The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence is absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. The underlying mechanisms are explained.

1.
P. E.
Rodi
,
S.
Emami
, and
C. A.
Trexler
, “
Unsteady pressure behavior in a ramjet/scramjet inlet
,”
J. Propul. Power
12
(
3
),
486
493
(
1996
).
2.
S. S.
Girimaji
,
J. R.
O’Neill
, and
D.
Yu
, “
Rapid distortion analysis of homogeneous turbulence subjected to rotating shear
,”
Phys. Fluids
8
,
085102
(
2006
).
3.
D.
Yu
and
S. S.
Girimaji
, “
Direct numerical simulations of homogeneous turbulence subject to periodic shear
,”
J. Fluid Mech.
566
,
117
151
(
2006
).
4.
J.
Chen
,
C.
Meneveau
, and
J.
Katz
, “
Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle
,”
J. Fluid Mech.
562
,
123
151
(
2006
).
5.
W. J. T.
Bos
,
T. T.
Clark
, and
R.
Rubinstein
, “
Small scale response and modeling of periodically forced turbulence
,”
Phys. Fluids
19
,
055107
(
2007
).
6.
P.
Gualtieri
and
C.
Meneveau
, “
Direct numerical simulations of turbulence subjected to a straining and destraining cycle
,”
Phys. Fluids
22
(
6
),
065104
(
2010
).
7.
I.
Hadzic
,
K.
Hanjalic
, and
D.
Laurence
, “
Modeling the response of turbulence subjected to cyclic irrotational strain
,”
Phys. Fluids
13
,
1739
(
2001
).
8.
P. E.
Hamlington
and
W. J. A.
Dahm
, “
Reynolds stress closure for non-equilibrium effects in turbulent flows
,”
Phys. Fluids
20
,
115101
(
2008
).
9.
S. F.
Al-Sharif
,
M. A.
Cotton
, and
T. J.
Craft
, “
Reynolds stress transport models in unsteady and non-equilibrium turbulent flows
,”
Int. J. Heat Fluid Flow
31
(
3
),
401
408
(
2010
).
10.
A. J.
Revell
,
T. J.
Craft
, and
D. R.
Laurence
, “
Turbulence modelling of unsteady turbulent flows using the stress strain lag model
,”
Flow, Turbul. Combust.
86
,
129
151
(
2011
).
11.
S.
Sarkar
, “
The stabilizing effect of compressibility in turbulent shear flow
,”
J. Fluid Mech.
282
,
163
186
(
1995
).
12.
C.
Cambon
,
G. N.
Coleman
, and
D. N. N.
Mansour
, “
Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number
,”
J. Fluid Mech.
257
,
641
665
(
1993
).
13.
C. A.
Gomez
and
S. S.
Girimaji
, “
Toward second-moment closure modelling of compressible shear flows
,”
J. Fliud Mech.
733
,
325
369
(
2013
).
14.
S.
Friedlander
and
M. M.
Vishik
, “
Instability criteria for the flow of an inviscid incompressible fluid
,”
Phys. Rev. Lett.
66
(
17
),
2204
2206
(
1991
).
15.
B. J.
Bayly
, “
Three-dimensional instability of elliptical flow
,”
Phys. Rev. Lett.
57
(
17
),
2160
2163
(
1986
).
16.
C.
Cambon
, “
Spectral study of an incompressible turbulent field, subject to coupled effects of deformation and rotation, externally imposed
,” Doctoral Dissertation (
University of Lyon
, France,
1982
).
17.
A.
Salhi
,
C.
Cambon
, and
C. G.
Speziale
, “
Linear stability analysis of plane quadratic flows in a rotating frame with applications to modeling
,”
Phys. Fluids
9
(
8
),
2300
2309
(
1997
).
18.
R.
Bertsch
,
S.
Suman
, and
S. S.
Girimaji
, “
Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes
,”
Phys. Fluids
24
,
125106
(
2012
).
19.
H.
Yu
and
S. S.
Girimaji
, “
Extension of compressible ideal-gas RDT to general mean velocity gradients
,”
Phys. Fluids
19
(
4
),
041702
(
2007
).
20.
T. A.
Lavin
,
S. S.
Girimaji
,
S.
Suman
, and
H.
Yu
, “
Flow-thermodynamics interactions in rapidly-sheared compressible turbulence
,”
Theor. Comput. Fluid Dyn.
26
,
501
522
(
2011
).
21.
S. C.
Kassinos
and
W. C.
Reynolds
, “
A particle representation model for the deformation of homogeneous turbulence
,” in
Annual Research Briefs
(
Center for Turbulence Research, NASA Ames/Stanford University
,
1996
), pp.
31
53
.
22.
T.
Lavin
, “
Reynolds and Favre-averaged rapid distortion theory for compressible, ideal gas turbulence
,” M.S. thesis,
Texas A&M University
, College Station,
2007
.
23.
S. S.
Girimaji
,
E.
Jeong
, and
S. V.
Poroseva
, “
Pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion
,”
Phys. Fluids
15
(
10
),
3209
3222
(
2003
).
24.
G.
Kumar
,
R. L.
Bertsch
, and
S. S.
Girimaji
, “
Stabilizing action of pressure in high speed compressible shear flows: Effect of Mach number and obliqueness
,”
J. Fluid Mech.
760
,
540
566
(
2014
).
25.
A.
Simone
,
G. N.
Coleman
, and
C.
Cambon
, “
The effect of compressibility on turbulent shear flow: A rapid distortion theory and direct numerical simulation study
,”
J. Fluid Mech.
330
,
307
338
(
1997
).
26.
D.
Livescu
and
C. K.
Madnia
, “
Small scale structure of homogeneous turbulent shear flow
,”
Phys. Fluids
16
(
8
),
2864
2876
(
2004
).
27.
D.
Livescu
,
F. A.
Jaberi
, and
C. K.
Madnia
, “
The effects of heat release on the energy exchange in reacting turbulent shear flow
,”
J. Fluid Mech.
450
,
35
66
(
2001
).
28.
R. L.
Bertsch
, “
Rapidly-sheared compressible turbulence: Characterization of different pressure regimes and effect of thermodynamic fluctuations
,” M.S. thesis,
Texas A&M University
, College Station,
2010
.
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