The butterfly effect and the transition to turbulence in a stratified shear layer
Journal
Journal of Fluid Mechanics
Series/Report No.
Journal of Fluid Mechanics
Journal Volume
953
Start Page
A43
ISSN
0022-1120
1469-7645
Date Issued
2022-12-25
Author(s)
Abstract
In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin-Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12%-15% and net mixing by a factor of 2.
Subjects
shear-flow instability
transition to turbulence
turbulent mixing
Publisher
Cambridge University Press (CUP)
Type
journal article