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

Abstract

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.

Observations of Small-Scale Secondary Instabilities during the Shoaling of Internal Bores on a Deep-Ocean Slope

“…At sufficiently high Reynolds numbers (Re . 900), but still far below what we observe here (Re ; 10 7 ), secondary instabilities of convective nature were also identified in other numerical studies focusing on Kelvin-Helmholtz instabilities (Klaassen and Peltier 1985;Mashayek andPeltier 2011, 2012a,b). Recent work suggests higher mixing efficiencies (G 2 [0.25, 1]) when the flow is populated with such convective instabilities (Mashayek and Peltier 2013).…”

“…900), but still far below what we observe here (Re ; 10 7 ), secondary instabilities of convective nature were also identified in other numerical studies focusing on Kelvin-Helmholtz instabilities (Klaassen and Peltier 1985;Mashayek andPeltier 2011, 2012a,b). Recent work suggests higher mixing efficiencies (G 2 [0.25, 1]) when the flow is populated with such convective instabilities (Mashayek and Peltier 2013). This is because convection is known for being a much more efficient mixing mechanism than shear-driven turbulence: for pure RayleighTaylor convection G ' 1 (Dalziel et al 2008;Gayen et al 2013).…”

“…These difficulties lie in the fact that turbulence is generally intermittent (the stationary hypothesis needed to compute G does not hold) and that separating reversible and nonreversible density fluctuations is complex, making any estimation of J b difficult (Bouffard et al 2013). This question was addressed in numerical (Slinn andRiley 1996, 1998;Umlauf and Burchard 2011;Mashayek and Peltier 2013) and laboratory studies (Ivey and Nokes 1989) but also from in situ measurements (van Haren et al 1994;Davis and Monismith 2011;Dunckley et al 2012;Walter et al 2014).…”

Quantification of the spatial and temporal evolution of stratified shear instabilities at high Reynolds number using quantitative acoustic scattering techniques

“…The balance between shear and stratification is parameterized by the gradient Richardson number = ( / ̅ )∆ ∆ /(∆ ) 2 where g is the gravitational constant, ̅ is the mean density and ∆ is the density difference and ∆ is the velocity difference across the shear layer of thickness ∆ . In agreement with the theoretical prediction by Miles [1961] stratified shear flow has been shown to be unstable when < ¼ in numerical, laboratory and field experiments [Fernando, 1991;Smyth, 2003;Mashayek and Peltier, 2012;Geyer and Smith, 1987].The spatial and temporal evolution of shear instabilities has been well documented in both numerical and laboratory experiments [Fernando, 1991;Smyth, 2003;Mashayek and Peltier, 2012].…”

Instabilities in laminar separation bubbles

“…Until now, the physical nature of the secondary instability mechanisms for an LSB has been unclear. However, the numerical studies of Mashayek & Peltier (2012) for stratified free shear layers have provided some promising leads showing that a shear layer can be the seat of a combination of several secondary instabilities associated with vortex cores or braid regions. Marxen et al explore this avenue in the case of short laminar separation bubbles.…”