The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1 Shear aligned convection, pairing, and braid instabilities

• Published in: Journal of fluid mechanics Vol. 708; pp. 5 - 44
• Main Authors: Mashayek, A., Peltier, W. R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.10.2012
• Subjects: Braiding; Earth, ocean, space; Exact sciences and technology; External geophysics; Fluid dynamics; Fluid flow; Fluid mechanics; Fundamental areas of phenomenology (including applications); Geophysics. Techniques, methods, instrumentation and models; Hydrodynamic stability; Instability; Instability of shear flows; Physics; Reynolds number; Secondary instability; Shear; Stability; Stability analysis; Stagnation point; Transition to turbulence; Turbulence; Turbulent flows, convection, and heat transfer; Wavenumber; stratified turbulencence; shear layer turbulence; transition to turbulence; Kelvin Helmholtz instability; Shear flow; Hydrodynamic instability; Modelling; Secondary flow; Geophysical fluid dynamics; Turbulent laminar transition
• DOI: 10.1017/jfm.2012.304
• ISSN: 0022-1120

We study the competition between various secondary instabilities that co-exist in a preturbulent stratified parallel flow subject to Kelvin–Helmholtz instability. In particular, we investigate whether a secondary braid instability might emerge prior to the overturning of the statically unstable regions that develop in the cores of the primary Kelvin–Helmholtz billows. We identify two groups of instabilities on the braid. One group is a shear instability which extracts its energy from the background shear and is suppressed by the straining contribution of the background flow. The other group, which seems to have no precedent in the literature, includes phase-locked modes which grow at the stagnation point on the braid and are almost entirely driven by the straining contributions of the background flow. For the latter group, the braid shear has a negative influence on the growth rate. Our analysis demonstrates that the probability of finite-amplitude growth of both braid instabilities is enhanced with increasing Reynolds number and Richardson number. We also show that the possibility of emergence of braid instabilities decreases with the Prandtl number for the shear modes and increases for the stagnation point instabilities. Through detailed non-separable linear stability analysis, we show that both braid instabilities are fundamentally three dimensional with the shear modes being of small wavenumbers and the stagnation point modes dominating at large wavenumber.