Amplitude and frequency modulation of the small scales in a jet

2015 ◽  
Vol 772 ◽  
pp. 756-783 ◽  
Author(s):  
D. Fiscaletti ◽  
B. Ganapathisubramani ◽  
G. E. Elsinga
Keyword(s):  
Amplitude Modulation ◽  
Frequency Modulation ◽  
High Speed ◽  
Large Scale ◽  
Spectral Band ◽  
Physical Space ◽  
Small Scale ◽  
Length Scale ◽  
Air Jet ◽  
Amplitude And Frequency Modulation

The present study is an experimental investigation of the relationship between the large- and small-scale motions in the far field of an air jet at high Reynolds number. In the first part of our investigation, the analysis is based on time series of hot-wire anemometry (HWA), which are converted into space series after applying the Taylor hypothesis. By using a spectral filter, two signals are constructed, one representative of the large-scale motions ($2{\it\lambda}_{T}-L$, where ${\it\lambda}_{T}$ is the Taylor length scale, and $L$ is the integral length scale) and the other representative of the small-scale motions ($1.5{-}5{\it\eta}$, where ${\it\eta}$ is the Kolmogorov length scale). The small-scale signal is found to be modulated both in amplitude and in frequency by the energy-containing scales in an analogous way, both at the centreline and around the centreline. In particular, for positive fluctuations of the large-scale signal, the small-scale signal is locally stronger in amplitude (amplitude modulation), and it locally exhibits a higher number of local maxima and minima (frequency modulation). The extent of this modulation is quantified based on the strength of the large-scale fluctuations. The response of the small-scale motions to amplitude modulation can be considered instantaneous, being on the order of one Kolmogorov time scale. In the second part of our investigation we use long-range ${\it\mu}$PIV to study the behaviour of the small-scale motions in relation to their position in either high-speed or low-speed regions of the flow. The spatially resolved velocity vector fields allow us to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25 % of the value measured from HWA. The remaining 75 % comes from the fixed spectral band filter used to obtain the large- and small-scale signals, which does not consider the local convection velocity. A very similar overestimation of amplitude modulation when quantified in the time-frame is also obtained analytically. Furthermore, the size of the structures of intense vorticity does not change significantly in relation to the large-scale velocity fluctuation, meaning that there is no significant spatial frequency modulation. The remaining amplitude modulation in space can be explained as a statistical coupling between the strength of the structures of vorticity and their preferential location inside large-scale high-velocity regions. Finally, the implications that the present findings have on amplitude and frequency modulation in turbulent boundary layers (TBLs) are discussed.

Amplitude and frequency modulation in wall turbulence

2012 ◽  
Vol 712 ◽  
pp. 61-91 ◽  
Author(s):  
B. Ganapathisubramani ◽  
N. Hutchins ◽  
J. P. Monty ◽  
D. Chung ◽  
I. Marusic
Keyword(s):  
Amplitude Modulation ◽  
Frequency Modulation ◽  
Large Scale ◽  
Small Scale ◽  
Wall Region ◽  
Phase Lag ◽  
Amplitude And Frequency Modulation ◽  
The Impact ◽  
Conditional Spectra ◽  
Near Wall

AbstractIn this study we examine the impact of the strength of the large-scale motions on the amplitude and frequency of the small scales in high-Reynolds-number turbulent boundary layers. Time series of hot-wire data are decomposed into large- and small-scale components, and the impact of the large scale on the amplitude and frequency of the small scales is considered. The amplitude modulation effect is examined by conditionally averaging the small-scale intensity (${ u}_{S}^{2} $) for various values of the large-scale fluctuation (${u}_{L} $). It is shown that ${ u}_{S}^{2} $ increases with increasing value of ${u}_{L} $ in the near-wall region, whereas, farther away from the wall, ${ u}_{S}^{2} $ decreases with increasing ${u}_{L} $. The rate of increase in small-scale intensity with the strength of the large-scale signal is neither symmetric (about ${u}_{L} = 0$) nor linear. The extent of the frequency modulation is examined by counting the number of occurrences of local maxima or minima in the small-scale signal. It is shown that the frequency modulation effect is confined to the near-wall region and its extent diminishes rapidly beyond ${y}^{+ } = 100$. A phase lag between the large- and small-scale fluctuations, in terms of amplitude modulation, has also been identified, which is in agreement with previous studies. The phase lag between large- and small-scale fluctuations for frequency modulation is comparable to that of amplitude modulation in the near-wall region. The combined effect of both amplitude and frequency modulation is also examined by computing conditional spectra of the small-scale signal conditioned on the large scales. In the near-wall region, the results indicate that the peak value of pre-multiplied spectra increases with increasing value of ${u}_{L} $, indicating amplitude modulation, while the frequency at which this peak occurs also increases with increasing value of ${u}_{L} $, revealing frequency modulation. The overall trends observed from the conditional spectra are consistent with the results obtained through statistical analyses. Finally, a physical mechanism that can capture most of the above observations is also presented.

Scale interactions in a mixing layer – the role of the large-scale gradients

2016 ◽  
Vol 791 ◽  
pp. 154-173 ◽  
Author(s):  
D. Fiscaletti ◽  
A. Attili ◽  
F. Bisetti ◽  
G. E. Elsinga
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Mixing Layer ◽  
Physical Space ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Small Scales ◽  
Low Pass ◽  
Scale Characteristics

The interaction between the large and the small scales of turbulence is investigated in a mixing layer, at a Reynolds number based on the Taylor microscale ($Re_{{\it\lambda}}$) of $250$, via direct numerical simulations. The analysis is performed in physical space, and the local vorticity root-mean-square (r.m.s.) is taken as a measure of the small-scale activity. It is found that positive large-scale velocity fluctuations correspond to large vorticity r.m.s. on the low-speed side of the mixing layer, whereas, they correspond to low vorticity r.m.s. on the high-speed side. The relationship between large and small scales thus depends on position if the vorticity r.m.s. is correlated with the large-scale velocity fluctuations. On the contrary, the correlation coefficient is nearly constant throughout the mixing layer and close to unity if the vorticity r.m.s. is correlated with the large-scale velocity gradients. Therefore, the small-scale activity appears closely related to large-scale gradients, while the correlation between the small-scale activity and the large-scale velocity fluctuations is shown to reflect a property of the large scales. Furthermore, the vorticity from unfiltered (small scales) and from low pass filtered (large scales) velocity fields tend to be aligned when examined within vortical tubes. These results provide evidence for the so-called ‘scale invariance’ (Meneveau & Katz, Annu. Rev. Fluid Mech., vol. 32, 2000, pp. 1–32), and suggest that some of the large-scale characteristics are not lost at the small scales, at least at the Reynolds number achieved in the present simulation.

scholarly journals Suppression of amplitude modulation induced by polarization mode dispersion using a multi-degree-of-freedom fiber filter

2018 ◽  
Vol 6 ◽  
Author(s):  
Rao Li ◽  
Youen Jiang ◽  
Zhi Qiao ◽  
Canhong Huang ◽  
Wei Fan ◽  
...  
Keyword(s):  
High Power ◽  
Amplitude Modulation ◽  
Transmission Spectrum ◽  
High Speed ◽  
Large Scale ◽  
Modulation Depth ◽  
Free Spectral Range ◽  
Polarization Mode Dispersion ◽  
Polarization Mode ◽  
Mode Dispersion

Polarization mode dispersion (PMD) in fibers for high-power lasers can induce significant frequency modulation to amplitude modulation (FM-to-AM) conversion. However, existing techniques are not sufficiently flexible to achieve efficient compensation for such FM-to-AM conversion. By analyzing the nonuniform transmission spectrum caused by PMD, we found that the large-scale envelope of the transmission spectrum has more serious impacts on the amount of AM. In order to suppress the PMD-induced FM-to-AM conversion, we propose a novel tunable spectral filter with multiple degrees of freedom based on a half-wave plate, a nematic liquid crystal, and an axis-rotated polarization-maintaining fiber. Peak wavelength, free spectral range (FSR), and modulation depth of the filter are decoupled and can be controlled independently, which is verified through both simulations and experiments. The filter is utilized to compensate for the PMD-induced FM-to-AM conversion in the front end of a high-power laser facility. The results indicate that, for a pulse with phase-modulation frequency of 22.82 GHz, the FM-to-AM conversion could be reduced from 18% to 3.2% within a short time and maintained below 6.5% for 3 h. The proposed filter is also promising for other applications that require flexible spectral control such as high-speed channel selection in optical communication networks.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

High-Speed Noncontact Profiling of Pavement Surface Texture and Its Significance

1986 ◽  
Vol 108 (3) ◽  
pp. 455-461
Author(s):  
J. C. Wambold ◽  
J. J. Henry
Keyword(s):  
Surface Texture ◽  
High Speed ◽  
Large Scale ◽  
Vision System ◽  
Small Scale ◽  
Skid Resistance ◽  
Texture Measurement ◽  
Pavement Surface ◽  
Texture Characteristics ◽  
Regression Techniques

It is generally agreed that the friction between a tire and a wet pavement (skid resistance) is controlled by the surface texture characteristics. Therefore, by measuring the relevant parameters describing texture, or by measuring a physical process dependent on texture, regression techniques can be used to relate skid resistance to the chosen texture parameter or process. Two scales of texture are of particular importance: microtexture (small-scale asperities) and macrotexture (large-scale asperities). This paper describes work performed to: (1) review candidate macrotexture and microtexture measurement methods that can be made at highway speeds (at or about 64 km/h [40 mph]), which are presently used or have potential for use in pavement texture measurement; (2) design and build a prototype of the most promising method; and (3) evaluate the effects of pavement surface texture on skid resistance. A prototype noncontact vision system that makes texture measurements at highway speeds was developed, and several improvements were made to upgrade the system to provide an improved prototype. Both hardware and software enhancements have yielded a texture measurement system that can obtain pavement macrotexture data in a fast, efficient, and reliable way.

scholarly journals Failure Mechanism of Rock Bridge Based on Acoustic Emission Technique

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Guoqing Chen ◽  
Yan Zhang ◽  
Runqiu Huang ◽  
Fan Guo ◽  
Guofeng Zhang
Keyword(s):  
Acoustic Emission ◽  
Failure Mechanism ◽  
High Speed ◽  
Large Scale ◽  
Small Scale ◽  
Failure Behavior ◽  
Long Distance ◽  
Rock Bridge ◽  
Rocky Slope ◽  
Landslide Model

Acoustic emission (AE) technique is widely used in various fields as a reliable nondestructive examination technology. Two experimental tests were carried out in a rock mechanics laboratory, which include (1) small scale direct shear tests of rock bridge with different lengths and (2) large scale landslide model with locked section. The relationship of AE event count and record time was analyzed during the tests. The AE source location technology and comparative analysis with its actual failure model were done. It can be found that whether it is small scale test or large scale landslide model test, AE technique accurately located the AE source point, which reflected the failure generation and expansion of internal cracks in rock samples. Large scale landslide model with locked section test showed that rock bridge in rocky slope has typical brittle failure behavior. The two tests based on AE technique well revealed the rock failure mechanism in rocky slope and clarified the cause of high speed and long distance sliding of rocky slope.

A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1

1980 ◽  
Vol 98 (1) ◽  
pp. 65-95 ◽  
Author(s):  
M. Sokolov ◽  
A. K. M. F. Hussain ◽  
S. J. Kleis ◽  
Z. D. Husain
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Large Scale ◽  
Mixing Layer ◽  
Streamwise Velocity ◽  
Reynolds Stresses ◽  
Free Shear Layer ◽  
Turbulent Spot ◽  
Air Jet ◽  
Phase Average

A three-dimensional ‘turbulent spot’ has been induced in the axisymmetric free mixing layer of a 12.7 cm diameter air jet by a spark generated at the nozzle boundary layer upstream of the exit. The spot coherent-structure signature, buried in the large-amplitude random fluctuating signal, has been educed at three downstream stations within the apparent self-preserving region of the mixing layer (i.e. x/D = 1.5, 3.0 and 4.5) at the jet exit speed of 20 ms−1. The eduction has been performed through digital phase averaging of the spot signature from 200 realizations. In order to reduce the effect of the turbulence-induced jitter on the phase average, individual filtered signal arrays were optimally time-aligned through an iterative process of cross-correlation of each realization with the ensemble average. Further signal enhancement was achieved through rejection of realizations requiring excessive time shifts for alignment. The number of iterations required and the fraction of realizations rejected progressively increase with the downstream distance and the radial position.The mixing-layer spot is a large-scale elongated structure spanning the entire width of the layer but does not appear to exhibit a self-similar shape. The dynamics of the mixing-layer spot and its eduction are more complicated than those of the boundary-layer spot. The spot initially moves downstream essentially at a uniform speed across the mixing layer, but further downstream it accelerates on the high-speed side and decelerates on the low-speed side. This paper discusses the data acquisition and processing techniques and the results based on the streamwise velocity signals. Phase average distributions of vorticity, pseudo-streamlines, coherent and background Reynolds stresses and further dynamics of the spot are presented in part 2 (Hussain, Kleis & Sokolov 1980).

Unsteady Structure Measurement of Cloud Cavitation on a Foil Section Using Conditional Sampling Technique

1989 ◽  
Vol 111 (2) ◽  
pp. 204-210 ◽  
Author(s):  
A. Kubota ◽  
H. Kato ◽  
H. Yamaguchi ◽  
M. Maeda
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Laser Doppler Anemometry ◽  
Low Frequency ◽  
Sampling Technique ◽  
Experimental Result ◽  
Small Scale ◽  
Conditional Sampling ◽  
Cloud Cavitation ◽  
Structure Of Flow

The structure of flow around unsteady cloud cavitation on a stationary two-dimensional hydrofoil was investigated experimentally using a conditional sampling technique. The unsteady flow velocity around the cloud cavitation was measured by a Laser Doppler Anemometry (LDA) and matched with the unsteady cavitation appearance photographed by a high-speed camera. This matching procedure was performed using data from pressure fluctuation measurements on the foil surface. The velocities were divided into two components using a digital filter, i.e., large-scale (low-frequency) and small-scale (high frequency) ones. The large-scale component corresponds with the large-scale unsteady cloud cavitation motion. In this manner, the unsteady structure of the cloud cavitation was successfully measured. The experimental result showed that the cloud cavitation observed at the present experiment had a vorticity extremum at its center and a cluster containing many small cavitation bubbles. The convection velocity of the cavitation cloud was much lower than the uniform velocity. The small-scale velocity fluctuation was not distributed uniformly in the cavitation cloud, but was concentrated near its boundary.

scholarly journals Optimization Problem of Pricing and Seat Allocation Based on Bilevel Multifollower Programming in High-Speed Railway

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Lianbo Deng ◽  
Jing Xu ◽  
Ningxin Zeng ◽  
Xinlei Hu
Keyword(s):  
Optimization Model ◽  
Dynamic Pricing ◽  
High Speed ◽  
Large Scale ◽  
Solution Method ◽  
Programming Model ◽  
Divide And Conquer ◽  
Small Scale ◽  
High Speed Railway ◽  
Seat Allocation

This paper studies the multistage pricing and seat allocation problems for multiple train services in a high-speed railway (HSR) with multiple origins and destinations (ODs). Taking the maximum total revenue of all trains as the objective function, a joint optimization model of multistage pricing and seat allocation is established. The actual operation constraints, including train seat capacity constraints, price time constraints in each period, and price space constraints among products, are fully considered. We reformulate the optimization model as a bilevel multifollower programming model in which the upper-level model solves the seat allocation problem for all trains serving multiple ODs in the whole booking horizon and the lower optimizes the pricing decisions for each train serving each OD in different decision periods. The upper and lower are a large-scale static seat allocation programming and many small-scale multistage dynamic pricing programming which can be solved independently, respectively. The solving difficulty can be significantly reduced by decomposing. Then, we design an effective solution method based on divide-and-conquer strategy. A real instance of the China’s Wuhan-Guangzhou high-speed railway is employed to validate the advantages of the proposed model and the solution method.

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