Streak Mode Research Articles

Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$ , and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.

Large-scale streaks in a turbulent bluff body wake

A turbulent circular disk wake database (Chongsiripinyo & Sarkar, J. Fluid Mech., vol. 885, 2020) at Reynolds number $Re = U_\infty D/\nu = 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks – coherent elongated regions of streamwise velocity. The unprecedented streamwise length – until $x/D \approx 120$ – of the simulation enables investigation of the near and far wakes. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $St = 0.135$ . After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $St \rightarrow 0$ , equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$ . Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweeps to events of intense $-u'_xu'_r$ . Spectral proper orthogonal decomposition is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition is conducted to reveal strong interaction between $m=1$ and $St = \pm 0.135$ modes to give the $m=2$ , $St \rightarrow 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2$ , $St \rightarrow 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors’ knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

Effect of cone rotation on the nonlinear evolution of Mack modes in supersonic boundary layers

In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$ , three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$ , which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$ . Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.

Heat transfer and behavior of the Reynolds stress in Mach 6 boundary layer transition induced by first-mode oblique waves

This paper investigates a Mach 6 oblique breakdown via direct numerical simulation in conjunction with stability and quadrant analyses. Particular emphasis is placed on, first, the heat transfer and mean flow distortion in the near-wall and outer transitional boundary layer, and, second, the flow events that are responsible for the production of the Reynolds stress. The energy budget reveals that enhancement of viscous dissipation due to mean flow distortion dominates the heat transfer overshoot, while the dissipation due to fluctuations is lesser but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (non-dimensionalized by the freestream temperature and local boundary layer thickness) varies little, owing to the occurrence of breakdown and the establishment of self-similarity. Renormalized by the boundary layer thickness, a new correlation of the Stanton number shows no overshoot or difference between the original overshoot region and the turbulent region, which indicates the possibility of similarity once breakdown has occurred. In the outer region, enhanced advective heat exchange strongly reshapes the mean temperature profile. Because of successive modal growth and nonlinear saturation, the contributions of the primary oblique mode, streak mode, and a superharmonic to the outer advective heat transfer are found to compete near the location of the peak heat flux. From the perspective of fluid motions, quadrant analysis highlights the evenly and broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress, while the PDF is concentrated around zero in the turbulent region. The flow event Q2 (ejection) overtakes Q4 (sweep) in the outer boundary layer of the transitional region, mainly owing to the primary mode, while the two events become attenuated and nearly achieve balance when transition is complete.

Revisit of the oblique-breakdown regime in supersonic boundary layers and mechanism of the extra amplification of streak modes

In the low-Mach-number supersonic boundary layers, the oblique-breakdown regime may be the most efficient route to trigger the laminar–turbulent transition, because the most unstable Mack first mode always appears as an oblique wave. In this paper, we revisit this issue by use of the nonlinear parabolized stability equation (NPSE) approach and particularly focus on the extra amplification of the streak mode generated by the direct interaction of the introduced oblique modes. This mechanism is then well explained based on the weakly nonlinear analysis, and its predictions on the evolution of the streak mode and the two-dimensional traveling-wave mode are quantitatively confirmed by the NPSE calculations. Additionally, the important role of the streak mode, leading to the secondary instability, on triggering the transition onset is identified.

Transition induced by wall-normal vibration in flow around a flat plate with roughness

The effects of wall-normal vibration on bypass transition in a boundary-layer flow over a flat plate with roughness elements in the form of circular cylinders are investigated using direct numerical simulations (DNS), linear Floquet analyses and dynamic mode decompositions (DMD). The vibration of the plate strengthens the streamwise vorticity, consequently enhancing the velocity streaks and reducing the critical Reynolds number for transition. A map is constructed to identify the coupling effect of the vibration amplitude and Reynolds number on transition. Among all investigated combinations of height and diameter of roughness, the critical Reynolds numbers at different vibration amplitude $A$ can be unified by a scaling function of $(1-10A)$ . Two instability modes are identified in the vibration-induced transition process: a wake mode immediately downstream of the roughness, related to the inviscid Kelvin–Helmholtz instability of the wall-normal shear in the wake; and a streak mode, in response to the spanwise shear of the streaky flow, occurring further downstream. The first one results in the generation of central hairpin vortices which then feed the second one. Further development of the streak instability leads to two arrays of hairpin vortices. Results from linear Floquet analyses and DMD further confirm the two modes of instability observed in DNS. A quantitative study suggests that the amplification of vibration-induced disturbance by the base shear dominates the production of streamwise vorticity and subsequently the hairpin vortices.

Drag reduction and transient growth of a streak in a spanwise wall-oscillatory turbulent channel flow

The drag-reduction mechanism of spanwise wall oscillation in a turbulent channel was investigated as an extension of the work of Yakeno et al. [“Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation,” Phys. Fluids 26, 085109 (2014)] at a low Reynolds number. Flow instability was evaluated by computing the transient energy growth under an oscillating base flow which governed the generation of a near-wall streak structure. Oscillation affected the optimal energy growth of the streak mode, whose characteristics were reasonably consistent with those in a direct numerical simulation. The optimal growth of the tilted-streak mode was enhanced with a thicker Stokes layer under longer oscillation periods, while that of the original streak mode was weakened. The transition of the optimal perturbation under oscillation showed that the spanwise Stokes layer shear contributed considerably more to modification than the spanwise velocity did. A new drag-reduction performance estimation model was suggested using the acceleration of the spanwise velocity shear based on streak formation modification under oscillation, which restrains energy transfer to streamwise vortices via a tilting delay due to oscillation. This simple model worked well even under long oscillation periods and was theoretically consistent with that of Yakeno et al. based on the change in the Reynolds shear stress due to a streamwise vortex at a low Reynolds number.

Control of oblique-type breakdown in a supersonic boundary layer employing streaks

The effectiveness of streak modes in controlling the oblique-type breakdown in a supersonic boundary-layer at Mach 2.0 is investigated using direct numerical simulations. Investigations in the literature have shown the effectiveness of streak modes in delaying the onset of transition dominated by two-dimensional waves, but in oblique breakdown, three-dimensional waves and a strong streak mode dominate the transition process. Paredes et al. (J. Fluid Mech., vol. 831, 2017, pp. 524–553) discussed the possible stabilization of supersonic boundary layers by optimally growing streaks using parabolized stability equations. However, no study has as yet been reported regarding direct nonlinear control of oblique breakdown. This study deals with the effects of large-amplitude decaying streak modes generated by a blowing–suction strip at the wall to control full breakdown in a reference case. Modes with four to five times the fundamental wavenumber are found to be beneficial for controlling the transition. In the first region after the control-mode forcing, the beneficial mean-flow distortion (MFD), generated by inducing the control mode, is solely responsible for hampering the growth of the fundamental-mode. On the whole, the MFD and the three-dimensional part of the control contribute equally towards controlling the oblique breakdown. The results show significant suppression of transition, and substantial improvements have been observed in the levels of the skin-friction coefficient and wall-temperature in comparison to the uncontrolled case. Moreover, refreshing the control using an additional downstream control strip increases the gain. However, the forcing amplitude must be carefully chosen in order not to introduce a generalized inflection point in the spanwise averaged mean flow invoking enhanced disturbance growth.

A computational streak mode cytometry biosensor for rare cell analysis.

Streak mode imaging flow cytometry for rare cell detection involves imaging moving fluorescently labeled cells in the video mode with a CCD camera. The path of the moving cells results in a "streak", whose length is proportional to the exposure time. The dynamic imaging conditions introduce detection challenges (e.g., images with high signal-to-noise ratio (SNR) backgrounds), especially for enumerating cells using low resolution webcams or smartphone cameras suitable for point of care testing (POCT). To overcome the imaging challenges, a new approach called a "computational biosensor" was developed. It involves combining biosensing hardware with computational algorithms to "computationally transduce" measureable signals from events captured by the hardware. The computational biosensor quantifies potential cells based on the streak intensity, length and relative location of the streaks in consecutive frames. Cell identification consists of three parts: (1) finding streaks, (2) identifying candidate cells, and (3) filtering out spurious cells to identify true cells. Samples of 1 cell per mL were analyzed in batch sizes of 30 mL at flow rates of 10 mL min-1 and imaged at 4 frames per second (fps). The detected cells were annotated, and the SNR was calculated. For images with SNR greater than 4.4 dB, the total detected cells (TD) compared with ground truth (GT) are 98%, while 66% were detected for low SNR. For true positive cells detected compared with ground truth (TP/GT), 91% were detected for high SNR. This demonstrated the new analytical capabilities of the computational biosensor to enumerate rare cells in large volumes not possible with current technologies.

Evaluation of a Methodology for Automated Cell Counting for Streak Mode Imaging Flow Cytometry

Identification of Circulating Tumor Cells (CTCs) has shown promising clinical applications, but since CTCs are found in very low concentration in blood large sample volumes are needed for meaningful enumeration. This issue impedes the analysis of CTCs using standard flow cytometry due to its low throughput. To address this issue, a high throughput microfluidic cytometer was recently developed using a wide field flow- flow cell instead of the conventional narrow hydrodynamic focusing cells (used in traditional flow cytometry) enabling analysis of large volumes at lower flow rate. This wide-field flow cytometer adopts a technique known as “streak photography” where exposure times and flow velocities are set such that the particles are imaged as short “streaks”. Since streaks are imaged with large number of pixels, they are easily distinguished from the noise which appears as “speckles” increasing the detection capabilities of the device, making it more suitable for analysis using current low sensitivity, high noise webcams or mobile phone cameras. The non-stationary nature of the high noisy background found in streak cytometry introduces additional challenges for automated cell counting methods using traditional cell detection techniques such TLC, CellProfiler, CellTracker and other tools based in traditional edge detection (e.g., Canny based filters) or manual thresholding. In order to address this issue, we developed a new automated enumeration approach that does not rely on edge detection or manual thresholding of individual cells, rather is based in image quantizing, morphological operations, 2D order-statistic filtering and decisions rules that take into account knowledge of the structure and expected location of the streaks in consecutive frames. We evaluated our approach comparing it with two current methods representing the major computational modalities for cell detection: CellTrack (based in edge detection) and MTrack2 (based in manual thresholding). Samples of 1 cell/mL nominal concentration were analyzed in batch size of 30 mL at flow rate of 10 mL/min and imaged at 4 frames per second (fps), the files were saved in uncompressed AVI format files. The cells were annotated and the signal to noise ratio (SNR) was calculated. For samples with average SNR greater than 4.4 dB, our method achieved a sensitivity of 91% compared to CellTrack (60%) and MTrack2 (71%). The True Positive Rate (TPR) of cells detected was 0.93 for our method compared with 0.80 for Mtrack2 and 0.29 for CellTrack. This demonstrated the ability of the algorithm to count rare cells with high accuracy for concentrations of 1 cell/mL with SNR greater than 4.4 dB. This cell counting capability will enable to automate low cost imaging flow cytometry based on CCD detector and the expansion of cell-based clinical diagnostics in resource-poor settings.

Deaccelerating films for picosecond new generation dissectors

This paper describes the selection of deaccelerating films made of aluminum of various thicknesses (300–500 nm) and intended for deacceleration of electrons (with an energy of tens of kiloelectron volts to tens of electron volts) in the developed new generation picosecond dissectors. The designed dissectors should be different by a higher temporal resolution as compared to the maximum reached (~20 ps) in LI-602 dissecting image-tube converters used for diagnosing synchrotron radiation. This paper also presents the results of comparative measurements of emission characteristics of manufactured films in the models of image-tube converters similar in design to a PIF-01/S1 device, which is the basis of the developed dissectors and which provides the maximum temporal resolution of up to 1 ps in the streak mode with the streak speed of ~1010 cm/s. It is established that, when the energy of the incident electron beam equals 10 to 12 keV, the optimum thickness of the deaccelerating aluminum film is 400 nm with the effective secondary emission coefficient equal to 0.7.

Automation Highlights from the Literature

Automation Highlights from the Literature

Cell streak imaging cytometry for rare cell detection

Detection of rare cells, such as circulating tumor cells, have many clinical applications. To measure rare cells with increased sensitivity and improved data managements, we developed an imaging flow cytometer with a streak imaging mode capability. The new streak mode imaging mode utilizes low speed video to capture moving fluorescently labeled cells in a flow cell. Each moving cell is imaged on multiple pixels on each frame, where the cell path is marked as a streak line proportional to the length of the exposure. Finding rare cells (e.g., <1 cell/mL) requires measuring larger sample volumes to achieve higher sensitivity, therefore we combined streak mode imaging with a “wide” high throughput flow cell (e.g. flow rates set to 10mL/min) in contrast to the conventional “narrow” hydrodynamic focusing cells typically used in cytometry that are inherently limited to low flow rates. The new flow cell is capable of analyzing 20mL/min of fluorescently labeled cells. To further increase sensitivity, the signal to noise ratio of the images was also enhanced by combining three imaging methods: (1) background subtraction, (2) pixel binning, and (3) CMOS color channel selection.The streaking mode cytometer has been used for the analysis of SYTO-9 labeled THP-1 human monocytes in buffer and in blood. Samples of cells at 1 cell/mL and 0.1 cell/mL were analyzed in 30mL with flow rates set to 10mL/min and frame rates of 4fps (frame per second). For the target of 1 cell/mL, an average concentration of 0.91 cell/mL was measured by cytometry, with a standard error of 0.03 (C95=0.85–0.97). For the target of 0.1 cell/mL, an average concentration of 0.083 cell/mL was measured, with a standard error of 0.01 (C95=0.065–0.102). Whole blood was also spiked with SYTO-9 labeled cells to a concentration of 10 cell/mL, and the average flow cytometry measurement was 8.7 cells/mL (i.e. 0.87 cells/mL in diluted blood) with a 95% CL of 8.1–9.2 cells/mL. This demonstrated the ability to detect rare cells in blood with high accuracy. Such detection approaches for rare cells have many potential clinical applications. Furthermore, the simplicity and low cost of this device may enable expansion of cell-based clinical diagnostics, especially in resource-poor settings.

Megahertz streak-mode Fourier domain optical coherence tomography

Here we present an ultrahigh-speed Fourier-domain optical coherence tomography (OCT) that records the OCT spectrum in streak mode with a high-speed area scan camera, which allows higher OCT imaging speed than can be achieved with a line-scan camera. Unlike parallel OCT techniques that also use area scan cameras, the conventional single-mode fiber-based point-scanning mechanism is retained to provide a confocal gate that rejects multiply scattered photons from the sample. When using a 1000 Hz resonant scanner as the streak scanner, 1,016,000 A-scans have been obtained in 1 s. This method's effectiveness has been demonstrated by recording in vivo OCT-image sequences of embryonic chick hearts at 1000 frames/s. In addition, 2-megahertz OCT data have been obtained with another high speed camera.

Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica

The dynamics of absorption after excitation of fused silica and BK7 glass with femtosecond laser radiation are visualized by transient absorption spectroscopy. Focusing laser radiation with pulse durations in the picosecond time regime in BK7 glass generates free electrons with relaxation by emission of radiation or by formation of defects. The temporal and spatial emission characteristics are observed by high-speed photography in the streak mode. The beam waist moves within the pulse duration towards the incoming laser radiation by self-focusing and with the laser radiation absorbed by multi-photon processes. The dynamics of the long lasting stress formation is visualized by time-resolved Nomarski-Photography. The modification of the glass is investigated during and after irradiation with ultra-short pulsed laser radiation (100 fs<tp<3 ps) at the wavelength λ=810 nm. The formation of a sound wave in fused silica and BK7 glass is observed and the mechanical stress, depending on the excitation pulse duration, is measured.

Spectroscopic Investigation of Z-Pinch with a Spatial and Temporal Resolution

Soft X-rays generated by a plasma focus device with an Ar gas puff are studied using a composite system which consists of an imaging Bragg spectrometer and a soft X-ray high speed imaging system. Two modes of soft X-ray emitting sources in Z-pinch plasma, filamentary and scattered spots, are generated in this experiment depending on the delay time from the gas puff to the main discharge. Spectroscopic observation revealed that even the case of the filamentary mode is not really filamentary but is actually X-ray emitting spots (hot spots) densely arranged in a column along the electrode axis. By using the soft X-ray high speed imaging system, the streak mode display is restructured from the data obtained in a single shot, Temporally resolved observations in streak mode showed that a spot appeared at a point near the electrode face first, then different hot spots appeared successively along the axis and in a direction away from the electrode face. It is clarified that the hot spot is a small region from which intense H-like and He-like spectral lines are emitted. The size and the distance between spots are from 0.1 to 0.5 mm in radius and similar to 0.5 mm in length, respectively. The lifetime of the spots is 5 similar to 10 ns. The average electron temperature and density calculated from the intensity ratio of those spectral lines are similar to 1.8 keV and 1.7 x 10(22) /cm(3), respectively. They did not show a notable change along the axis.

Spectroscopic Study of Soft X-Ray Sources Generated in a Plasma Focus with Neon Gas Puffing

Soft X-ray emitting spots (hot spots) generated in a plasma focus with a gas puffing are investigated using a streak mode imaging system for the soft X-ray region and a convex Bragg spectrometer wh...

500-fs photoelectron gun for time-resolved electron diffraction experiments

A photoelectron gun as a source of a photoinduced, monoen- ergetic (energy spread ,0.5 eV), well-collimated (divergence ,0.5 deg), sharp (diameter ,0.7 mm at the 1/e level), and ultrashort (<500 fs) bunch of electrons to be used for time-resolved electron diffraction (TRED) experiments is computer designed, assembled, and tested. In single-shot mode, it generates up to 10 3 of 30 keV electrons, and the electron pulse can be either measured in streak mode or focused onto a solid state target chosen from a set of interchangeable targets. High temporal resolution enables measurement with femtosecond precision of the diffraction pattern perturbation after the exiting laser radiation drops onto a target. Demonstration experiments with a 300-A A1 target in transmission-type mode result in diffraction images of reasonable quality under accumulation of up to 4310 4 500-fs photoelectron pulses. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)00508-X)

Initial dual-sweep streak camera measurements on the Duke storage ring OK-4 UV/visible FEL

Initial measurements at the Duke storage ring free electron laser (FEL) of both spontaneous emission radiation (SER) from the OK-4 and FEL radiation outcoupled from the oscillator cavity have been done with a dual-sweep streak camera. In the SER case, ANL's Hamamatsu C5680 streak camera was used to characterize stored electron-beam bunch lengths versus rf gap voltage and single-bunch current. Electron-beam bunch lengths were observed in a range from 50 to 300 ps (FWHM). Particle beam energies of 270 and 500 MeV in the storage ring (SR) were used with the OK-4 to generate SER from 500 nm to less than 200 nm. Sensitivity to single-bunch, single-turn SER was shown down to ∼4 μA beam current at λ=450 nm. By operating in the synchroscan mode and at bunch currents less than 1 mA, beam orbit length vs. the resonator round-trip time was investigated by detecting the relative arrival time of the second pass outcoupled from the resonator at λ≈200 nm. These measurements were used in support of first lasing in the UV-visible regime in November 1996. The dual-sweep streak mode was then used to monitor lasing intensity variations on the 1 and 50 ms time scales, to measure a lasing pulse length as short as ∼3 ps ( σ) at λ=388 nm at low beam current, and to track the orbit length detuning curve.

An image converting system in framing and streak mode for impulsive soft x-ray observation

A high-speed image converting system is described. The system is capable of display both in multiframing- and streak-mode image for a pulsed x-ray source. The system relies on a new concept without employing an image converter tube. To achieve both temporally and spatially resolved display, the image of the x-ray source is acquired with a pinhole camera and with multichannel arrayed scintillator–photomultiplier combinations, which are used complementarily. The temporal resolution is 3 ns. This system is successfully used to observe the time evolution of soft x-ray emissions around 4 Å in plasma focus discharges with puffed Ar.