Abstract

Progress in analysis of the growth rate of low-speed variable-density spatially developing turbulent planar shear layers is examined from the viewpoint of global trends across the relevant parameter space. Several approaches have been shown to agree with available measurements. Here, it is noted that comparable agreement is also obtained using a simple extension of the canonical Kelvin–Helmholtz linear stability theory. Beyond the range of the experimentally explored parameter space, available predictions disagree qualitatively as well as quantitatively. To a degree that is not generally recognized, this indicates that the governing parameter dependences and associated phenomenology are open questions. Further investigation needed to address these questions is discussed.

References

1.
Pantano
,
C.
, and
Sarkar
,
S.
,
2002
, “
A Study of Compressibility Effects in the High-Speed Turbulent Shear Layer Using Direct Simulation
,”
J. Fluid Mech.
,
451
, pp.
329
371
.10.1017/S0022112001006978
2.
Almagro
,
A.
,
Garcia-Villalba
,
M.
, and
Flores
,
O.
,
2017
, “
A Numerical Study of a Variable-Density Low-Speed Turbulent Mixing Layer
,”
J. Fluid Mech.
,
830
, pp.
569
601
.10.1017/jfm.2017.583
3.
Ramshaw
,
J. D.
,
2000
, “
Simple Model for Mixing at Accelerated Fluid Interfaces With Shear and Compression
,”
Phys. Rev. E
,
61
(
5
), pp.
5339
5344
.10.1103/PhysRevE.61.5339
4.
Dimotakis
,
P. E.
,
1986
, “
Two-Dimensional Shear-Layer Entrainment
,”
AIAA J.
,
24
(
11
), pp.
1791
1796
.10.2514/3.9525
5.
Clemens
,
N. T.
, and
Paul
,
P. H.
,
1995
, “
Effects of Heat Release on the Near Field Flow Structure of Hydrogen Jet Diffusion Flames
,”
Combust. Flame
,
102
(
3
), pp.
271
284
.10.1016/0010-2180(94)00277-Y
6.
Charonko
,
J. J.
, and
Prestridge
,
K.
,
2017
, “
Variable-Density Mixing in Turbulent Jets With Coflow
,”
J. Fluid Mech.
,
825
, pp.
887
921
.10.1017/jfm.2017.379
7.
Maxwell
,
B.
, and
Melguizo-Gavilanes
,
J.
,
2022
, “
Origins of Instabilities in Turbulent Mixing Layers Behind Detonation Propagation Into Reactive–Inert Gas Interfaces
,”
Phys. Fluids
,
34
(
10
), p.
106107
.10.1063/5.0113073
8.
Sandham
,
N. D.
, and
Reynolds
,
W. C.
,
1990
, “
Compressible Mixing Layer: Linear Theory and Direct Simulation
,”
AIAA J.
,
28
(
4
), pp.
618
624
.10.2514/3.10437
9.
Morris
,
P. J.
,
Giridharan
,
M. G.
, and
Lilley
,
G. M.
,
1990
, “
On the Turbulent Mixing of Compressible Free Shear Layers
,”
Proc. R. Soc. Lond. A
,
431
(
1882
), pp.
219
243
.10.1098/rspa.1990.0128
10.
Ashurst
,
W. T.
, and
Kerstein
,
A. R.
,
2005
, “
One-Dimensional Turbulence: Variable-Density Formulation and Application to Mixing Layers
,”
Phys. Fluids
,
17
(
2
), p.
025107
.10.1063/1.1847413
11.
Brown
,
G. L.
, and
Roshko
,
A.
,
1974
, “
On Density Effects and Large Structure in Turbulent Mixing Layers
,”
J. Fluid Mech.
,
64
(
4
), pp.
775
816
.10.1017/S002211207400190X
12.
Abramovich
,
G. M.
,
1963
,
The Theory of Turbulent Jets
,
MIT Press
,
Cambridge, MA
.
13.
Sabin
,
C. M.
,
1965
, “
An Analytical and Experimental Study of the Plane, Incompressible, Turbulent Free-Shear Layer With Arbitrary Velocity Ratio and Pressure Gradient
,”
ASME J. Fluids Eng.
,
87
(
2
), pp.
421
428
.10.1115/1.3650566
14.
Chandrashekhar
,
S.
,
1961
,
Hydrodynamic and Hydromagnetic Stability
,
Clarendon Press
,
Oxford, UK
.
15.
Drazin
,
P. G.
, and
Reid
,
W. H.
,
2004
,
Hydrodynamic Stability
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.
16.
Dimotakis
,
P. E.
,
1991
, “
Turbulent Free Shear Layer Mixing and Combustion
,”
High-Speed Flight Propulsion Systems
,
S. N. B.
Murthy
and
E. T.
Curran
, eds.,
Progress in Astronautics and Aeronautics, AIAA
,
Washington, DC
, pp.
265
340
.
17.
Dimotakis
,
P. E.
, and
Brown
,
G. L.
,
1976
, “
The Mixing Layer at High Reynolds Number: Large-Structure Dynamics and Entrainment
,”
J. Fluid Mech.
,
78
(
3
), pp.
535
560
.10.1017/S0022112076002590
You do not currently have access to this content.