [formula omitted] Any statistical increase in u from the transient “lift-up†mechanism will thus reduce the mean shear [formula omitted] and consequently the source of the transient growth. Note that this effect scales as [formula omitted] if ε measures the size of υ.
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39
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0000132403
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reply to “Observations regarding ‘Coherence and chaos in a model of turbulent boundary layer,’ by X. Zhou and L. Sirovich
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(1994)
Phys. Fluids
, vol.6
, pp. 1579
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Sirovich, L.1
Zhou, X.2
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