scholarly journals Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer

2002 ◽  
Vol 14 (8) ◽  
pp. L57-L60 ◽  
Author(s):  
Carlo Cossu ◽  
Luca Brandt
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

scholarly journals Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011 ◽  
Vol 681 ◽  
pp. 116-153 ◽  
Author(s):  
NICHOLAS J. VAUGHAN ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Low Frequency ◽  
Finite Amplitude ◽  
Base Flow ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Tollmien Schlichting

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the Tollmien–Schlichting (T–S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

scholarly journals The mechanics of the Tollmien-Schlichting wave

1996 ◽  
Vol 312 ◽  
pp. 107-124 ◽  
Author(s):  
Peter G. Baines ◽  
Sharan J. Majumdar ◽  
Humio Mitsudera
Keyword(s):  
Boundary Layer ◽  
Outer Part ◽  
Slip Boundary Condition ◽  
Slip Condition ◽  
Linear Solution ◽  
Slip Boundary ◽  
Uniform Shear ◽  
Blasius Boundary Layer ◽  
Partial Mode ◽  
Tollmien Schlichting

We describe a mechanistic picture of the essential dynamical processes in the growing Tollmien-Schlichting wave in a Blasius boundary layer and similar flows. This picture depends on the interaction between two component parts of a disturbance (denoted ‘partial modes’), each of which is a complete linear solution in some idealization of the system. The first component is an inviscid mode propagating on the vorticity gradient of the velocity profile with the free-slip boundary condition, and the second, damped free viscous modes in infinite uniform shear with the no-slip condition. There are two families of these viscous modes, delineated by whether the phase lines of the vorticity at the wall are oriented with or against the shear, and they are manifested as resonances in a forced system. The interaction occurs because an initial ‘inviscid’ disturbance forces a viscous response via the no-slip condition at the wall. This viscous response is large near the resonance associated with the most weakly damped viscous mode, and in the unstable parameter range it has suitable phase at the outer part of the boundary layer to increase the amplitude of the inviscid partial mode by advection.

Instability and Breakdown of a Zero Net Mass-Flux Jet in a Blasius Boundary Layer

2009 ◽  
Author(s):  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Three Dimensional ◽  
Base Flow ◽  
Hot Wire ◽  
Control Applications ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting ◽  
Laminar Flow Control ◽  
Zero Net Mass Flux

Hot–wire measurements reveal the evolution of three-dimensional TS (Tollmien-Schlichting) waves and other nonlinear disturbances generated by a ZNMF (Zero Net Mass-Flux) jet. The base flow consists of a highly two-dimensional Blasius boundary layer with extremely small extraneous background disturbance levels (u/U1 < 0.08 %). The response is shown to be linear and symmetrical for sufficiently small actuator amplitudes and under these conditions the TS wave motions conform with the PSE (Parabolized Stability Equations) results of Mack & Herbert (1995). The observations suggest that a small-amplitude ZNMF jet would be a suitable device for active LFC (Laminar Flow Control) applications. For larger actuator amplitudes, other short–wavelength instabilities develop and grow with streamwise development and they ultimately breakdown to form a turbulent wedge. There is an actuator amplitude threshold below which these instabilities do not form, and a larger threshold below which the instabilities do not grow with streamwise development. The characteristics of the turbulent wedge are also considered in some detail.

Boundary-layer transition by interaction of discrete and continuous modes

2008 ◽  
Vol 604 ◽  
pp. 199-233 ◽  
Author(s):  
YANG LIU ◽  
TAMER A. ZAKI ◽  
PAUL A. DURBIN
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Length Scale ◽  
Bypass Transition ◽  
Continuous Mode ◽  
Layer Transition ◽  
Boundary Layer Turbulence ◽  
Tollmien Schlichting

The natural and bypass routes to boundary-layer turbulence have traditionally been studied independently. In certain flow regimes, both transition mechanisms might coexist, and, if so, can interact. A nonlinear interaction of discrete and continuous Orr-Sommerfeld modes, which are at the origin of orderly and bypass transition, respectively, is found. It causes breakdown to turbulence, even though neither mode alone is sufficient. Direct numerical simulations of the interaction shows that breakdown occurs through a pattern of Λ-structures, similar to the secondary instability of Tollmien–Schlichting waves. However, the streaks produced by the Orr-Sommerfeld continuous mode set the spanwise length scale, which is much smaller than that of the secondary instability of Tollmien–Schlichting waves. Floquet analysis explains some of the features seen in the simulations as a competition between destabilizing and stabilizing interactions between finite-amplitude distortions.

Stability of Blasius Boundary-Layer Flow Interacting With a Compliant Panel

2014 ◽  
Author(s):  
Konstantinos Tsigklifis ◽  
Anthony D. Lucey
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Travelling Wave ◽  
Unstable Flow ◽  
Blasius Boundary Layer ◽  
Compliant Wall ◽  
Plate Spring ◽  
Difference Form ◽  
Tollmien Schlichting ◽  
Layer Flow

We develop a model to study the fluid-structure interaction (FSI) of a compliant panel with a Blasius boundary-layer flow. We carry out a two-dimensional global linear stability analysis modeling the flow using a combination of vortex and source boundary-element sheets on a computational grid while the dynamics of a plate-spring compliant wall are represented in finite-difference form. The system is then couched as an eigenvalue problem and the eigenvalues of the various flow- and wall-based instabilities are analyzed for two distinct sets of system parameters. Key findings are that coalescence — or resonance — of a structural eigenmode with either the most unstable flow-based Tollmien-Schlichting Wave (TSW) or wall-based travelling-wave flutter (TWF) modes can occur. This renders the convective nature of these instabilities to become global for a finite compliant wall, a phenomenon that has not hitherto been reported in the literature.

The flat plate boundary layer. Part 3. Comparison of theory with experiment

1970 ◽  
Vol 43 (4) ◽  
pp. 819-832 ◽  
Author(s):  
J. A. Ross ◽  
F. H. Barnes ◽  
J. G. Burns ◽  
M. A. S. Ross
Keyword(s):  
Boundary Layer ◽  
Plate Boundary ◽  
Wave Number ◽  
Stream Velocity ◽  
Flow Conditions ◽  
Blasius Boundary Layer ◽  
Perturbation Velocity ◽  
Tollmien Schlichting ◽  
Theoretical Results ◽  
Good Flow

A study of Tollmien–Schlichting waves in the Blasius boundary layer has been carried out under good flow conditions. The maximum r.m.s. amplitude of u, the downstream component of perturbation velocity, was limited to about 0·06% of U0, the free-stream velocity. Measurements of the wave-number and of the distribution of u/U0 normal to the plate agree closely with the theoretical results obtained in parts 1 and 2 of this paper. The experimental critical Reynolds number, Rc, is 400; the theoretical Rc derived from the imaginary part of the eigenvalue is 500 (part 2), but additional amplification carried by the eigenvector removes most of this discrepancy.

The upper branch stability of the Blasius boundary layer, including non-parallel flow effects

1981 ◽  
Vol 375 (1760) ◽  
pp. 65-92 ◽  
Keyword(s):  
Boundary Layer ◽  
Parallel Flow ◽  
Neutral Stability ◽  
Relative Order ◽  
Numerical Work ◽  
Blasius Boundary Layer ◽  
Stability Structure ◽  
Tollmien Schlichting ◽  
Flow Effects ◽  
The Stability

The stability of the Blasius boundary layer is studied theoretically, with the aim of fixing the character of the upper branch of the neutral stability curve(s) and its dependence on non-parallel flow effects. Unlike most previous studies this work has a rational basis since, throughout, we consider the linear stability structure for asymptotically large Reynolds numbers ( Re ). The structure is five-zoned and quite complicated, more so than the structure (discussed in Smith (1979 a )) governing the lower branch stability properties, but nevertheless it lends itself to the systematic determination of the neutral frequency and of the influence of non-parallelism. The four leading terms in the asymptotic expansion of the neutral frequency are determined and then the non-parallel flow effects are considered. The latter are shown to be of relative order Re -3/10 in general, much larger than the relative order Re -1/2 suggested by the parallel flow approximations used extensively in the literature. The cause of this discrepancy lies partly in the relatively large wavelength of the Tollmien-Schlichting modes but, more especially, in a ‘transmission feature’, associated with the stability structure and brought about by the major determining role played by the small curvature of the boundary layer profile at the critical layer. This transmission feature enables even quite small effects in the disturbance velocity field to produce a much more profound effect in the neutral stability criteria. The results of this study are not inconsistent overall with previous numerical work but they do tend to suggest that linear non-parallel flow stability theory may well explain most of the related experimental observations, even near the critical Reynolds number.

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