Dou, Hua-Shu; Khoo, Boo Cheong Criteria of turbulent transition in parallel flows. (English) Zbl 1195.76149 Mod. Phys. Lett. B 24, No. 13, 1437-1440 (2010). Summary: Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is the presence of the velocity inflection point in the averaged flow. For shear driven flow, the necessary and sufficient condition for turbulent transition is the existence of zero velocity gradient in the averaged flow profile. It is shown that turbulent transition can be effected via a singularity of the energy gradient function which may be associated with the chaotic attractor in dynamic system. The role of disturbance in the transition is also clarified in causing the energy gradient function to approach the singularity. Finally, it is interesting that turbulence can be controlled by modulating the distribution of the energy gradient function. Cited in 2 Documents MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 76F10 Shear flows and turbulence Keywords:turbulent transition; criteria; energy gradient; role of disturbance; singularity PDFBibTeX XMLCite \textit{H.-S. Dou} and \textit{B. C. Khoo}, Mod. Phys. Lett. B 24, No. 13, 1437--1440 (2010; Zbl 1195.76149) Full Text: DOI arXiv References: [1] DOI: 10.1103/PhysRevLett.91.244502 · doi:10.1103/PhysRevLett.91.244502 [2] DOI: 10.1016/j.ijnonlinmec.2005.12.002 · Zbl 1160.76353 · doi:10.1016/j.ijnonlinmec.2005.12.002 [3] DOI: 10.1016/j.ijthermalsci.2007.12.012 · doi:10.1016/j.ijthermalsci.2007.12.012 [4] DOI: 10.1142/S0217984909018643 · Zbl 1173.76016 · doi:10.1142/S0217984909018643 [5] DOI: 10.1017/S0022112075003254 · doi:10.1017/S0022112075003254 [6] DOI: 10.1017/S0022112008003315 · Zbl 1178.76041 · doi:10.1017/S0022112008003315 [7] DOI: 10.1017/S0022112004009346 · Zbl 1065.76072 · doi:10.1017/S0022112004009346 [8] DOI: 10.1063/1.861265 · Zbl 0309.76039 · doi:10.1063/1.861265 [9] DOI: 10.1017/S0022112067001740 · doi:10.1017/S0022112067001740 [10] DOI: 10.1115/1.2909605 · Zbl 1146.76601 · doi:10.1115/1.2909605 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.