Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process

E-ISSN： 1467-9590|22-2526|3|319-343

ISSN： 0022-2526

Source： STUDIES IN APPLIED MATHEMATICS, Vol.22-2526, Iss.3, 1995-10, pp. : 319-343

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Abstract

Transition from laminar to turbulent flows has generally been studied by considering the linear and weakly nonlinear evolution of small disturbances to the laminar flow. That approach has been fruitless for many shear flows, and a last hope for its success has been the existence of transient growth phenomena. The physical origin of those linear transient effects is elucidated, revealing serious limitations both of previous analyses and of the phenomena themselves, which preclude them from causing direct transition. Nonetheless, some transient effects are symptomatic of one element of a nonlinear process that becomes self‐sustaining at a small enough dissipation. The process is identified, and its description requires a departure from the traditional focus on the laminar flow. A theory is outlined in which the mean flow has an intrinsic spanwise variation. Evidence indicates this is also the central mechanism in the near wall‐region of fully turbulent shear flows.