×

zbMATH — the first resource for mathematics

Energy growth in viscous channel flows. (English) Zbl 0789.76026
The authors study energy growth for two- and three-dimensional Poiseuille and Couette flows using energy methods, linear stability analysis, and a direct numerical procedure for computing the transient growth that occurs before the decay of small perturbations. Application of the Hille-Yosida theorem to the governing linear operator gives conditions for energy non- growth. The authors conclude that subcritical transition takes place due to non-orthogonality of eigenfunctions of this operator.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1007/BF00266474 · Zbl 0141.43803 · doi:10.1007/BF00266474
[2] DOI: 10.1007/BF00250190 · Zbl 0136.23402 · doi:10.1007/BF00250190
[3] Herron, Stud. Appl. Maths 85 pp 269– (1991) · Zbl 0737.76023 · doi:10.1002/sapm1991853269
[4] DOI: 10.1007/BF00276872 · Zbl 0622.76061 · doi:10.1007/BF00276872
[5] DOI: 10.1063/1.866609 · doi:10.1063/1.866609
[6] DOI: 10.1017/S0022112092001046 · doi:10.1017/S0022112092001046
[7] Synge, Semicentenn. Publ. Amer. Math. Soc. 2 pp 227– (1938)
[8] DOI: 10.1007/BF00281139 · Zbl 0181.54703 · doi:10.1007/BF00281139
[9] DOI: 10.1017/S0022112089000819 · Zbl 0667.76060 · doi:10.1017/S0022112089000819
[10] DOI: 10.1017/S0022112069002217 · Zbl 0214.25404 · doi:10.1017/S0022112069002217
[11] DOI: 10.1063/1.858367 · doi:10.1063/1.858367
[12] DOI: 10.1137/0153002 · Zbl 0778.34060 · doi:10.1137/0153002
[13] DOI: 10.1063/1.858386 · doi:10.1063/1.858386
[14] DOI: 10.1007/BF01591113 · Zbl 0164.29003 · doi:10.1007/BF01591113
[15] DOI: 10.1017/S0022112069000115 · doi:10.1017/S0022112069000115
[16] Benney, Stud. Appl. Maths 64 pp 185– (1981) · Zbl 0481.76048 · doi:10.1002/sapm1981643185
[17] DOI: 10.1017/S0022112071002842 · Zbl 0237.76027 · doi:10.1017/S0022112071002842
[18] Orr, Proc. R. Irish Acad. 27 pp 69– (1907)
[19] DOI: 10.1063/1.863040 · Zbl 0421.76039 · doi:10.1063/1.863040
[20] DOI: 10.1146/annurev.fl.20.010188.002415 · doi:10.1146/annurev.fl.20.010188.002415
[21] Henningson, Stud. Appl. Maths 87 pp 15– (1992) · Zbl 0751.76032 · doi:10.1002/sapm199287115
[22] DOI: 10.1017/S0022112093001429 · Zbl 0773.76030 · doi:10.1017/S0022112093001429
[23] Henningson, Stud. Appl. Maths 78 pp 31– (1988) · Zbl 0642.76023 · doi:10.1002/sapm198878131
[24] DOI: 10.1017/S0022112080000079 · Zbl 0432.76049 · doi:10.1017/S0022112080000079
[25] DOI: 10.1017/S002211209100174X · Zbl 0717.76044 · doi:10.1017/S002211209100174X
[26] Gustavsson, Stud. Appl. Maths 75 pp 227– (1986) · Zbl 0614.76039 · doi:10.1002/sapm1986753227
[27] DOI: 10.1017/S0022112091003130 · Zbl 0850.76256 · doi:10.1017/S0022112091003130
[28] DOI: 10.1017/S0022112080000122 · Zbl 0428.76049 · doi:10.1017/S0022112080000122
[29] DOI: 10.1137/0128061 · Zbl 0276.76023 · doi:10.1137/0128061
[30] Joseph, Q. Appl. Maths 26 pp 575– (1969)
[31] DOI: 10.1017/S0022112069001959 · Zbl 0175.52402 · doi:10.1017/S0022112069001959
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.