Journal ArticleDOI
Subcritical transition to turbulence in plane channel flows
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In this paper, a linear three dimensional mechanism for the transition of plane Poiseuille flows to turbulence is presented which provides good agreement with experimental observations, which is based on the evolution of states within a band of quasi-equilibria which slowly approach the stable upper branch solutions for flow energy but are strongly unstable to infinitesimal three-dimensional disturbances.Abstract:
A linear three dimensional mechanism for the transition of plane Poiseuille flows to turbulence is presented which provides good agreement with experimental observations. The mechanism is based on the evolution of states within a band of quasi-equilibria which slowly approach the stable upper branch solutions for the evolution of flow energy but which are strongly unstable to infinitesimal three-dimensional disturbances. Numerical simulation has shown that if two-dimensional flow persists long enough for the three-dimensional perturbations to attain finite amplitude, the resulting three dimensional flow quickly develops a turbulent character with nonperiodic behavior, and thus transition can be predicted from knowledge of the initial two- and three-dimensional energies and time scales. The mechanism predicts transition to turbulence at Reynolds numbers greater than 1000, as observed in experiments, and implies higher threshold three-dimensional energies in plane Couette flow.read more
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Journal ArticleDOI
Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Journal ArticleDOI
Secondary Instability of Boundary Layers
TL;DR: The transition from laminar to turbulent flow in viscous bound-ary layers is of great practical interest as mentioned in this paper, however, the empirical en-criterion is still the standard tool in engineering practice, although it is known to ignore essential ingredients of the physics of transition and therefore may dangerously mislead if used beyond the supporting data base.
Journal ArticleDOI
Secondary instability of wall-bounded shear flows
TL;DR: In this paper, it was shown that two-dimensional, finite amplitude waves are exponentially unstable to infinitimal three-dimensional disturbances, and that the threedimensional instability requires that a threshold 2-dimensional amplitude be achieved.
Journal ArticleDOI
The two- and three-dimensional instabilities of a spatially periodic shear layer
TL;DR: In this paper, the two-dimensional stability properties of coherent shear-layer vortices discovered by Stuart are investigated, and the stability problem is formulated as a non-separable eigenvalue problem in two independent variables, and solved numerically using spectral methods.
Journal ArticleDOI
Enhanced Angular Momentum Transport in Accretion Disks
TL;DR: In this paper, the status of angular momentum transport in accretion disks is reviewed and the last decade has seen a dramatic increase both in the recognition of key physical properties and in the understanding of the transport.