Aluie, H.
2013
Scale decomposition in compressible turbulence. Physica D
247 (1), 54–65.

Anand, R. K., Boersma, B. J. & Agrawal, A.
2009
Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion. Exp. Fluids
47 (6), 995–1007.

Attili, A. & Bisetti, F.
2012
Statistics and scaling of turbulence in a spatially developing mixing layer at *Re*
_{𝜆} = 250. Phys. Fluids
24 (3), 035109.

Ayachit, U.
2015
The Paraview Guide: A Parallel Visualization Application. Kitware, Inc.

Babu, P. C. & Mahesh, K.
2004
Upstream entrainment in numerical simulations of spatially evolving round jets. Phys. Fluids
16 (10), 3699–3705.

Barone, M. F., Oberkampf, W. L. & Blottner, F. G.
2006
Validation case study: prediction of compressible turbulent mixing layer growth rate. AIAA J.
44 (7), 1488–1497.

Becker, H. A. & Yamazaki, S.
1978
Entrainment, momentum flux and temperature in vertical free turbulent diffusion flames. Combust. Flame
33, 123–149.

Bernal, L. P. & Roshko, A.
1986
Streamwise vortex structure in plane mixing layers. J. Fluid Mech.
170, 499–525.

Bilger, R. W.
1976
The structure of diffusion flames. Combust. Sci. Technol.
13 (1–6), 155–170.

Bisset, D. K., Hunt, J. C. R. & Rogers, M. M.
2002
The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech.
451, 383–410.

Bogdanoff, D. W.
1983
Compressibility effects in turbulent shear layers. AIAA J.
21 (6), 926–927.

Borrell, G. & Jiménez, J.
2016
Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech.
801, 554–596.

Brown, G. L.
1975
The entrainment and large structure in turbulent mixing layers. In 5th Australasian Conference on Hydraulics and Fluid Mechanics, vol. 1, pp. 352–359. University of Adelaide.

Brown, G. L. & Roshko, A.
1974
On density effects and large structure in turbulent mixing layers. J. Fluid Mech.
64 (04), 775–816.

Burke, S. P. & Schumann, T. E. W.
1928
Diffusion flames. Ind. Engng Chem.
20 (10), 998–1004.

Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I.
2014
The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech.
742, 119–151.

Chinzei, N., Masuya, G., Komuro, T., Murakami, A. & Kudou, K.
1986
Spreading of two-stream supersonic turbulent mixing layers. Phys. Fluids
29 (5), 1345–1347.

Corrsin, S. & Kistler, A.1955 Free-stream boundaries of turbulent flows. *NACA Tech. Rep.* TN-1244, Washington, DC.

Dahm, W. J. A.
2005
Effects of heat release on turbulent shear flows. Part 2. Turbulent mixing layers and the equivalence principle. J. Fluid Mech.
540, 1–19.

Dahm, W. J. A. & Dimotakis, P. E.
1987
Measurements of entrainment and mixing in turbulent jets. AIAA J.
25 (9), 1216–1223.

Debisschop, J. R., Chambers, O. & Bonnet, J. P.
1994
Velocity field characteristics in supersonic mixing layers. Exp. Thermal Fluid Sci.
9 (2), 147–155.

Dimotakis, P. E.
1986
Two-dimensional shear-layer entrainment. AIAA J.
24 (11), 1791–1796.

Dimotakis, P. E.
1991
Turbulent free shear layer mixing and combustion. High Speed Flight Propulsion Systems
137, 265–340.

Dimotakis, P. E.
2000
The mixing transition in turbulent flows. J. Fluid Mech.
409, 69–98.

Dimotakis, P. E.
2005
Turbulent mixing. Annu. Rev. Fluid Mech.
37, 329–356.

Dimotakis, P. E. & Brown, G. L.
1976
The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J. Fluid Mech.
78 (03), 535–560.

Ern, A. & Giovangigli, V.
1994
Multicomponent Transport Algorithms, vol. 24. Springer.

Faeth, G. M. & Samuelsen, G. S.
1986
Fast reaction nonpremixed combustion. Prog. Energy Combust. Sci.
12 (4), 305–372.

Ferré, J. A., Mumford, J. C., Savill, A. M. & Giralt, F.
1990
Three-dimensional large-eddy motions and fine-scale activity in a plane turbulent wake. J. Fluid Mech.
210, 371–414.

Gampert, M., Narayanaswamy, V., Schaefer, P. & Peters, N.
2013
Conditional statistics of the turbulent/non-turbulent interface in a jet flow. J. Fluid Mech.
731, 615–638.

Gottlieb, D. & Turkel, E.
1976
Dissipative two-four methods for time-dependent problems. Maths. Comput.
30 (136), 703–723.

Hadjadj, A., Yee, H. C. & Sjögreen, B.
2012
Les of temporally evolving mixing layers by an eighth-order filter scheme. Intl J. Numer. Meth. Fluids
70 (11), 1405–1427.

Haynes, W. M.
2014
CRC Handbook of Chemistry and Physics. CRC Press.

Hazewinkel, M.
2002
Minimal Surface. Encyclopedia of Mathematics. Springer.

Hermanson, J. C. & Dimotakis, P. E.
1989
Effects of heat release in a turbulent, reacting shear layer. J. Fluid Mech.
199, 333–375.

Hickey, J., Hussain, F. & Wu, X.
2013
Role of coherent structures in multiple self-similar states of turbulent planar wakes. J. Fluid Mech.
731, 312–363.

Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A.
2007
Small-scale aspects of flows in proximity of the turbulent/non-turbulent interface. Phys. Fluids
19 (7), 071702.

Holzner, M. & Lüthi, B.
2011
Laminar superlayer at the turbulence boundary. Phys. Rev. Lett.
106 (13), 134503.

Holzner, M. & van Reeuwijk, M.
2017
The turbulent/nonturbulent interface in penetrative convection. J. Turbul.
1–11.

Hunt, J. C. R., Eames, I., da Silva, C. B. & Westerweel, J.
2011
Interfaces and inhomogeneous turbulence. Phil. Trans. R. Soc. Lond. A
369 (1937), 811–832.

Hunt, J. C. R., Eames, I. & Westerweel, J.
2006
Mechanics of inhomogeneous turbulence and interfacial layers. J. Fluid Mech.
554, 499–519.

Jahanbakhshi, R.2016 DNS of compressible reacting turbulent shear layer. PhD thesis, State University of New York at Buffalo.

Jahanbakhshi, R. & Madnia, C. K.
2016
Entrainment in a compressible turbulent shear layer. J. Fluid Mech.
797, 564–603.

Jahanbakhshi, R., Vaghefi, N. S. & Madnia, C. K.
2015
Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer. Phys. Fluids
27 (10), 105105.

Khashehchi, M., Ooi, A., Soria, J. & Marusic, I.
2013
Evolution of the turbulent/non-turbulent interface of an axisymmetric turbulent jet. Exp. Fluids
54 (1), 1–12.

Kida, S. & Orszag, S. A.
1990
Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput.
5 (2), 85–125.

Klein, M., Sadiki, A. & Janicka, J.
2003
A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys.
186 (2), 652–665.

Kritsuk, A. G., Norman, M. L., P., P. & Wagner, R.
2007
The statistics of supersonic isothermal turbulence. Astrophys. J.
665 (1), 416.

Krug, D., Chung, D., Philip, J. & Marusic, I.
2017
Global and local aspects of entrainment in temporal plumes. J. Fluid Mech.
812, 222–250.

Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A.
2015
The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech.
765, 303–324.

Kundu, P. K., Cohen, I. M. & Dowling, D. R.
2015
Fluid Mechanics, 6th edn. Academic Press.

Kuo, K. K.
2005
Principles of Combustion. John Wiley & Sons.

Lee, J., Sung, H. J. & Zaki, T. A.
2017
Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers. J. Fluid Mech.
819, 165–187.

Lee, J. & Zaki, T. A.
2016
Turbulent/non-turbulent interface in transitional and turbulent boundary layers. In 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada, ICTAM.

Liepmann, D. & Gharib, M.
1992
The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech.
245, 643–668.

Livescu, D., Jaberi, F. A. & Madnia, C. K.
2002
The effects of heat release on the energy exchange in reacting turbulent shear flow. J. Fluid Mech.
450, 35–66.

Mahle, I.2007 Direct and large-eddy simulation of inert and reacting compressible turbulent shear layers. PhD thesis, Universität München.

Mahle, I., Foysi, H., Sarkar, S. & Friedrich, R.
2007
On the turbulence structure in inert and reacting compressible mixing layers. J. Fluid Mech.
593, 171–180.

Mathew, J. & Basu, A. J.
2002
Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids
14 (7), 2065–2072.

Mathew, J., Mahle, I. & Friedrich, R.
2008
Effects of compressibility and heat release on entrainment processes in mixing layers. J. Turbul. (9), N14.

McMurtry, P. A., Riley, J. J. & Metcalfe, R. W.
1989
Effects of heat release on the large-scale structure in turbulent mixing layers. J. Fluid Mech.
199, 297–332.

Miller, R. S., Madnia, C. K. & Givi, P.
1995
Numerical simulation of non-circular jets. Comput. Fluids
24 (1), 1–25.

Mistry, D., Philip, J., Dawson, J. R. & Marusic, I.
2016
Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech.
802, 690–725.

Morton, B. R., Taylor, G. & Turner, J. S.
1956
Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A
234 (1196), 1–23.

Mungal, M. G., Karasso, P. S. & Lozano, A.
1991
The visible structure of turbulent jet diffusion flames: large-scale organization and flame tip oscillation. Combust. Sci. Technol.
76 (4–6), 165–185.

Muniz, L. & Mungal, M. G.
2001
Effects of heat release and buoyancy on flow structure and entrainment in turbulent nonpremixed flames. Combust. Flame
126 (1), 1402–1420.

O’Brien, J., Urzay, J., Ihme, M., Moin, P. & Saghafian, A.
2014
Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers. J. Fluid Mech.
743, 554–584.

Oevermann, M.
2000
Numerical investigation of turbulent hydrogen combustion in a scramjet using flamelet modeling. Aerosp. Sci. Technol.
4 (7), 463–480.

Pantano, C. & Sarkar, S.
2002
A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech.
451, 329–371.

Pantano, C., Sarkar, S. & Williams, F. A.
2003
Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech.
481, 291–328.

Pantano-Rubino, C. A.2000 Compressibility effects in turbulent nonpremixed reacting shear flows. PhD thesis, University of California San Diego.

Papamoschou, D. & Roshko, A.
1988
The compressible turbulent shear layer: an experimental study. J. Fluid Mech.
197, 453–477.

Philip, J., Bermejo-Moreno, I., Chung, D. & Marusic, I.2015 Characteristics of the entrainment velocity in a developing wake. *International Symposium on Turbulence and Shear Flow Phenomena, TSFP-9, Melbourne, Australia*. TSFP.

Philip, J. & Marusic, I.
2012
Large-scale eddies and their role in entrainment in turbulent jets and wakes. Phys. Fluids
24 (5), 055108.

Philip, J., Meneveau, C., de Silva, C. M. & Marusic, I.
2014
Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids
26 (1), 015105.

Pitsch, H. & Peters, N.
1998
A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combust. Flame
114 (1), 26–40.

Poinsot, T. & Veynante, D.
2005
Theoretical and Numerical Combustion. RT Edwards.

Pope, S. B.
1988
The evolution of surfaces in turbulence. Intl J. Engng Sci.
26 (5), 445–469.

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

Ragab, S. A. & Wu, J. L.
1989
Linear instabilities in two-dimensional compressible mixing layers. Phys. Fluids A
1 (6), 957–966.

Redford, J. A., Castro, I. P. & Coleman, G. N.
2012
On the universality of turbulent axisymmetric wakes. J. Fluid Mech.
710, 419–452.

van Reeuwijk, M. & Holzner, M.
2014
The turbulence boundary of a temporal jet. J. Fluid Mech.
739, 254–275.

van Reeuwijk, M., Krug, D. & Holzner, M.
2018
Small-scale entrainment in inclined gravity currents. Environ. Fluid Mech.
18 (1), 225–239.

Ricou, F. P. & Spalding, D. B.
1961
Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech.
11 (01), 21–32.

Rogers, M. M. & Moser, R. D.
1994
Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids
6 (2), 903–923.

Saghafian, A.2014 High-fidelity simulations and modeling of compressible reacting flows. PhD thesis, Stanford University.

Samimy, M. & Elliott, G. S.
1990
Effects of compressibility on the characteristics of free shear layers. AIAA J.
28, 439–445.

Schmidt, W., Federrath, C. & Klessen, R.
2008
Is the scaling of supersonic turbulence universal?
Phys. Rev. Lett.
101 (19), 194505.

Sekar, B. & Mukunda, H. S.
1991
A computational study of direct simulation of high speed mixing layers without and with chemical heat release. In Symposium (International) on Combustion, vol. 23, pp. 707–713. Elsevier.

da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J.
2014a
Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech.
46, 567–590.

da Silva, C. B. & Pereira, J. C. F.
2008
Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/non-turbulent interface in jets. Phys. Fluids
20 (5), 55101–55101.

da Silva, C. B., dos Reis, R. J. N. & Pereira, J. C. F.
2011
The intense vorticity structures near the turbulent/non-turbulent interface in a jet. J. Fluid Mech.
685, 165–190.

da Silva, C. B. & Silva, T. S.
2016
High Reynolds numbers scaling of the turbulent/non-turbulent interface. In APS Meeting Abstracts: APS Division of Fluid Dynamics Conference 2016. APS.

da Silva, C. B., Taveira, R. R. & Borrell, G.
2014b
Characteristics of the turbulent/non-turbulent interface in boundary layers, jets and shear-free turbulence. J. Phys.
506, 012015.

Soteriou, M. C. & Ghoniem, A. F.
1995
Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys. Fluids
7 (8), 2036–2051.

Sutherland, W.
1893
Lii. the viscosity of gases and molecular force. London Edinburgh Dublin Philos. Mag. J. Sci.
36 (223), 507–531.

Taveira, R. R., Diogo, J. S., Lopes, D. C. & da Silva, C. B.
2013
Lagrangian statistics across the turbulent/non-turbulent interface in a turbulent plane jet. Phys. Rev. E
88 (4), 043001.

Taveira, R. R. & da Silva, C. B.
2013
Kinetic energy budgets near the turbulent/non-turbulent interface in jets. Phys. Fluids
25 (1), 015114.

Thompson, K. W.
1990
Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys.
89 (2), 439–461.

Townsend, A. A.
1976
The Structure of Turbulent Shear Flow. Cambridge University Press.

Tritton, D. J.
2012
Physical Fluid Dynamics. Springer.

Tsinober, A.
2000
Vortex stretching versus production of strain/dissipation. Turbul. Struct. Vortex Dyn.
164–191.

Tsinober, A.
2009
An Informal Conceptual Introduction to Turbulence. vol. 483. Springer.

Turner, J. S.
1986
Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech.
173, 431–471.

Vaghefi, N. S.2014 Simulation and modeling of compressible turbulent mixing layer. PhD thesis, State University of New York at Buffalo.

Vaghefi, N. S. & Madnia, C. K.
2015
Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech.
774, 67–94.

Vaghefi, N. S., Nik, M. B., Pisciuneri, P. H. & Madnia, C. K.
2013
A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence. J. Turbul.
14 (9), 43–61.

Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. & Chen, S.
2013
Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett.
110 (21), 214505.

Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R.
2005
Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett.
95 (17), 174501.

Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R.
2009
Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech.
631, 199–230.

Williams, F. A.
1985
Combustion Theory. Benjamin-Cummings.

Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A.
2013
Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech.
731, 95–116.

Yule, A. J.
1978
Large-scale structure in the mixing layer of a round jet. J. Fluid Mech.
89 (03), 413–432.