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Journal articles on the topic 'Boundary-Layer Instability'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Kerschen, E. J. "Boundary Layer Receptivity Theory." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S152—S157. http://dx.doi.org/10.1115/1.3120795.

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The receptivity mechanisms by which free-stream disturbances generate instability waves in laminar boundary layers are discussed. Free-stream disturbances have wavelengths which are generally much longer than those of instability waves. Hence, the transfer of energy from the free-stream disturbance to the instability wave requires a wavelength conversion mechanism. Recent analyses using asymptotic methods have shown that the wavelength conversion takes place in regions of the boundary layer where the mean flow adjusts on a short streamwise length scale. This paper reviews recent progress in the theoretical understanding of these phenomena.

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2

Staley, D. O. "Boundary-Layer Damping of Baroclinic Instability." Journal of the Atmospheric Sciences 50, no. 5 (March 1993): 772–77. http://dx.doi.org/10.1175/1520-0469(1993)050<0772:bldobi>2.0.co;2.

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3

NASH, EMMA C., MARTIN V. LOWSON, and ALAN McALPINE. "Boundary-layer instability noise on aerofoils." Journal of Fluid Mechanics 382 (March 10, 1999): 27–61. http://dx.doi.org/10.1017/s002211209800367x.

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An experimental and theoretical investigation has been carried out to understand the tonal noise generation mechanism on aerofoils at moderate Reynolds number. Experiments were conducted on a NACA0012 aerofoil section in a low-turbulence closed working section wind tunnel. Narrow band acoustic tones were observed up to 40 dB above background noise. The ladder structure of these tones was eliminated by modifying the tunnel to approximate to anechoic conditions. High-resolution flow velocity measurements have been made with a three-component laser-Doppler anemometer (LDA) which have revealed the presence of strongly amplified boundary-layer instabilities in a region of separated shear flow just upstream of the pressure surface trailing edge, which match the frequency of the acoustic tones. Flow visualization experiments have shown these instabilities to roll up to form a regular Kármán-type vortex street.A new mechanism for tonal noise generation has been proposed, based on the growth of Tollmien–Schlichting (T–S) instability waves strongly amplified by inflectional profiles in the separating laminar shear layer on the pressure surface of the aerofoil. The growth of fixed frequency, spatially growing boundary-layer instability waves propagating over the aerofoil pressure surface has been calculated using experimentally obtained boundary-layer characteristics. The effect of boundary-layer separation has been incorporated into the model. Frequency selection and prediction of T–S waves are in remarkably good agreement with experimental data.

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4

Parziale, N. J., J. E. Shepherd, and H. G. Hornung. "Observations of hypervelocity boundary-layer instability." Journal of Fluid Mechanics 781 (September 16, 2015): 87–112. http://dx.doi.org/10.1017/jfm.2015.489.

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A novel optical method is used to measure the high-frequency (up to 3 MHz) density fluctuations that precede transition to turbulence within a laminar boundary layer in a hypervelocity flow. This optical method, focused laser differential interferometry, enables measurements of short-wavelength, high-frequency disturbances that are impossible with conventional instrumentation such as pressure transducers or hot wires. In this work, the T5 reflected-shock tunnel is used to generate flows in air, nitrogen and carbon dioxide with speeds between 3.5 and $5~\text{km}~\text{s}^{-1}$ (Mach numbers between 4 and 6) over a 5° half-angle cone at zero angle of attack. Simultaneous measurements are made at two locations approximately midway along a generator of the 1-m-long cone. With increasing Reynolds number (unit values were between 2 and $5\times 10^{6}~\text{m}^{-1}$), density fluctuations are observed to grow in amplitude and transition from a single narrow band of frequencies consistent with the Mack or second mode of boundary-layer instability to bursts of large-amplitude and spectrally broad disturbances that appear to be precursors of turbulent spots. Disturbances that are sufficiently small in initial amplitude have a wavepacket-like signature and are observed to grow in amplitude between the upstream and downstream measurement locations. A cross-correlation analysis indicates propagation of wavepackets at speeds close to the edge velocity. The free stream flow created by the shock tunnel and the resulting boundary layer on the cone are computed, accounting for chemical and vibrational non-equilibrium processes. Using this base flow, local linear and parabolized stability (PSE) analyses are carried out and compared with the experimental results. Reasonable agreement is found between measured and predicted most unstable frequencies, with the greatest differences being approximately 15 %. The scaling of the observed frequency with the inverse of boundary-layer thickness and directly with the flow velocity are consistent with the characteristics of Mack’s second mode, as well as results of previous researchers on hypersonic boundary layers.

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5

Grenier, Emmanuel, Yan Guo, and Toan T. Nguyen. "Spectral instability of characteristic boundary layer flows." Duke Mathematical Journal 165, no. 16 (November 2016): 3085–146. http://dx.doi.org/10.1215/00127094-3645437.

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6

Thompson, Charles, Vineet Mehta, and Arun Mulpur. "Secondary instability of a Stokes boundary layer." Journal of the Acoustical Society of America 91, no. 4 (April 1992): 2352. http://dx.doi.org/10.1121/1.403459.

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7

Roberts, P. J. D., J. M. Floryan, G. Casalis, and D. Arnal. "Boundary layer instability induced by surface suction." Physics of Fluids 13, no. 9 (September 2001): 2543–52. http://dx.doi.org/10.1063/1.1384868.

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8

Craig, Stuart A., and William S. Saric. "Crossflow instability in a hypersonic boundary layer." Journal of Fluid Mechanics 808 (October 27, 2016): 224–44. http://dx.doi.org/10.1017/jfm.2016.643.

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The crossflow instability in a hypersonic, laminar boundary layer is investigated using point measurements inside the boundary layer for the first time. Experiments are performed on a 7° right, circular cone with an adiabatic wall condition at 5.6° angle of incidence in the low-disturbance Mach 6 Quiet Tunnel at Texas A&M University. Measurements are made with a constant-temperature hot-wire anemometer system with a frequency response up to 180 kHz. Stationary crossflow waves are observed to grow and saturate. A travelling wave coexists with the stationary wave and occurs in a frequency band centred around 35 kHz. A type-I secondary instability is also observed in a frequency band centred around 110 kHz. The behaviour of all three modes is largely consistent with their low-speed counterparts prior to saturation of the stationary wave. Afterward, the behaviour remains in partial agreement with the low-speed case. Neither type-II secondary instability nor transition to turbulence are observed in this study.

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9

Gudkov, V. A. "Effect of instability on boundary layer detachment." Journal of Applied Mechanics and Technical Physics 32, no. 5 (1992): 703–6. http://dx.doi.org/10.1007/bf00851938.

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10

de Luca, L., G. Cardone, D. Aymer de la Chevalerie, and A. Fonteneau. "Goertler instability of a hypersonic boundary layer." Experiments in Fluids 16, no. 1 (November 1993): 10–16. http://dx.doi.org/10.1007/bf00188500.

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11

Dou, Hua-Shu, Wenqian Xu, and Boo Cheong Khoo. "Stability of boundary layer flow based on energy gradient theory." Modern Physics Letters B 32, no. 12n13 (May 10, 2018): 1840003. http://dx.doi.org/10.1142/s0217984918400031.

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The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier–Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

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12

Silveira, F. E. M. "Rayleigh-Taylor Instability with Finite Skin Depth." PLASMA PHYSICS AND TECHNOLOGY 5, no. 3 (2018): 95–98. http://dx.doi.org/10.14311/ppt.2018.3.95.

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In this work, the Rayleigh-Taylor instability is addressed in a viscous-resistive current slab, by assuming a finite electron skin depth. The formulation is developed on the basis of an extended form of Ohm’s law, which includes a term proportional to the explicit time derivative of the current density. In the neighborhood of the rational surface, a viscous-resistive boundary-layer is defined in terms of a resistive and a viscous boundary layers. As expected, when viscous effects are negligible, it is shown that the viscous-resistive boundary-layer is given by the resistive boundary-layer. However, when viscous effects become important, it is found that the viscous-resistive boundary-layer is given by the geometric mean of the resistive and viscous boundary-layers. Scaling laws of the time growth rate of the Rayleigh-Taylor instability with the plasma resistivity, fluid viscosity, and electron number density are discussed.

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13

Wenegrat, Jacob O., Jörn Callies, and Leif N. Thomas. "Submesoscale Baroclinic Instability in the Bottom Boundary Layer." Journal of Physical Oceanography 48, no. 11 (November 2018): 2571–92. http://dx.doi.org/10.1175/jpo-d-17-0264.1.

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AbstractWeakly stratified layers over sloping topography can support a submesoscale baroclinic instability mode, a bottom boundary layer counterpart to surface mixed layer instabilities. The instability results from the release of available potential energy, which can be generated because of the observed bottom intensification of turbulent mixing in the deep ocean, or the Ekman adjustment of a current on a slope. Linear stability analysis suggests that the growth rates of bottom boundary layer baroclinic instabilities can be comparable to those of the surface mixed layer mode and are relatively insensitive to topographic slope angle, implying the instability is robust and potentially active in many areas of the global oceans. The solutions of two separate one-dimensional theories of the bottom boundary layer are both demonstrated to be linearly unstable to baroclinic instability, and results from an example nonlinear simulation are shown. Implications of these findings for understanding bottom boundary layer dynamics and processes are discussed.

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14

Xiong, Youde, Tao Yu, Liquan Lin, Jiaquan Zhao, and Jie Wu. "Nonlinear Instability Characterization of Hypersonic Laminar Boundary Layer." AIAA Journal 58, no. 12 (December 2020): 5254–63. http://dx.doi.org/10.2514/1.j059263.

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15

Zhang, Y., and M. Oberlack. "Inviscid instability of compressible exponential boundary layer flows." AIP Advances 11, no. 10 (October 1, 2021): 105308. http://dx.doi.org/10.1063/5.0062795.

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16

Kohama, Y., and K. Suda. "Crossflow instability in a spinning disk boundary layer." AIAA Journal 31, no. 1 (January 1993): 212–14. http://dx.doi.org/10.2514/3.11344.

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17

Zhang, Yong-Ming, and Ji-Sheng Luo. "Application of Arnoldi method to boundary layer instability." Chinese Physics B 24, no. 12 (December 2015): 124701. http://dx.doi.org/10.1088/1674-1056/24/12/124701.

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18

Lee, S. L., T. S. Chen, and B. F. Armaly. "NONPARALLEL WAVE INSTABILITY ANALYSIS OF BOUNDARY-LAYER FLOWS." Numerical Heat Transfer 12, no. 3 (October 1987): 349–66. http://dx.doi.org/10.1080/10407788708913591.

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19

Lee, S. L., T. S. Chen, and B. F. Armaly. "Nonparallel Wave Instability Analysis of Boundary-Layer Flows." Numerical Heat Transfer, Part B: Fundamentals 12, no. 3 (1987): 349–66. http://dx.doi.org/10.1080/10407798708552584.

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20

Healey, J. J. "Characterizing boundary-layer instability at finite Reynolds numbers." European Journal of Mechanics - B/Fluids 17, no. 2 (March 1998): 219–37. http://dx.doi.org/10.1016/s0997-7546(98)80060-5.

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21

Ermolaev, Yu G., A. D. Kosinov, V. Ya Levchenko, and N. V. Semenov. "Instability of a three-dimensional supersonic boundary layer." Journal of Applied Mechanics and Technical Physics 36, no. 6 (November 1995): 840–43. http://dx.doi.org/10.1007/bf02369379.

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22

Hwang, Young-Kyu, and Yun-Yong Lee. "Theoretical flow instability of the Kármán boundary layer." KSME International Journal 14, no. 3 (March 2000): 358–68. http://dx.doi.org/10.1007/bf03186429.

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23

Dovgal, A. V., V. V. Kozlov, and A. Michalke. "Laminar boundary layer separation: Instability and associated phenomena." Progress in Aerospace Sciences 30, no. 1 (January 1994): 61–94. http://dx.doi.org/10.1016/0376-0421(94)90003-5.

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24

Fedorov, Alexander V., and Andrew P. Khokhlov. "Prehistory of Instability in a Hypersonic Boundary Layer." Theoretical and Computational Fluid Dynamics 14, no. 6 (July 1, 2001): 359–75. http://dx.doi.org/10.1007/s001620100038.

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25

Jensen, Mogens H. "Boundary layer instability in a coupled-map model." Physica D: Nonlinear Phenomena 38, no. 1-3 (September 1989): 203–7. http://dx.doi.org/10.1016/0167-2789(89)90192-9.

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26

Zanin, B. Yu. "Parameters of wave instability in a boundary layer." Journal of Engineering Physics 53, no. 4 (October 1987): 1183–87. http://dx.doi.org/10.1007/bf00872452.

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27

Derbyshire, S. H. "Boundary-Layer Decoupling over Cold Surfaces as a Physical Boundary-Instability." Boundary-Layer Meteorology 90, no. 2 (February 1999): 297–325. http://dx.doi.org/10.1023/a:1001710014316.

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28

Vedeneev, Vasily. "Interaction of panel flutter with inviscid boundary layer instability in supersonic flow." Journal of Fluid Mechanics 736 (November 4, 2013): 216–49. http://dx.doi.org/10.1017/jfm.2013.522.

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AbstractWe investigate the stability of an elastic plate in supersonic gas flow. This problem has been studied in many papers regarding panel flutter, where uniform flow is usually considered. In this paper, we take the boundary layer on the plate into account and investigate its influence on plate stability. Three problem formulations are studied. First, we investigate the stability of travelling waves in an infinite-length plate. Second, the nature of the instability (absolute or convective instability) is examined. Finally, by using solutions of the first two problems, instability of a long finite-length plate is studied by using Kulikovskii’s global instability criterion. The following results are obtained. All the eigenmodes of a finite-length plate are split into two types, which we call subsonic and supersonic. The influence of the boundary layer on these eigenmodes can be of two kinds. First, for a generalized convex boundary layer profile (typical for accelerating flow), supersonic eigenmodes are stabilized by the boundary layer, whereas subsonic disturbances are destabilized. Second, for a profile with a generalized inflection point (typical for constant and decelerating flows), supersonic eigenmodes are destabilized in a thin boundary layer and stabilized in a thick layer; subsonic eigenmodes are damped. The correspondence between the influence of the boundary layer on panel flutter and the stability of the boundary layer over a rigid wall is established. Examples of stable boundary layer profiles of both types are given.

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29

Fu, Yibin, and Philip Hall. "Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer." Journal of Fluid Mechanics 247 (February 1993): 503–25. http://dx.doi.org/10.1017/s0022112093000540.

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In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Görtler vortices is the temperature adjustment layer sitting at the edge of the boundary layer. This temperature adjustment layer is also the most dangerous site for Rayleigh instability. In this paper, we investigate how the existence of large-amplitude Görtler vortices affects the growth rate of Rayleigh instability. The effects of wall cooling and gas dissociation on this instability are also studied. We find that all these mechanisms increase the growth rate of Rayleigh instability and are therefore destabilizing.

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30

Yarantsev, D., I. Selivonin, and I. Moralev. "Influence of the surface DBD parameters on the streaks development in the boundary layer." Journal of Physics: Conference Series 2100, no. 1 (November 1, 2021): 012027. http://dx.doi.org/10.1088/1742-6596/2100/1/012027.

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Abstract The effect of the filamentary barrier discharge parameters on the boundary layer streaks generation and instability was studied. The streaks are formed near the constricted discharge channels due to vortices formation driven by spanwise Coulomb volume force. The secondary instability of the streaky structures can lead to the laminar-turbulent transition of the boundary layer. This work demonstrates that supply voltage parametrs affect the period of the constricted channels and thus the streaks transversal period within the boundary layer. For the various streaks periods, different modes of streak instability are shown to dominate.

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31

SCHRADER, LARS-UVE, LUCA BRANDT, and TAMER A. ZAKI. "Receptivity, instability and breakdown of Görtler flow." Journal of Fluid Mechanics 682 (July 11, 2011): 362–96. http://dx.doi.org/10.1017/jfm.2011.229.

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Receptivity, disturbance growth and breakdown to turbulence in Görtler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Görtler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Görtler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Görtler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Görtler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Görtler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Görtler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Görtler modes.

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32

ANDERSSON, PAUL, LUCA BRANDT, ALESSANDRO BOTTARO, and DAN S. HENNINGSON. "On the breakdown of boundary layer streaks." Journal of Fluid Mechanics 428 (February 10, 2001): 29–60. http://dx.doi.org/10.1017/s0022112000002421.

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A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplification consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modified mean fields; the need to consider a base flow which includes mean flow modification and harmonics of the fundamental streak is clearly demonstrated.

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33

Wenegrat, Jacob O., and Leif N. Thomas. "Centrifugal and Symmetric Instability during Ekman Adjustment of the Bottom Boundary Layer." Journal of Physical Oceanography 50, no. 6 (June 2020): 1793–812. http://dx.doi.org/10.1175/jpo-d-20-0027.1.

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AbstractFlow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.

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34

Liu, Zhi Yong, and Xiang Jiang Yuan. "Linear Instability Analysis of Confined Compressible Boundary/Mixing Layers Flow." Applied Mechanics and Materials 275-277 (January 2013): 522–26. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.522.

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A compressible supersonic confluent flow composed of boundary layers and mixing layers are studied by linear stability theory. The flow is confined in a two-dimensional adiabatic channel. A slower flow lying in the center mixes with faster boundary layer flows on both sides and two mixing layers are evolved near the centerline. Different unstable modes were discovered and the first mode was found to be most unstable. Three-dimensional disturbances were investigated and comparison of instability features was made with unconfined boundary layer flows. The investigation of different slow flow widths was also made and a smaller spacing between the boundary layer and mixing layer was found to suppress the growth of disturbance.

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35

Blackaby, Nicholas D., Stephen J. Cowley, and Philip Hall. "On the instability of hypersonic flow past a flat plate." Journal of Fluid Mechanics 247 (February 1993): 369–416. http://dx.doi.org/10.1017/s0022112093000503.

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The instability of hypersonic boundary-layer flow over a flat plate is considered. The viscosity of the fluid is taken to be governed by Sutherland's formula, which gives a more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapman's approximate linear law. A Prandtl number of unity is assumed. Attention is focused on inviscid instability modes of viscous hypersonic boundary layers. One such mode, the ‘vorticity’ mode, is thought to be the fastest growing disturbance at high Mach numbers, M [Gt ] 1; in particular it is believed to have an asymptotically larger growth rate than any viscous instability. As a starting point we investigate the instability of the hypersonic boundary layer which exists far downstream from the leading edge of the plate. In this regime the shock that is attached to the leading edge of the plate plays no role, so that the basic boundary layer is non-interactive. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained if a Chapman viscosity law is assumed. In particular, we find that the growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O((log M)½). Next, the development of the vorticity mode as the wavenumber decreases is described. It is shown, inter alia, that when the wavenumber is reduced to O(M-3/2) from the O(1) initial, ‘vorticity-mode’ scaling, ‘acoustic’ modes emerge.Finally, the inviscid instability of the boundary layer near the leading-edge interaction zone is discussed. Particular attention is focused on the strong-interaction zone which occurs sufficiently close to the leading edge. We find that the vorticity mode in this regime is again unstable. The fastest growing mode is centred in the adjustment layer at the edge of the boundary layer where the temperature changes from its large, O(M2). value in the viscous boundary layer, to its O(1) free-stream value. The existence of the shock indirectly, but significantly, influences the instability problem by modifying the basic flow structure in this layer.

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36

Cassel, K. W., F. T. Smith, and J. D. A. Walker. "The onset of instability in unsteady boundary-layer separation." Journal of Fluid Mechanics 315 (May 25, 1996): 223–56. http://dx.doi.org/10.1017/s0022112096002406.

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The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous—inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought.

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37

COOPER, A. J., and PETER W. CARPENTER. "The stability of rotating-disc boundary-layer flow over a compliant wall. Part 2. Absolute instability." Journal of Fluid Mechanics 350 (November 10, 1997): 261–70. http://dx.doi.org/10.1017/s0022112097006964.

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A numerical study has been undertaken of the influence of a compliant boundary on absolute instability. In a certain parameter range absolute instability occurs in the boundary layer on a rotating disc, thereby instigating rapid transition to turbulence. The conventional use of wall compliance as a laminar-flow control technique has been to lower growth rates of convective instabilities. This has the effect of reducing amplification of disturbances as they propagate downstream. For absolute instability, however, only the suppression of its onset would be a significant gain. This paper addresses the question of whether passive wall compliance can be advantageous when absolute instability exists in a boundary layer.A theoretical model of a single-layer viscoelastic compliant wall was used in conjunction with the sixth-order system of differential equations which govern the stability of the boundary-layer flow over a rotating disc. The absolute/convective nature of the flow was ascertained by using a spatio-temporal analysis. Pinch-point singularities of the dispersion relation and a point of zero group velocity identify the presence of absolute instability. It was found that only a low level of wall compliance was enough to delay the appearance of absolute instability to higher Reynolds numbers. Beyond a critical level of wall compliance results suggest that complete suppression of absolute instability is possible. This would then remove a major route to transition in the rotating-disc boundary layer.

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38

Carpenter, Peter W., and Lee J. Porter. "Effects of Passive Porous Walls on Boundary-Layer Instability." AIAA Journal 39, no. 4 (April 2001): 597–604. http://dx.doi.org/10.2514/2.1381.

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39

Ma’mun, Mochamad Dady, and Masahito Asai. "Influences of Oblique Surface Corrugation on Boundary-Layer Instability." Journal of the Physical Society of Japan 83, no. 8 (August 15, 2014): 084402. http://dx.doi.org/10.7566/jpsj.83.084402.

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40

Wheaton, Bradley M., and Steven P. Schneider. "Roughness-Induced Instability in a Hypersonic Laminar Boundary Layer." AIAA Journal 50, no. 6 (June 2012): 1245–56. http://dx.doi.org/10.2514/1.j051199.

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41

Timoshin, S. N. "Feedback Instability in a Boundary‐Layer Flow Over Roughness." Mathematika 52, no. 1-2 (December 2005): 161–68. http://dx.doi.org/10.1112/s0025579300000437.

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42

Rast, Mark P., and Juri Toomre. "Compressible Convection with Ionization. II. Thermal Boundary-Layer Instability." Astrophysical Journal 419 (December 1993): 240. http://dx.doi.org/10.1086/173478.

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43

Ruden, E. L. "Rayleigh-Taylor instability with a sheared flow boundary layer." IEEE Transactions on Plasma Science 30, no. 2 (April 2002): 611–15. http://dx.doi.org/10.1109/tps.2002.1024296.

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44

EGAMI, Yasuhiro, and Yasuaki KOHAMA. "Traveling Instabilities on a Crossflow Instability Dominant Boundary Layer." Transactions of the Japan Society of Mechanical Engineers Series B 64, no. 618 (1998): 327–33. http://dx.doi.org/10.1299/kikaib.64.327.

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45

TAO, J. "Nonlinear global instability in buoyancy-driven boundary-layer flows." Journal of Fluid Mechanics 566 (October 5, 2006): 377. http://dx.doi.org/10.1017/s0022112006002369.

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46

Paredes, Pedro, Meelan M. Choudhari, and Fei Li. "Instability wave–streak interactions in a supersonic boundary layer." Journal of Fluid Mechanics 831 (October 13, 2017): 524–53. http://dx.doi.org/10.1017/jfm.2017.630.

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Abstract:

The interaction of stationary streaks undergoing non-modal growth with modally unstable instability waves in a supersonic flat-plate boundary-layer flow is studied using numerical computations. For incompressible flows, previous studies have shown that boundary-layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien–Schlichting instability waves, resulting in a delay in the onset of laminar–turbulent transition. In the supersonic regime, the most-amplified linear waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a strong amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks in a two-dimensional, Mach 3 adiabatic flat-plate boundary-layer flow, followed by the modal instability characteristics of the perturbed, streaky boundary-layer flow. Both parts of the investigation are performed with the plane-marching parabolized stability equations. Consistent with previous findings, the present study shows that optimally growing stationary streaks can destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a potential transition delay that may be comparable to the length of the laminar region in the uncontrolled case.

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47

Savenkov, I. V. "Instability of the boundary layer on a curved surface." Fluid Dynamics 25, no. 1 (1990): 151–54. http://dx.doi.org/10.1007/bf01051312.

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48

Petrov, G. V. "Two-dimensional absolute instability of a supersonic boundary layer." Fluid Dynamics 23, no. 1 (1988): 147–50. http://dx.doi.org/10.1007/bf01051563.

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Kingan, Michael J., and John R. Pearse. "Laminar boundary layer instability noise produced by an aerofoil." Journal of Sound and Vibration 322, no. 4-5 (May 2009): 808–28. http://dx.doi.org/10.1016/j.jsv.2008.11.043.

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Katasonov, M. M., S. H. Park, H. J. Sung, and V. V. Kozlov. "Instability of streaky structure in a Blasius boundary layer." Experiments in Fluids 38, no. 3 (February 8, 2005): 363–71. http://dx.doi.org/10.1007/s00348-004-0917-9.

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