Streamwise Velocity Spectra Research Articles

Very-large-scale fluctuations in turbulent channel flow at low Reynolds number

It is known that there exist very large features in turbulent channel flow at high Reynolds number as well as in pipe flow and turbulent boundary layer. In addition, a low frequency peak was observed in spectra of the streamwise velocity fluctuation in transitional and low-Reynolds-number but turbulent channel flows. In this study, the large-scale fluctuation observed at the low Reynolds number has been experimentally explored with increasing Reynolds number by means of a hot wire anemometry. There are two peaks in the streamwise velocity spectra for transitional flow for 1800 ≤ Re ≤ 2600, where Re is the Reynolds number based on the bulk velocity and the channel width. The high-frequency peak corresponds to the turbulent vortices that have the same order of magnitude as the channel width, while the low-frequency peak is due to passages of the turbulent patches whose streamwise scale is greater than ten channel widths. It is surprising that the low frequency peak remains even up to Re=3000 at which the flow is fully turbulent. Furthermore, a spectral plateau around the frequency corresponding to 25 channel widths is confirmed up to Re=4000, indicating that there exist very-large-scale fluctuations in turbulent channel flow even at low Reynolds number.

Inner–outer interactions in rough-wall turbulence

ABSTRACTHere we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u* signal does depend on roughness Reynolds number (k+s), but is robust to changes in friction Reynolds number (δ+). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

AbstractDirect numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin–Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress–strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

Scaling of pressure spectrum in turbulent boundary layers

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Reθ = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress than when scaled with the local turbulent kinetic energy

Velocity statistics in turbulent channel flow up to

AbstractThe high-Reynolds-number behaviour of the canonical incompressible turbulent channel flow is investigated through large-scale direct numerical simulation (DNS). A Reynolds number is achieved ($Re_{\tau } = h/\delta _v \approx 4000$, where $h$ is the channel half-height, and $\delta _v$ is the viscous length scale) at which theory predicts the onset of phenomena typical of the asymptotic Reynolds number regime, namely a sensible layer with logarithmic variation of the mean velocity profile, and Kolmogorov scaling of the velocity spectra. Although higher Reynolds numbers can be achieved in experiments, the main advantage of the present DNS study is access to the full three-dimensional flow field. Consistent with refined overlap arguments (Afzal & Yajnik, J. Fluid Mech. vol. 61, 1973, pp. 23–31; Jiménez & Moser, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007, pp. 715–732), our results suggest that the mean velocity profile never achieves a truly logarithmic profile, and the logarithmic diagnostic function instead exhibits a linear variation in the outer layer whose slope decreases with the Reynolds number. The extrapolated value of the von Kármán constant is $k \approx 0.41$. A near logarithmic layer is observed in the spanwise velocity variance, as predicted by Townsend’s attached eddy hypothesis, whereas the streamwise variance seems to exhibit a shoulder, perhaps being still affected by low-Reynolds-number effects. Comparison with previous DNS data at lower Reynolds number suggests enhancement of the imprinting effect of outer-layer eddies onto the near-wall region. This mechanisms is associated with excess turbulence kinetic energy production in the outer layer, and it reflects in flow visualizations and in the streamwise velocity spectra, which exhibit sharp peaks in the outer layer. Associated with the outer energy production site, we find evidence of a Kolmogorov-like inertial range, limited to the spanwise spectral density of $u$, whereas power laws with different exponents are found for the other spectra. Finally, arguments are given to explain the ‘odd’ scaling of the streamwise velocity variances, based on the analysis of the kinetic energy production term.

On the scaling in sink-flow turbulent boundary layers

AbstractScaling of the streamwise velocity spectrum ${\phi }_{11} ({k}_{1} )$ in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the ${ k}_{1}^{- 1} $ scaling i.e. ${\phi }_{11} ({k}_{1} )= {A}_{1} { U}_{\tau }^{2} { k}_{1}^{- 1} $, where ${k}_{1} $ is the streamwise wavenumber and ${U}_{\tau } $ is the friction velocity. Interestingly, this ${ k}_{1}^{- 1} $ scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient ${A}_{1} $ in the present sink-flow data is seen to be non-universal, i.e. ${A}_{1} $ varies with height from the wall; the scaling exponent −1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral ${ k}_{1}^{- 1} $ scaling, is also seen to be non-universal, consistent with the non-universality of ${A}_{1} $. These observations are to be contrasted with the universal value of ${A}_{1} $ (along with the universal scaling exponent of −1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient ${A}_{1} $ non-universal while leaving the scaling exponent −1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun et al., J. Fluid Mech., vol. 715, 2013, pp. 477–498); the present paper establishes the link between these two. The variability of ${A}_{1} $ accommodated in the present framework serves to clarify the ideas of universality of the ${ k}_{1}^{- 1} $ scaling.

Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers

AbstractWell-resolved streamwise velocity spectra are reported for smooth- and rough-wall turbulent pipe flow over a large range of Reynolds numbers. The turbulence structure far from the wall is seen to be unaffected by the roughness, in accordance with Townsend’s Reynolds number similarity hypothesis. Moreover, the energy spectra within the turbulent wall region follow the classical inner and outer scaling behaviour. While an overlap region between the two scalings and the associated${ k}_{x}^{- 1} $law are observed near${R}^{+ } \approx 3000$, the${ k}_{x}^{- 1} $behaviour is obfuscated at higher Reynolds numbers due to the evolving energy content of the large scales (the very-large-scale motions, or VLSMs). We apply a semi-empirical correction (del Álamo & Jiménez,J. Fluid Mech., vol. 640, 2009, pp. 5–26) to the experimental data to estimate how Taylor’s frozen field hypothesis distorts the pseudo-spatial spectra inferred from time-resolved measurements. While the correction tends to suppress the long wavelength peak in the logarithmic layer spectrum, the peak nonetheless appears to be a robust feature of pipe flow at high Reynolds number. The inertial subrange develops around${R}^{+ } \gt 2000$where the characteristic${ k}_{x}^{- 5/ 3} $region is evident, which, for high Reynolds numbers, persists in the wake and logarithmic regions. In the logarithmic region, the streamwise wavelength of the VLSM peak scales with distance from the wall, which is in contrast to boundary layers, where the superstructures have been shown to scale with boundary layer thickness throughout the entire shear layer. Moreover, the similarity in the streamwise wavelength scaling of the large- and very-large-scale motions supports the notion that the two are physically interdependent.

Spectral analysis of turbulent viscoelastic and Newtonian channel flows

The one-dimensional spectra in the streamwise direction of the velocity and vorticity fields in turbulent channel flows of Newtonian and non-Newtonian viscoelastic fluids are presented for friction Reynolds numbers up to Reτ0=1000.The most striking feature induced by viscoelasticity is a marked drop, as rapid as k−5, in the energy level of the streamwise velocity spectra at high wave-numbers, and in agreement with experimental data by Warholic et al. (1999) [15]. The scaling of the streamwise velocity spectra for viscoelastic flow share some characteristics with the Newtonian spectra, but also exhibit unique properties. In particular, the logarithmic correction to the usual k−1 law at the intermediate scales (eddies with size one to ten times the distance from the wall), found by del Álamo et al. (2004) [7] in the case of Newtonian turbulence, still holds in viscoelastic flows; although, with different scaling coefficients. In contrast, the longest modes of the spectra of the streamwise velocity component are found to behave differently. These modes are longer in viscoelastic flows and their scaling with the channel centerline velocity, here confirmed for Newtonian flow, fails for high drag reduction viscoelastic turbulent flows.As for vorticity, it is found that the spectra of its cross-flow component in viscoelastic flows exhibit a significantly higher energy level at large scales, with a tendency towards a k−1 law for high drag reduction and high Reynolds number.

Effects of external intermittency and mean shear on the spectral inertial-range exponent in a turbulent square jet

This study investigates by experiment the dependence of the inertial-range exponent m of the streamwise velocity spectrum on the external intermittency factor γ (≡ the fraction of time the flow is fully turbulent) and the mean shear S in a turbulent square jet. Velocity measurements were made using hot-wire anemometry in the jet at 15 < x/D(e) < 40, where D(e) denotes the exit equivalent diameter, and for an exit Reynolds number of Re = 50,000. The Taylor microscale Reynolds number R(λ) varies from about 70 to 450 in the present study. The TERA (turbulent energy recognition algorithm) method proposed by Falco and Gendrich [in Near-Wall Turbulence: 1988 Zoran Zariç Memorial Conference, edited by S. J. Kline and N. H. Afgan (Hemisphere Publishing Corp., Washington, DC, 1990), pp. 911-931] is discussed and applied to estimate the intermittency factor from velocity signals. It is shown that m depends strongly on γ but negligibly on S. More specifically, m varies with γ following m=m(t)+(lnγ(-0.0173))(1/2), where m(t) denotes the spectral exponent found in fully turbulent regions.

Effect of a standing baffle on the flow structure in a rectangular open channel

The effect of an intermediate standing baffle on the flow structure in a rectangular open channel has been investigated by a three-dimensional acoustic Doppler velocimeter. Investigation of time-averaged velocity profiles at different streamwise positions reveals that the approach flow is fully developed upstream of the baffle. By analysing the space-averaged power spectra of streamwise velocity, a peak structure was observed in the upstream baffle region. Downstream of the baffle this peak structure has been alleviated by the baffle. The same analysis for the vertical component indicates the existence of a peak structure both up- and downstream of the baffle. Consequently, a baffle affects the streamwise energy dissipation but not the vertical energy dissipation.

On the wake with and without vortex shedding suppression behind a two-dimensional square cylinder in proximity to a plane wall

A comparative study of the wake characteristics behind a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e. G/ D=0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. For the system G/ D=0.5, a regular Karman-like vortex shedding at fD/ U 0=0.13 was found by inspection of the streamwise velocity spectra. When the gap width is reduced to G/ D=0.25, a low-speed separation bubble was formed in the region 4.25< x/ D<9.25, while the intermittent existence of large-scale vortices at the reduced frequency fD/ U 0=0.116 was identified in the upper shear layer. The convective vortex dynamics were analyzed in terms of the cross-correlation of the wall-pressure fluctuation, coherence and cross-correlation of wall-pressure fluctuations with velocity fluctuations at various positions located at the lower edge of the cylinder ( y/ D= G/ D) and the outer edge of the upper shear layer. The convection velocities of the Karman-like vortices in the system G/ D=0.5 was determined to be U c / U 0=0.64. However, in the system G/ D=0.25 the convection velocities before and behind x/ D=3.25 were determined to be U c / U 0=0.32 and 0.64, respectively.

Vortex dynamics and mass entrainment in turbulent lobed jets with and without lobe deflection angles

Passive control of jet flows in order to enhance mixing and entrainment is of wide applicative interest. Our purpose is to develop new air diffusers for HVAC systems, by using lobed geometry nozzles, in order to ameliorate users the thermal comfort. Two turbulent 6-lobed air jets with and without lobe deflection angles were studied experimentally and compared with a reference circular jet having the same initial Reynolds number. The main objective was to analyze the modifications occurring in the vortex dynamics of the flow, firstly by replacing a circular tube with a straight lobed tube, and secondly by a lobed tube having a double inclination of the lobes. Rapid visualizations of the flows and hot-wire measurements of the streamwise velocity spectra allow understanding the vortex roll-up mechanisms. Unlike the circular jet, where the primary rings are continuous, the Kelvin–Helmholtz vortices in the lobed jet flows were found to be discontinuous. The resulting “ring segments” detach at different frequencies whether they are shed in the lobe troughs or at the lobe sides. One explanation relies on the strong variation of the exit plane curvature. Additionally, a speculative scenario of the vortical dynamics is advanced by the authors. The discontinuous nature of the K–H vortices enables the development of secondary streamwise structures, non-influenced by the passage of the primary structures as in the case of the circular jet. Thus, the momentum flux transport role played by the streamwise structures is rendered more efficient and leads to a spectacular increase in the entrainment rate in the initial region. The amount of fluid being entrained in the lobed jet by the streamwise structures is drastically amplified by the double inclination of the nozzle exit boundary.

The effect of waves on subgrid-scale stresses, dissipation and model coefficients in the coastal ocean bottom boundary layer

Six sets of particle image velocimetry (PIV) data from the bottom boundary layer of the coastal ocean are examined. The data represent periods of high, moderate and weak mean flow relative to the amplitude of wave-induced motion, which correspond to high, moderate and low Reynolds numbers based on the Taylor microscale (Re). The two-dimensional PIV velocity distributions enable spatial filtering to calculate some of the subgrid-scale (SGS) stresses, from which we can estimate the SGS dissipation, and evaluate the performance of typically used SGS stress models. The previously reported mismatch between the SGS and viscous dissipation at moderate and low Reynolds numbers appears to be related to the sparsity of large vortical structures that dominate energy fluxes.Conditional sampling of SGS stresses and dissipation based on wave phase using Hilbert transforms demonstrate persistent and repeatable direct effects of large-scale but weak straining by the waves on the SGS energy flux at small scales. The SGS energy flux is phase-dependent, peaking when the streamwise-wave-induced velocity is accelerating, and lower when this velocity is decelerating. Combined with strain rate generated by the mean flow, the streamwise wave strain causes negative energy flux (backscatter), whereas the vertical wave strain causes a positive flux. The phase-dependent variations and differences between horizontal and vertical contributions to the cascading process extend to strains that are substantially higher than the wave-induced motion. These trends may explain the measured difference between spatial energy spectra of streamwise velocity fluctuations and spectra of the wall-normal component, i.e. the formation of spectral bumps in the spectra of the streamwise component at the wavenumbers for the transition between inertial and dissipation scales.All the model coefficients of typical SGS stress models measured here are phase dependent and show similar trends. Thus, the variations of measured SGS dissipation with phase are larger than those predicted by the model variables. In addition, the measured coefficients of the static Smagorinsky SGS stress model decrease with decreasing turbulence levels, and increase with filter size. The dynamic model provides higher correlation coefficients than the Smagorinsky model, but the substantial fluctuations in their values indicate that ensemble averaging is required. The ‘global’ dynamic model coefficients indicate that the use of a scale-dependent dynamic model may be appropriate. The structure function model yields poor correlation coefficients and is found to be over-dissipative under all but the highest turbulence levels. The nonlinear model has higher correlations with measured stresses, as expected, but it also does not reproduce the trends with wave phase.

Evidence of thek1−1Law in a High-Reynolds-Number Turbulent Boundary Layer

Dimensional analysis and overlap arguments lead to a prediction of a region in the streamwise velocity spectrum of wall-bounded turbulent flows in which the dependence on the streamwise wave number, kappa(1), is given by kappa(1)(-1). Some recent experiments have questioned the existence of this region. In this Letter, experimental spectra are presented which support the existence of the kappa(1)(-1) law in a high-Reynolds-number boundary layer. This Letter presents the experimental results and discusses the theoretical and experimental issues involved in examining the existence of the kappa(1)(-1) law and the reasons why it has proved so elusive.

Turbulence spectra and local similarity scaling in a strongly stratified oceanic bottom boundary layer

In the turbulence inertial subrange, wavenumber spectra of vertical velocity and streamwise velocity in a strongly stratified oceanic bottom boundary layer agree with the local similarity scaling laws found previously in the stable atmospheric boundary layer. At scales greater than the turbulence inertial subrange, oceanic velocity spectra exceed the universal spectra. This additional energy at large scales could be due either to internal waves, inappropriate estimates of turbulence parameters, or non-stationarity of the data. Providing that the energy containing eddies in the stratified boundary layer have a scale close to the Ozmidov scale, ε 1/2 N −3/2, where ε is the turbulence kinetic energy dissipation rate and N is the buoyancy frequency, the universal model spectrum leads to a turbulent scaling ε= βNσ w 2, where β is a dimensionless constant 0.6–1.5 and σ w 2 is the vertical velocity variance. This scaling law of ε has been found in free shear flows in the ocean and atmosphere. The turbulence Reynolds stress is related to the vertical velocity variance as −〈 u′ w′〉=1/4 σ w 2. The strong stratification in the observed tidal bottom boundary layer is maintained by the advective density gradient. Results reported here include the effects of horizontal advection.

Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow.

Spectra of the streamwise velocity component in fully developed turbulent pipe flow are presented for Reynolds numbers up to 5.7x10(6). Even at the highest Reynolds number, streamwise velocity spectra exhibit incomplete similarity only: while spectra collapse with both classical inner and outer scaling for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete, and a region varying with the inverse of the streamwise wave number, k(1), is not expected, and any apparent k(-1)(1) range does not attract any special significance and does not involve a universal constant. Reasons for this are suggested.

Spectral characteristics of velocity and vorticity fluxes in an unstratified turbulent boundary layer

Wavenumber spectral characteristics of the velocity and vorticity fluxes in an unstratified turbulent boundary layer are presented. The observed vertical and streamwise velocity spectra agree with empirical forms found in the atmospheric boundary layer. Spectral ratios of 4/3 between the vertical and streamwise velocity spectra and the agreement between the observed vorticity flux quad spectrum and that of isotropic turbulence suggest local isotropy at scales smaller than Z. The normalized cospectrum of the momentum flux agrees remarkably well with the empirical form found in the atmospheric boundary layer. In the inertial subrange the momentum flux cospectrum shows a clear spectral slope of −7/3. The observed composite vorticity flux cospectrum has most of its variance at the streamwise wavenumber kx = (1–10) Z−1 and has a spectral slope of −7/3 in the inertial subrange. The −7/3 spectral slope is consistent with a dimensional argument, assuming that the vorticity flux cospectrum is proportional to the gradient of the mean vorticity, and depends on the turbulence kinetic energy dissipation rate ϵ and the wavenumber. A model turbulent vorticity flux cospectrum is constructed based on the shape of observed spectra, a −7/3 spectral slope in the inertial subrange, and the similarity scaling of the vorticity flux in an unstratified turbulent boundary layer. The turbulence vorticity flux is directly related to the divergence of turbulence momentum flux, the force exerted by turbulence on the mean flow. Therefore our proposed empirical cospectral form of the vorticity fluxes might be useful for turbulence parameterization in numerical models.

Numerical Simulation of 3D Flow around a Circular Cylinder. 1st Report. Analysis of Time and Space Correlation.

Three dimensional flow field around a circular cylinder was analyzed by using a third-order upwind finite-difference method for Reynolds number=1000. Lift and drag force spectrum have some peaks near main karman frequency. It was also found that streamwise velocity and pressure spectrum around separation point have some peaks with a difference mode of these peaks (beat mode). Spanwise flow structure is formed by such modes that have nearly half frequency of Karman mode (half mode) and which are created by three-dimensional vortices. In the present analysis, three dimensional vortices induce half modes and a beat mode additional to Karman mode, resulting in the observation of complex three dimensional flow field.

Investigation of turbulent flows via pseudo flow visualization part II: Lobed mixer

Multipoint, single-component hot-wire anemometer measurements obtained with a rake of probes downstream of a lobed mixer are examined using a pseudo flow visualization (PFV) technique. PFV is a visualization procedure that manipulates data obtained from an array of probes to create a graphical representation of the instantaneous velocity components of a flow field. The indicator function was employed to identify the frequency content of each velocity-time trace, giving insight into the analysis of the visualizations. From this application, shedding frequencies of the large-scale structures were identified to range from 200–700 Hz, averaging around 550 Hz. In general, these results are comparable with streamwise velocity spectra obtained from the same flow field locations. Mean streamwise velocity and turbulence intensity profiles reveal that the turbulence intensity increases substantially at the expense of the mean shear, targeting the region of increased mixing to occur between z l a = 3.9 and 5.2 downstream of the trailing edge of the mixer. The ruffle-shaped shear layer is further warped by the secondary velocities in the region where the mean momentum flow emanates from the lobe troughs. This evolution of the shear layer continues until it collapses onto itself, resulting in a burst of turbulent energy that paves the path for turbulence-dominated mixing. The validity of these techniques was successfully verified in the more familiar and fundamental flow field of the near-field axisymmetric jet mixing layer, as described in Part I of this investigation, before they were applied to the flow field downstream of the lobed mixer.

Linear and nonlinear evolution of boundary layer instabilities generated by acoustic-receptivity mechanisms

Experimental results are presented concerning the evolution of instabilities generated by the interaction between low-level broad-band acoustic waves and small two-dimensional roughness elements. Streamwise perturbation velocity spectra are measured and it is found that on the smooth plate, naturally-occurring Tollmien-Schlicting (T-S) waves grow in a manner consistent with a resonant subharmonic wave interaction. However, in the presence of small two-dimensional roughness elements, a strong primary T-S mode is forced by an interaction with the background acoustic field. This leads to a K-type of nonlinear interaction characterized by the generation of harmonics (up to six harmonics are observed) at the expense of the subharmonic. The scaling of the T-S waves and their harmonics with the number and amplitude of the wall roughness is also considered.