Premium
From Disorder to Order August 2000
Author(s) -
Malkus Willem V. R.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01421
Subject(s) - couette flow , turbulence , laminar flow , hagen–poiseuille equation , reynolds number , laminar sublayer , perturbation (astronomy) , inviscid flow , physics , mechanics , shear flow , boundary layer , classical mechanics , flow (mathematics) , mathematics , statistical physics , quantum mechanics
Recently the “turbulent sublayer” was explored using a shear flow idealization akin to L. N. Howard's study of turbulent thermal convection [2]. There, the growing diffusive layers were studied to determine when they became unstable. Here, that work is extended to the first transitions of Couette and Poiseuille parallel flow. The merging boundary layers of the presumed flows pose a linear nonautonomous problem of following the time dependent first Lyapunov vector. As in Blasius flow, the first results emerge from perturbation theory, with corrections for streamwise evolution of the velocity profiles. The estimated critical Reynolds numbers for [back] transition from disorder to the laminar state are within 15% of the observations.