Armenio, V. & Sarkar, S.
2002
An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech.
459, 1–42.

Barry, M. E., Ivey, G. N., Winters, K. B. & Imberger, J.
2001
Measurements of diapycnal diffusivities in stratified fluids. J. Fluid Mech.
442, 267–291.

Batchelor, G. K.
1959
Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech.
5, 113–133.

Billant, P. & Chomaz, J.-M.
2001
Self-similarity of strongly stratified inviscid flows. Phys. Fluids
13, 1645–1651.

Bouffard, D. & Boegman, L.
2013
A diapycnal diffusivity model for stratified environmental flows. Dyn. Atmos. Oceans
61–62, 14–34.

Bradshaw, P. & Huang, G. P.
1995
The law of the wall in turbulent flow. Proc. R. Soc. Lond. A
451, 165–188.

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.

Britter, R. E.1974 An experiment on turbulence in a density stratified fluid. PhD thesis, Monash University, Victoria, Australia.

de Bruyn Kops, S. M.
2015
Classical scaling and intermittency in strongly stratified boussinesq turbulence. J. Fluid Mech.
775, 436–463.

Caulfield, C. P. & Peltier, W. R.
2000
The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech.
413, 1–47.

Caulfield, C. P., Tang, W. & Plasting, S. C.
2004
Reynolds number dependence of an upper bound for the long-time-averaged buoyancy flux in plane stratified Couette flow. J. Fluid Mech.
498, 315–332.

Chung, D. & Matheou, G.
2012
Direct numerical simulation of stationary homogeneous stratified sheared turbulence. J. Fluid Mech.
696, 434–467.

Davidson, P. A.
2004
Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.

Davis, K. A. & Monismith, S. G.
2011
The modification of bottom boundary layer turbulence and mixing by internal waves shoaling on a barrier reef. J. Phys. Oceanogr.
41, 2223–2241.

Deusebio, E., Caulfield, C. P. & Taylor, J. R.
2015
The intermittency boundary in stratified plane Couette flow. J. Fluid Mech.
781, 298–329; referred to in the text as DCT.

Diamessis, P. J., Spedding, G. R. & Domaradzki, J. A.
2011
Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes. J. Fluid Mech.
671, 52–95.

van Driest, E. R.
1956
On turbulent flow near a wall. J. Aero. Sci.
23, 1007–1011.

Eaves, T. S. & Caulfield, C. P.
2015
Disruption of SSP/VWI states by a stable stratification. J. Fluid Mech.
784, 548–564.

Ellison, T. H.
1957
Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech.
2, 456–466.

Fernando, H. J. S.
1991
Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech.
23, 455–493.

Flores, O. & Riley, J. J.
2011
Analysis of turbulence collapse in stably stratified surface layers using direct numerical simulation. Boundary-Layer Meteorol.
139, 241–259.

Foken, T.
2006
50 years of the Monin–Obukhov similarity theory. Boundary-Layer Meteorol.
119, 431–447.

Galperin, B., Sukoriansky, S. & Anderson, P. S.
2007
On the critical Richardson number in stably stratified turbulence. Atmos. Sci. Lett.
8, 65–69.

García-Villalba, M. & del Álamo, J. C.
2011
Turbulence modification by stable stratification in channel flow. Phys. Fluids
23, 045104.

García-Villalba, M., Azagra, E. & Uhlmann, M.
2011a
A numerical study of turbulent stably-stratified plane Couette flow. In High Performance Computing in Science and Engineering ’10 (ed. Nagel, W. E.
et al. ), pp. 251–261. Springer.

García-Villalba, M., Azagra, E. & Uhlmann, M.
2011b
Mixing efficiency in stably-stratified plane Couette flow. In Proceedings of the 7th International Symposium on Stratified Flows, Rome, Italy, August 2011. IAHR.

Holford, J. M. & Linden, P. F.
1999
Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans
30, 173–198.

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

Ivey, G. N., Winters, K. B. & Koseff, J. R.
2008
Density stratification, turbulence, but how much mixing?
Annu. Rev. Fluid Mech.
40, 169–184.

Karimpour, F. & Venayagamoorthy, S. K.
2014
A simple turbulence model for stably stratified wall-bounded flows. J. Geophys. Res.
119, 870–880.

Karimpour, F. & Venayagamoorthy, S. K.
2015
On turbulent mixing in stably stratified wall-bounded flows. Phys. Fluids
27, 046603.

Lilly, D. K.
1983
Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci.
40, 749–761.

Linden, P. F.
1979
Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn.
13, 3–23.

Linden, P. F.
1980
Mixing across a density interface produced by grid turbulence. J. Fluid Mech.
100, 691–703.

Lozovatsky, I. D. & Fernando, H. J. S.
2013
Mixing efficiency in natural flows. Phil. Trans. R. Soc. Lond. A
371, 20120213.

Maffioli, A., Brethouwer, G. & Lindborg, E.
2016
Mixing efficiency in stratified turbulence. J. Fluid Mech.
794, R3.

Maffioli, A. & Davidson, P. A.
2015
Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number. J. Fluid Mech.
786, 210–233.

Mahrt, L.
1999
Stratified atmospheric boundary layers. Boundary-Layer Meteorol.
90, 375–396.

Mahrt, L.
2014
Stably stratified atmospheric boundary layers. Annu. Rev. Fluid Mech.
46, 23–45.

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.

Mater, B. D. & Venayagamoorthy, S. K.
2014
The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows. Geophys. Res. Lett.
41, 4646–4653.

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

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

Osborn, T. R.
1980
Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr.
10, 83–89.

Park, Y. G., Whitehead, J. A. & Gnanadeskian, A.
1994
Turbulent mixing in stratified fluids: layer formation and energetics. J. Fluid Mech.
279, 279–311.

Peltier, W. R. & Caulfield, C. P.
2003
Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech.
35, 135–167.

Pham, H. T., Sarkar, S. & Winters, K. B.
2013
Large-eddy simulation of deep-cycle turbulence in an Equatorial Undercurrent model. J. Phys. Oceanogr.
43, 2490–2502.

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

Pope, S. B.
2000
Turbulent Flows. Cambridge University Press.

van Reeuwijk, M. & Hadžiabdić, M.
2015
Modelling high schmidt number turbulent mass transfer. Intl J. Heat Fluid Flow
51, 42–49.

Riley, J. J. & de Bruyn Kops, S. M.
2003
Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids
15, 2047.

Riley, J. J. & Lindborg, E.
2012
Recent progress in stratified turbulence. In Ten Chapters in Turbulence (ed. Davidson, P. A., Kaneda, Y. & Sreenivasan, K. R.), pp. 269–317. Cambridge University Press.

Rohr, J. & Van Atta, C.
1987
Mixing efficiency in stably stratified growing turbulence. J. Geophys. Res.
92, 5481–5488.

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

Salehipour, H. & Peltier, W. R.
2015
Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech.
775, 464–500.

Salehipour, H., Peltier, W. R. & Mashayek, A.
2015
Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at high Reynolds number. J. Fluid Mech.
773, 178–223.

Schlichting, H. & Gersten, K.
2003
Boundary-Layer Theory. Springer.

Scotti, A.
2015
Biases in Thorpe-scale estimates of turbulence dissipation. Part II: energetics arguments and turbulence simulations. J. Geophys. Res.
45, 2522–2543.

Scotti, A. & White, B.
2016
The mixing efficiency of stratified turbulent boundary layers. J. Phys. Oceanogr.
46, 3181–3191.

Shih, L. H., Koseff, J. R., Ferziger, J. H. & Rehmann, C. R
2000
Scaling and parameterization of stratified homogeneous turbulent shear flow. J. Fluid Mech.
412, 1–20.

Shih, L. H., Koseff, J. R., Ivey, G. N. & Ferziger, J. H.
2005
Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. J. Fluid Mech.
525, 193–214.

Smyth, W. D. & Moum, J. N.
2013
Marginal instability and deep cycle turbulence in the eastern equatorial Pacific Ocean. Geophys. Res. Lett.
40, 6181–6185.

Smyth, W. D., Moum, J. N. & Caldwell, D. R.
2001
The efficiency of mixing in turbulent patches: inferences from direct simulations and microstructure observations. J. Phys. Oceanogr.
31, 1969–1992.

Sukoriansky, S. & Galperin, B.
2013
An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification. Phil. Trans. R. Soc. Lond. A
371, 20120212.

Tang, W., Caulfield, C. P. & Kerswell, R. R.
2009
A prediction for the optimal stratification for turbulent mixing. J. Fluid Mech.
634, 487–497.

Tastula, E.-M., Galperin, B., Sukoriansky, S., Luhar, A. & Anderson, P.
2015
The importance of surface layer parameterization in modeling of stable atmospheric boundary layers. Atmos. Sci. Lett.
16, 83–88.

Taylor, J. R.2008 Numerical simulations of the stratified oceanic bottom boundary layer. PhD thesis, University of California, San Diego.

Taylor, J. R., Sarkar, S. & Armenio, V.
2005
Large eddy simulation of stably stratified open channel flow. Phys. Fluids
17, 116602.

Thorpe, S. A. & Liu, Z.
2009
Marginal instability?
J. Phys. Oceanogr.
39, 2373–2381.

Turner, J. S.
1973
Buoyancy Effects in Fluids. Cambridge University Press.

Venayagamoorthy, S. K. & Stretch, D. D.
2010
On the turbulent Prandtl number in homogeneous stably stratified turbulence. J. Fluid Mech.
644, 359–369.

Walter, R. K., Squibb, M. E., Woodson, C. B., Koseff, J. R. & Monismith, S. G.
2014
Stratified turbulence in the nearshore coastal ocean: dynamics and evolution in the presence of internal bores. J. Phys. Oceanogr.
119, 8709–8730.

Wells, M., Cenedese, C. & Caulfield, C. P.
2010
The relationship between flux coefficient and entrainment ratio in density currents. J. Phys. Oceanogr.
40, 2713–2727.

Wilson, J. M. & Venayagamoorthy, S. K.
2015
A shear-based parameterization of turbulent mixing in the stable atmospheric boundary layer. J. Atmos. Sci.
72, 1713–1726.

Wyngaard, J. C.
2010
Turbulence in the Atmosphere. Cambridge University Press.

Zhou, Q.2015 Far-field evolution of turbulence-emitted internal waves and Reynolds number effects on a localized stratified turbulent flow. PhD thesis, Cornell University, Ithaca, New York.