Arratia, C., Caulfield, C. P. & Chomaz, J.-M.
2013
Transient perturbation growth in time-dependent mixing layers. J. Fluid Mech.
717, 90–133.

Balmforth, N. J., Roy, A. & Caulfield, C. P.
2012
Dynamics of vorticity defects in stratified shear flow. J. Fluid Mech.
694, 292–331.

Bretherton, F. P.
1966
Critical layer instability in baroclinic flows. Q. J. R. Meteorol. Soc.
92, 325–334.

Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J.-M.
2007
Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech.
585, 343–368.

Cairns, R. A.
1979
The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech.
92, 1–14.

Carpenter, J. R., Balmforth, N. J. & Lawrence, G. A.
2010a
Identifying unstable modes in stratified shear layers. Phys. Fluids
22, 054104.

Carpenter, J. R., Tedford, E. W., Heifetz, E. & Lawrence, G. A.
2011
Instability in stratified shear flow: Review of a physical interpretation based on interacting waves. Appl. Mech. Rev.
64, 060801.

Carpenter, J. R., Tedford, E. W., Rahmani, M. & Lawrence, G. A.
2010b
Holmboe wave fields in simulation and experiment. J. Fluid Mech.
648, 205–223.

Case, K. M.
1960
Stability of inviscid plane Couette flow. Phys. Fluids
3, 143–148.

Caulfield, C. P.
1994
Multiple linear instability of layered stratified shear flow. J. Fluid Mech.
258, 255–285.

Caulfield, C. P. & Peltier, W. R.
2000
The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech.
412, 1–47.

Caulfield, C. P., Peltier, W. R., Yoshida, S. & Ohtani, M.
1995
An experimental investigation of the instability of a shear flow with multilayered density stratification. Phys. Fluids
7, 3028–3041.

Churilov, S. M.
2016
Stability of shear flows with multilayered density stratification and monotonic velocity profiles having no inflection points. Geophys. Astrophys. Fluid Dyn.
110, 78–108.

Craik, A. D.
1988
Wave Interactions and Fluid Flows. Cambridge University Press.

Fjortoft, R.
1950
Application of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vortex. Geophys. Publ.
17, 1–52.

Goldstein, S.
1931
On the stability of superposed streams of fluids of different densities. Proc. R. Soc. Lond.
132, 524–548.

Guha, A. & Lawrence, G. A.
2014
A wave interaction approach to studying non-modal homogeneous and stratified shear instabilities. J. Fluid Mech.
755, 336–364.

van Haren, H., Gostiaux, L., Morozov, E. & Tarakanov, R.
2014
Extremely long Kelvin–Helmholtz billow trains in the Romanche fracture zone. Geophys. Res. Lett.
41, 8445–8451.

Haurwitz, B.
1931
Zur Theorie der Wellenbewegungen in Luft und Wasser (On the theory of wave motion in air and water). Geophysikalischen Institut der Universität Leipzig.

Hazel, P.
1972
Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech.
51, 39–61.

Heifetz, E. & Mak, J.
2015
Stratified shear flow instabilities in the non-Boussinesq regime. Phys. Fluids
27, 086601.

Helmholtz, H.
1868
On discontinuous movements of fluids. Phil. Mag.
36, 337–346.

Holmboe, J.
1962
On the behavior of symmetric waves in stratified shear layers. Geophys. Publ.
24, 67–113.

Howard, L. N.
1961
Note on a paper of John W. Miles. J. Fluid Mech.
10, 509–512.

Huppert, H. E.
1973
On Howard’s technique for perturbing neutral solutions of the Taylor–Goldstein equation. J. Fluid Mech.
57, 361–368.

Lord Kelvin
1871
Hydrokinetic solutions and observations. Phil. Mag.
42, 362–377.

Lawrence, G. A., Browand, F. K. & Redekopp, L. G.
1991
The stability of a sheared density interface. Phys. Fluids A
3, 2360–2370.

Lee, V. & Caulfield, C. P.
2001
Nonlinear evolution of a layered stratified shear flow. Dyn. Atmos. Oceans
34, 103–124.

Lindzen, R. S. & Barker, R. S.
1985
Instability and wave over-reflection in stably stratified shear flow. J. Fluid Mech.
151, 189–217.

Lindzen, R. S. & Rambaldi, S.
1986
A study of over-reflection in viscous Poiseuille flow. J. Fluid Mech.
165, 355–372.

Mashayek, A., Caulfield, C. P. & Peltier, W. R.
2013
Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux. J. Fluid Mech.
736, 570–593.

Mashayek, A. & Peltier, W. R.
2012a
The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1. Shear aligned convection, pairing, and braid instabilities. J. Fluid Mech.
708, 5–44.

Mashayek, A. & Peltier, W. R.
2012b
The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 2. The influence of stratification. J. Fluid Mech.
708, 45–70.

Mashayek, A. & Peltier, W. R.
2013
Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?
J. Fluid Mech.
725, 216–261.

Meyer, C. R. & Linden, P. F.
2014
Stratified shear flow: experiments in an inclined duct. J. Fluid Mech.
753, 242–253.

Miles, J. W.
1961
On the stability of heterogeneous shear flows. J. Fluid Mech.
10, 496–508.

Moser, R. D. & Rogers, M. M.
1991
Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A
3, 1128–1134.

Oglethorpe, R. L. F., Caulfield, C. P. & Woods, A. W.
2013
Spontaneous layering in stratified turbulent Taylor–Couette flow. J. Fluid Mech.
721, R3.

Orr, W. M. F.
1907
The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part I. A perfect liquid. Proc. R. Irish Acad. A
27, 9–68.

Phillips, O. M.
1972
Turbulence in a strongly stratified fluid – is it unstable?
Deep-Sea Res.
19, 79–81.

Lord Rayleigh
1880
On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc.
11, 57–72.

Romanov, V. A.
1973
Stability of plane-parallel Couette flow. Funct. Anal. Applics.
7, 137–146.

Rosenhead, L.
1931
The formation of vortices from a surface discontinuity. Proc. R. Soc. Lond. A
124, 170–192.

Salehipour, H., Caulfield, C. P. & Peltier, C. P.
2016
Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech.
803, 591–621.

Scinocca, J. F. & Ford, R.
2000
The nonlinear forcing of large-scale internal gravity waves by a stratified shear instability. J. Atmos. Sci.
57, 653–672.

Smyth, W. D., Klaasen, G. P. & Peltier, W. R.
1988
Finite amplitude Holmboe waves. J. Geophys. Astrophys. Fluid Dyn.
43, 181–222.

Smyth, W. D., Moum, J. N. & Nash, J. D.
2011
Narrowband oscillations in the upper equatorial ocean. Part II. Properties of shear instabilities. J. Phys. Oceanogr.
41, 412–428.

Smyth, W. D. & Winters, K. B.
2003
Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr.
33, 694–711.

Squire, H. B.
1933
On the stability of three-dimensional disturbances of viscous flow between parallel walls. Proc. R. Soc. Lond. A
142, 621–628.

Sutherland, B. R.
2010
Internal Gravity Waves. Cambridge University Press.

Taylor, G. I.
1931
Effect of variation in density on the stability of superposed streams of fluid. Proc. R. Soc. Lond.
132, 449–523.

Taylor, J. R.2008 Numerical simulations of the stratified oceanic bottom boundary layer. PhD thesis, Mech. Eng., UCSD.

Tedford, E. W., Pieters, R. & Lawrence, G. A.
2009
Symmetric Holmboe instabilities in a laboratory exchange flow. J. Fluid Mech.
636, 137–153.

Thorpe, S. A.
1968
A method of producing a shear flow in a stratified fluid. J. Fluid Mech.
32, 693–704.

Yih, C.-S.
1955
Stability of two-dimensional parallel flows for three-dimensional disturbances. Q. Appl. Maths
12, 434–435.

Zhu, D. Z. & Lawrence, G. A.
2001
Holmboe’s instability in exchange flows. J. Fluid Mech.
429, 391–409.