Brown, S. N., Rosen, A. S. & Maslowe, S. A.
1981
The evolution of a quasi-steady critical layer in a stratified viscous shear layer. Proc. R. Soc. Lond. A
375 (1761), 271–293.
Chandler, G. J. & Kerswell, R. R.
2013
Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow. J. Fluid Mech.
722, 554–595.
Churilov, S. M. & Shukhman, I. G.
1987
Nonlinear stability of a stratified shear flow: a viscous critical layer. J. Fluid Mech.
180, 1–20.10.1017/S0022112087001708
Defina, A., Lanzoni, S. & Susin, F. M.
1999
Stability of a stratified viscous shear flow in a tilted tube. Phys. Fluids
11 (2), 344–355.
Dijkstra, H. A., Wubs, F. W., Cliffe, A. K., Doedel, E., Dragomirescu, I. F., Eckhardt, B., Gelfgat, A. Y., Hazel, A. L., Lucarini, V., Salinger, A. G.
et al.
2014
Numerical bifurcation methods and their application to fluid dynamics: Analysis beyond simulation. Commun. Comput. Phys.
15 (1), 1–45.
Drazin, P. G.
1958
The stability of a shear layer in an unbounded heterogeneous inviscid fluid. J. Fluid Mech.
4 (2), 214–224.
Edwards, W. S., Tuckerman, L. S., Friesner, R. A. & Sorensen, D. C.
1994
Krylov methods for the incompressible Navier–Stokes equations. J. Comput. Phys.
110 (1), 82–102.
Haines, P. E., Hewitt, R. E. & Hazel, A. L.
2011
The Jeffery–Hamel similarity solution and its relation to flow in a diverging channel. J. Fluid Mech.
687, 404–430.
Hazel, P.
1972
Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech.
51 (1), 39–61.
Holmboe, J.1960 Unpublished lecture notes.
Howard, L. N.
1961
Note on a paper of John W. Miles. J. Fluid Mech.
10 (4), 509–512.
Howland, C. J., Taylor, J. R. & Caulfield, C. P.
2018
Testing linear marginal stability in stratified shear layers. J. Fluid Mech.
839, R4.
Kaminski, A. K., Caulfield, C. P. & Taylor, J. R.
2014
Transient growth in strongly stratified shear layers. J. Fluid Mech.
758, R4.
Kaminski, A. K., Caulfield, C. P. & Taylor, J. R.
2017
Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers. J. Fluid Mech.
825, 213–244.
Keller, H. B.
1977
Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. Rabinowitz, P. H.), pp. 359–384. Academic Press.
Klaassen, G. P. & Peltier, W. R.
1985
Evolution of finite amplitude Kelvin–Helmholtz billows in two spatial dimensions. J. Atmos. Sci.
42 (12), 1321–1339.
Lott, F. & Teitelbaum, H.
1992
Nonlinear dissipative critical level interaction in a stratified shear flow: instabilities and gravity waves. Geophys. Astrophys. Fluid Dyn.
66 (1–4), 133–167.
Mallier, R.
2003
Stuart vortices in a stratified mixing layer: the Holmboe model. J. Engng. Maths.
47 (2), 121–136.
Maslowe, S. A.
1973
Finite-amplitude Kelvin–Helmholtz billows. Boundary-Layer Meteorol.
5 (1), 43–52.
Maslowe, S. A.
1977
Weakly nonlinear stability theory of stratified shear flows. Q. J. R. Meteorol. Soc.
103 (438), 769–783.
Miles, J. W.
1961
On the stability of heterogeneous shear flows. J. Fluid Mech.
10 (4), 496–508.
Miles, J. W.
1963
On the stability of heterogeneous shear flows. Part 2. J. Fluid Mech.
16 (2), 209–227.
Miller, R. L. & Lindzen, R. S.
1988
Viscous destabilization of stratified shear flow for Ri > 1/4. Geophys. Astrophys. Fluid Dyn.
42 (1–2), 49–91.
Mkhinini, N., Dubos, T. & Drobinski, P.
2013
On the nonlinear destabilization of stably stratified shear flow. J. Fluid Mech.
731, 443–460.
Nagata, M.
1990
Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech.
217, 519–527.
Net, M. & Sánchez, J.
2015
Continuation of bifurcations of periodic orbits for large-scale systems. SIAM J. Appl. Dyn. Syst.
14 (2), 674–698.
Saad, Y. & Schultz, M. H.
1986
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Comput.
7 (3), 856–869.
Salinger, A. G., Bou-Rabee, N. M., Burroughs, E. A., Pawlowski, R. P., Lehoucq, R. B., Romero, L. & Wilkes, E. D.2002 LOCA 1.0 Library of continuation algorithms: theory and implementation manual.
Sánchez, J. & Net, M.
2016
Numerical continuation methods for large-scale dissipative dynamical systems. Eur. Phys. J. Spec. Top.
225 (13), 2465–2486.
Smyth, W. D. & Carpenter, J. R.
2019
Instability in Geophysical Flows. Cambridge University Press.
Smyth, W. D., Nash, J. D. & Moum, J. N.
2019
Self-organized criticality in geophysical turbulence. Sci. Rep.
9 (1), 3747.
Smyth, W. D. & Peltier, W. R.
1991
Instability and transition in finite-amplitude Kelvin–Helmholtz and Holmboe waves. J. Fluid Mech.
228, 387–415.
Strogatz, S. H.
2014
Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering. CRC Press.
Taylor, J. R.2008 Numerical simulations of the stratified oceanic bottom layer. PhD thesis.
Thorpe, S. A., Smyth, W. D. & Li, L.
2013
The effect of small viscosity and diffusivity on the marginal stability of stably stratified shear flows. J. Fluid Mech.
731, 461–476.