Modelling fluid turbulence is perhaps one of the hardest problems in Applied Mathematics. In a recent paper, the author argued that the classical Navier–Stokes equation is not sufficient to describe the transition to turbulence, but that a Reiner–Rivlin type equation is needed instead. This is explored here for the simplest of all viscous fluid flows, the Couette flow, which is a simple shear between two moving plates. It is found that at high wavenumbers, the transition to unstable flow at the critical Reynolds number is characterized by a large number of eigenvalues of the Orr–Sommerfeld equation moving into the unstable zone essentially simultaneously. This would generate high-dimensional chaos almost immediately, and is a suggested mechanism for the transition to turbulence. Stability zones are illustrated for the flow, and a simple asymptotic solution confirms some of the features of these numerical results. doi:10.1017/S1446181115000176
@article{8756,
title = {Transition to turbulence from plane Couette flow},
journal = {ANZIAM Journal},
volume = {56},
year = {2016},
doi = {10.21914/anziamj.v57i0.8756},
language = {EN},
url = {http://dml.mathdoc.fr/item/8756}
}
Forbes, Larry K. Transition to turbulence from plane Couette flow. ANZIAM Journal, Tome 56 (2016) . doi : 10.21914/anziamj.v57i0.8756. http://gdmltest.u-ga.fr/item/8756/