Review of Linear Compressible Stability Theory

Mack, Leslie M.

doi:10.1007/978-1-4612-4724-1_9

Cited by 118 publications

(100 citation statements)

References 5 publications

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“…Results for Rl{co} are shown in Figure 23. Two modes were found, the first (mode I) originates at a = 0, with a wavespeed co = 1 -1/MO" = 0.5, and as such is typical of so-called "first modes" observed in supersonic boundary I---r stability studies (e.g., Mack, 1987). Mode II, on the other hand, originates with a wavespeed co Z 1.48, and consequently is more typical of the bounded flow modes observed in previous sections of this paper.…”

Section: A Change Of Boundary Conditionsmentioning

confidence: 69%

“…Most of the work (which has for the most part been based on the parallel mean flow assumption) has been with regard to boundary-layer flows (e.g., Lees and Lin 1946, Mack 1963, 1965a,b, 1959, 1984, 1987) and more recently to jets and shear layers (e.g., Tam and Hu 1989a,b, Greenough et al 1988, Papageorgiou 1990, Jackson and Grosch 1989, Mack 1990). …”

Section: Ic-c'j < A(are)- (11)mentioning

confidence: 99%

“…Such neutral modes are readily distinguishable, because of the oo..illatory nature of the eigensolutions in the free sLream, while subsonic neutral modes exhibit exponential decay of their eigensolutions in the free stream. Mack (1963Mack ( , 1965aMack ( ,b, 1969Mack ( , 1984Mack ( , 1987Mack ( , 1990 has shown how such modes are extremely important in compressible boundary-layer flows, particularly in the case of boundary layers on cooled walls, where these modes are often associated with the largest amplification rates. Such modes have also been shown to exist and be important in other classes of flow by Tam and Hu (1989), Greenough (1989), Zhuang, Kubota, and Dimotakis (1990) (confined twodimensional supersonic mixing layers), Macaraeg (1990), and by Jackson and Grosch (1989) (compressible mixing layers).…”

Section: Ic-c'j < A(are)- (11)mentioning

confidence: 99%

“…Equations (5.1) and (5.2) may be combined to yield the single second order equation (see for example Mack 1984Mack , 1987 d f (Uo-c)oy Uo,Ool =o 2 (AU-CO)…”

Section: Inviscid Disturbance Equationsmentioning

confidence: 99%

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On the linear stability of compressible plane Couette flow

1994

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91-11267 ABSTRACTThe linear stability of compressible plane Couette flow is investigated. The correct and proper basic velocity and temperature distributions are perturbed by a small amplitude normal mode disturbance. The full small amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in sene detail. It is found that instability can occur, although the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wavespeed of the disturbances approaches the velocity of either of the walls, and these regimes are also analyzed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

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Section: A Change Of Boundary Conditionsmentioning

confidence: 69%

Section: Ic-c'j < A(are)- (11)mentioning

confidence: 99%

Section: Ic-c'j < A(are)- (11)mentioning

confidence: 99%

“…Equations (5.1) and (5.2) may be combined to yield the single second order equation (see for example Mack 1984Mack , 1987 d f (Uo-c)oy Uo,Ool =o 2 (AU-CO)…”

Section: Inviscid Disturbance Equationsmentioning

confidence: 99%

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On the linear stability of compressible plane Couette flow

1994

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“…The solvability condition (22) We differentiate the first-order equations (15) (31) to determine a_./3xa, using the same procedure as for the first-order equations, but for a nonhomogeneous set of equations.…”

Section: B Second-order Equationsmentioning

confidence: 99%