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At least 1,261 records · Page 70
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NASA NTRS2002

Radial Field Piezoelectric Diaphragms

A series of active piezoelectric diaphragms were fabricated and patterned with several geometrically defined Inter-Circulating Electrodes "ICE" and Interdigitated Ring Electrodes "ICE". When a voltage potential is applied to the electrodes, the result is a radially distributed electric field that mechanically strains the piezoceramic along the Z-axis (perpendicular to the applied electric field). Unlike other piezoelectric bender actuators, these Radial Field Diaphragms (RFDs) strain concentrically yet afford high displacements (several times that of the equivalent Unimorph) while maintaining a constant circumference. One of the more intriguing aspects is that the radial strain field reverses itself along the radius of the RFD while the tangential strain remains relatively constant. The result is a Z-deflection that has a conical profile. This paper covers the fabrication and characterization of the 5 cm. (2 in.) diaphragms as a function of poling field strength, ceramic thickness, electrode type and line spacing, as well as the surface topography, the resulting strain field and displacement as a function of applied voltage at low frequencies. The unique features of these RFDs include the ability to be clamped about their perimeter with little or no change in displacement, the environmentally insulated packaging, and a highly repeatable fabrication process that uses commodity materials.

Bryant, R. G.↗
NASA NTRS2004

Assessing Videogrammetry for Static Aeroelastic Testing of a Wind-Tunnel Model

The Videogrammetric Model Deformation (VMD) technique, developed at NASA Langley Research Center, was recently used to measure displacements and local surface angle changes on a static aeroelastic wind-tunnel model. The results were assessed for consistency, accuracy and usefulness. Vertical displacement measurements and surface angular deflections (derived from vertical displacements) taken at no-wind/no-load conditions were analyzed. For accuracy assessment, angular measurements were compared to those from a highly accurate accelerometer. Shewhart's Variables Control Charts were used in the assessment of consistency and uncertainty. Some bad data points were discovered, and it is shown that the measurement results at certain targets were more consistent than at other targets. Physical explanations for this lack of consistency have not been determined. However, overall the measurements were sufficiently accurate to be very useful in monitoring wind-tunnel model aeroelastic deformation and determining flexible stability and control derivatives. After a structural model component failed during a highly loaded condition, analysis of VMD data clearly indicated progressive structural deterioration as the wind-tunnel condition where failure occurred was approached. As a result, subsequent testing successfully incorporated near- real-time monitoring of VMD data in order to ensure structural integrity. The potential for higher levels of consistency and accuracy through the use of statistical quality control practices are discussed and recommended for future applications.

Spain, Charles V.↗
NASA NTRS2004

Characterization of Piezoelectric Actuators for Flow Control over a Wing

During the past decade, piezoelectric actuators as the active element in synthetic jets demonstrated that they could significantly enhance the overall lift on an airfoil. However, durability, system weight, size, and power have limited their use outside a laboratory. These problems are not trivial, since piezoelectric actuators are physically brittle and display limited displacement. The objective of this study is to characterize the relevant properties for the design of a synthetic jet utilizing three types of piezoelectric actuators as mechanical diaphragms, Radial Field Diaphragms, Thunders, and Bimorphs so that the shape cavity volume does not exceed 147.5 cubic centimeters on a 7centimeter x 7centimeter aerial coverage. These piezoelectric elements were selected because of their geometry, and overall free-displacement. Each actuator was affixed about its perimeter in a cavity, and relevant parameters such as clamped displacement variations with voltage and frequency, air velocities produced through an aperture, and sound pressure levels produced by the piezoelectric diaphragms were measured.

Mossi, Karla M.↗
NASA NTRS2002

Modulation of head movement control in humans during treadmill walking

The purpose of this study was to investigate the coordination of the head relative to the trunk within a gait cycle during gaze fixation. Nine normal subjects walked on a motorized treadmill driven at 1.79 m/s (20 s trials) while fixing their gaze on a centrally located earth-fixed target positioned at a distance of 2 m from their eyes. The net and relative angular motions of the head about the three axes of rotations, as well as the corresponding values for the moments acting on it relative to the trunk during the gait cycle were quantified and used as measures of coordination. The average net moment, as well as the average moments about the different axes were significantly different (P<0.01) between the high impact and low/no impact phases of the gait cycle. However, the average net angular displacement as well as the average angular displacement about the axial rotation axis of the head relative to the trunk was maintained uniform (P>0.01) throughout the gait cycle. The average angular displacement about the lateral bending axis was significantly increased (P<0.01) during the high impact phase while that about the flexion-extension axis was significantly decreased (P<0.01) throughout the gait cycle. Thus, the coordination of the motion of the head relative to the trunk during walking is dynamically modulated depending on the behavioral events occurring in the gait cycle. This modulation may serve to aid stabilization of the head by counteracting the force variations acting on the upper body that may aid in the visual fixation of targets during walking.

Clinical Trial↗
NASA NTRS2004

Characterization of Transport Errors in Chemical Forecasts from a Global Tropospheric Chemical Transport Model

We propose a new methodology to characterize errors in the representation of transport processes in chemical transport models. We constrain the evaluation of a global three-dimensional chemical transport model (GEOS-CHEM) with an extended dataset of carbon monoxide (CO) concentrations obtained during the Transport and Chemical Evolution over the Pacific (TRACE-P) aircraft campaign. The TRACEP mission took place over the western Pacific, a region frequently impacted by continental outflow associated with different synoptic-scale weather systems (such as cold fronts) and deep convection, and thus provides a valuable dataset. for our analysis. Model simulations using both forecast and assimilated meteorology are examined. Background CO concentrations are computed as a function of latitude and altitude and subsequently subtracted from both the observed and the model datasets to focus on the ability of the model to simulate variability on a synoptic scale. Different sampling strategies (i.e., spatial displacement and smoothing) are applied along the flight tracks to search for systematic model biases. Statistical quantities such as correlation coefficient and centered root-mean-square difference are computed between the simulated and the observed fields and are further inter-compared using Taylor diagrams. We find no systematic bias in the model for the TRACE-P region when we consider the entire dataset (i.e., from the surface to 12 km ). This result indicates that the transport error in our model is globally unbiased, which has important implications for using the model to conduct inverse modeling studies. Using the First-Look assimilated meteorology only provides little improvement of the correlation, in comparison with the forecast meteorology. These general statements can be refined when the entire dataset is divided into different vertical domains, i.e., the lower troposphere (less than 2 km), the middle troposphere (2-6 km), and the upper troposphere (greater than 6 km). The best agreement between the observations and the model is found in the lower and middle troposphere. Downward displacements in the lower troposphere provide a better fit with the observed value, which could indicate a problem in the representation of boundary layer height in the model. Significant improvement is also found for downward and southward displacements in the upper troposphere. There are several potential sources of errors in our simulation of the continental outflow in the upper troposphere which could lead to such biases, including the location and/or the strength of deep convective cells as well as that of wildfires in Southeast Asia.

Bey, I.↗
NASA NTRS1999

The response of lazy-2 tomato seedlings to curvature-inducing magnetic gradients is modulated by light

Shoots of the lazy-2 mutant of tomato (Lycopersicon esculentum Mill., cv. Ailsa Craig) exhibit negative gravitropism in the dark, but respond positively gravitropically in (red) light. In order to test whether high-gradient magnetic fields (HGMFs) exert only ponderomotive effects on amyloplasts or affect other physiological processes, we induced magnetophoretic curvature in wild-type (WT) and lazy-2 mutant seedlings. Straight hypocotyls of 4-d-old plants were selected and the tips of their hooks were placed in an HGMF near the edge of a magnetized ferromagnetic wedge [grad (H2/2) approximately 10(9)-10(10) Oe2/cm] and mounted on a 1-rpm clinostat. After 4 h in the dark, 85% of WT hypocotyls and 67% of mutant hypocotyls curved toward the wedge. When the seedlings were exposed to red light for 1 h prior to and during the application of the HGMF, 78% of the WT seedlings curved toward the magnetic gradient, but the majority of the lazy-2 seedlings (75%) curved away from the stronger field area. Intracellular amyloplast displacement in the HGMF was similar for both varieties and resembled the displacement after horizontal reorientation. The WT showed a distinct graviresponse pattern depending on the orientation of the hook, even after excision of the apex. Application of HGMFs to decapitated hypocotyls resulted in curvature consistent with that obtained after horizontal reorientation. After light exposure, decapitated lazy-2 seedlings did not respond positively gravitropically. The data imply that the lazy-2 mutants perceive the displacement of amyloplasts in a similar manner to the WT and that the HGMF does not affect the graviresponse mechanism. The study demonstrates that ponderomotive forces due to HGMFs are useful for the analysis of the gravity-sensing mechanism in plants.

NASA Discipline Plant Biology↗
NASA NTRS2000

Analysis of cell mechanics in single vinculin-deficient cells using a magnetic tweezer

A magnetic tweezer was constructed to apply controlled tensional forces (10 pN to greater than 1 nN) to transmembrane receptors via bound ligand-coated microbeadswhile optically measuring lateral bead displacements within individual cells. Use of this system with wild-type F9 embryonic carcinoma cells and cells from a vinculin knockout mouse F9 Vin (-/-) revealed much larger differences in the stiffness of the transmembrane integrin linkages to the cytoskeleton than previously reported using related techniques that measured average mechanical properties of large cell populations. The mechanical properties measured varied widely among cells, exhibiting an approximately log-normal distribution. The median lateral bead displacement was 2-fold larger in F9 Vin (-/-) cells compared to wild-type cells whereas the arithmetic mean displacement only increased by 37%. We conclude that vinculin serves a greater mechanical role in cells than previously reported and that this magnetic tweezer device may be useful for probing the molecular basis of cell mechanics within single cells. Copyright 2000 Academic Press.

Non-NASA Center↗
NASA NTRS2004

Experimental Results From Stitched Composite Multi-Bay Fuselage Panels Tested Under Uni-Axial Compression

The experimental results from two stitched VARTM composite panels tested under uni-axial compression loading are presented. The curved panels are divided by frames and stringers into five or six bays with a column of three bays along the compressive loading direction. The frames are supported at the ends to resist out-of-plane translation. Back-to-back strain gages are used to record the strain and displacement transducers were used to record the out-of-plane displacements. In addition a full-field measurement technique that utilizes a camera-based-stero-vision system was used to record displacements. The panels were loaded in increments to determine the first bay to buckle. Loading was discontinued at limit load and the panels were removed from the test machine for impact testing. After impacting at 20 ft-lbs to 25 ft-lbs of energy with a spherical indenter, the panels were loaded in compression until failure. Impact testing reduced the axial stiffness 4 percent and less than 1 percent. Postbuckled axial panel stiffness was 52 percent and 70 percent of the pre-buckled stiffness.

Baker, Donald J.↗
NASA NTRS2002

Mountain-Top-to-Mountain-Top Optical Link Demonstration

A mountain-top-to-mountain-top optical communications demonstration was conducted between the JPL Table Mountain Facility (TMF), Wrightwood, California, and Strawberry Peak (SP), Lake Arrowhead, California, during the months of August and September of 2000. The link was nearly horizontal at an altitude of 2 km and spanned a range of 46.8 km. A 780-nm multibeam beacon broadcast from TMF was received by the JPL Optical Communications Demonstrator (OCD) located at SP. The received beacon was utilized as a pointing reference to retransmit an 852-nm communications laser beam, modulated at 400 Mb/s by a PN7 pseudo-random bit stream (PRBS) sequence. The long atmospheric path resulted in atmospheric-turbulence-induced angle-of-arrival fluctuations of the beacon at the OCD aperture. A .ne-steering control loop was used to track the resulting beacon centroid motion and update the pointing of the communications laser beam transmitted from SP to TMF. Fried parameters, or r0, inferred from focal spot sizes received at SP were 4 to 5 cm whereas, using the spot sizes received at TMF, they were 2 to 3 cm. In both cases, theory predicts larger r0 values. The predicted angle-of-arrival fluctuations compare well with measured rms displacements exhibited by the focal spots at either end of the link. An uncompensated error of ~1.1 rad in the x-axis and ~2 rad in the y-axis was obtained using centroid data logged by the OCD. Average bit-error rates of 10-5 were recorded for extended periods of time. An atmospheric coherence length r0 of 3 to 5 cm was inferred using the focal-plane spot size measured on the CCD tracking sensor and compared to a predicted value of 5 to 7 cm using reasonable atmospheric models. The irradiance bounds required for the CCD tracking sensor to perform centroiding was found to range from 2000 to 3000 integrated pixel counts, although a more reliable range was 600 to 3000, indicating a dynamic range of 6 to 11 dB. The motion of the spot on the focal plane was also recorded and yielded rms angle-of-arrival-induced focal-plane displacement of 9 to 11 m, compared to a predicted value of 7.8 to 11 m. The irradiance measurements made with the OCD clearly indicate that best tracking performance is obtained when the mean received signal is 2000 to 2200 counts. The best tracking performance resulted in an rms uncompensated error of 1.1 rad. The uncompensated error appeared to increase with either an increase or decrease in mean beacon-signal level. The rms uncompensated error determined by deriving the beacon displacement power spectral density from the beacon centroid-versustime data and the rejection function of the control loop yielded a higher value of 3.4 rad.

Biswas, A.↗
NASA NTRS2005

Quantifying Exact Motions Along Lineaments on Europa

Evaluating the precise motions along lineaments on the surface of Jupiter's icy moon, Europa, is a valuable tool for interpreting the development and history of lineaments of various morphologies. Such morphologies include strike-slip faults, dilational bands, ridges, and convergence zones. However, the exact mode of origin and kinematic behavior of these various lineaments are not obvious based on morphology alone. In fact, the apparent motions implied by displaced crosscut features can provide misleading indications of true motions along lineaments. Identifying the precise motions (combinations of sliding and opening/closing) is critical to the accurate characterization and interpretation of each of these lineament types. Lineaments of interest (i.e., those having displaced relatively older features in some manner) are identified on Galileo spacecraft images and measurements are made of the total offset, the separation, and relative orientations of crosscut features with respect to the lineament of interest. Specifically, by using these measured quantities and a series of trigonometric equations, the precise motions (i.e., dilation, convergence, strike-slip, or a combination of strike-slip and dilation or convergence) can be determined. These measurements are, however, limited by the resolution of the available images. This study focuses on motion analysis techniques for Europan lineaments and the precise characterization of fault-orthogonal and/or strike-slip motion along lineaments of varying morphologies. We highlight potential pitfalls of cursory analyses of motion indicators. For example, lineaments with obvious lateral offsets have typically been identified simply as strike-slip faults. This assumption may actually be incorrect, as fault-orthogonal motions may contribute to apparent lateral displacements (offsets or separations). Also, variability in the amount of fault motion along the trace length should theoretically be identifiable using the outlined technique. Strike-slip faults on Europa have conventionally been presumed to have a constant slip magnitude along their lengths; however, we posit that variable distributions of slip may be common, as is typical along terrestrial strike-slip faults.

Vetter, J. C.↗
NASA NTRS1998

Model-Trained Neural Networks and Electronic Holography Demonstrated to Detect Damage in Blades

Detect Damage in Blades Electronic holography can show damaged regions in fan blades at 30 frames/sec. The electronic holograms are transformed by finite-element-model-trained artificial neural networks to visualize the damage. The trained neural networks are linked with video and graphics to visualize the bending-induced strain distribution, which is very sensitive to damage. By contrast, it is very difficult to detect damage by viewing the raw, speckled, characteristic fringe patterns. For neural-network visualization of damage, 2 frames or 2 fields are used, rather than the 12 frames normally used to compute the displacement distribution from electronic holograms. At the NASA Lewis Research Center, finite element models are used to compute displacement and strain distributions for the vibration modes of undamaged and cracked blades. A model of electronic time-averaged holography is used to transform the displacement distributions into finite-element-resolution characteristic fringe patterns. Then, a feedforward neural network is trained with the fringe-pattern/strain-pattern pairs, and the neural network, electronic holography, and video are implemented on a workstation. Now that the neural networks have been tested successfully at 30 frames/sec on undamaged and cracked cantilevers, the electronic holography and neural-network processing are being adapted for onsite damage inspection of twisted fan blades and rotormounted blades. Our conclusion is that model-trained neural nets are effective when they are trained with good models whose application is well understood. This work supports the aeromechanical testing portion of the Advanced Subsonic Technology Project.

Decker, Arthur J.↗
NASA NTRS2005

Single Particle Damage Events in Candidate Star Camera Sensors

Si charge coupled devices (CCDs) are currently the preeminent detector in star cameras as well as in the near ultraviolet (uv) to visible wavelength region for astronomical observations in space and in earth-observing space missions. Unfortunately, the performance of CCDs is permanently degraded by total ionizing dose (TID) and displacement damage effects. TID produces threshold voltage shifts on the CCD gates and displacement damage reduces the charge transfer efficiency (CTE), increases the dark current, produces dark current nonuniformities and creates random telegraph noise in individual pixels. In addition to these long term effects, cosmic ray and trapped proton transients also interfere with device operation on orbit. In the present paper, we investigate the dark current behavior of CCDs - in particular the formation and annealing of hot pixels. Such pixels degrade the ability of a CCD to perform science and also can present problems to the performance of star camera functions (especially if their numbers are not correctly anticipated). To date, most dark current radiation studies have been performed by irradiating the CCDs at room temperature but this can result in a significantly optimistic picture of the hot pixel count. We know from the Hubble Space Telescope (HST) that high dark current pixels (so-called hot pixels or hot spikes) accumulate as a function of time on orbit. For example, the HST Advanced Camera for Surveys/Wide Field Camera instrument performs monthly anneals despite the loss of observational time, in order to partially anneal the hot pixels. Note that the fact that significant reduction in hot pixel populations occurs for room temperature anneals is not presently understood since none of the commonly expected defects in Si (e.g. divacancy, E center, and A-center) anneal at such a low temperature. A HST Wide Field Camera 3 (WFC3) CCD manufactured by E2V was irradiated while operating at -83C and the dark current studied as a function of temperature while the CCD was warmed to a sequence of temperatures up to a maximum of +30C. The device was then cooled back down to -83 and re-measured. Hot pixel populations were tracked during the warm-up and cool-down. Hot pixel annealing began below 40C and the anneal process was largely completed before the detector reached +3OC. There was no apparent sharp temperature dependence in the annealing. Although a large fraction of the hot pixels fell below the threshold to be counted as a hot pixel, they nevertheless remained warmer than the remaining population. The details of the mechanism for the formation and annealing of hot pixels is not presently understood, but it appears likely that hot pixels are associated with displacement damage occurring in high electric field regions.

Marshall, Paul↗
NASA NTRS2005

Fluid-structural dynamics of ground-based and microgravity caloric tests

Microgravity caloric tests aboard the 1983 SpaceLab1 mission produced nystagmus results with an intensity comparable to those elicited during post- and pre- flight tests, thus contradicting the basic premise of Barany's convection hypothesis for caloric stimulation. In this work, we present a dynamic fluid structural analysis of the caloric stimulation of the lateral semicircular canal based on two simultaneous driving forces for the endolymphatic flow: natural convection driven by the temperature-dependent density variation in the bulk fluid and expansive convection caused by direct volumetric displacement of the endolymph during the thermal irrigation. Direct numerical simulations indicate that on earth, the natural convection mechanism is dominant. But in the microgravity environment of orbiting spacecraft, where buoyancy effects are mitigated, expansive convection becomes the sole mechanism for producing cupular displacement. A series of transient 1 g and microgravity case studies are presented to delineate the differences between the dynamics of the 1 g and microgravity endolymphatic flows. The impact of these different flow dynamics on the endolymph-cupula fluid-structural interactions is also analyzed based on the time evolutions of cupular displacement and velocity and the transcupular pressure differences.

Gravitation↗
NASA NTRS2006

Probabilistic Structural Evaluation of Uncertainties in Radiator Sandwich Panel Design

The Jupiter Icy Moons Orbiter (JIMO) Space System is part of the NASA's Prometheus Program. As part of the JIMO engineering team at NASA Glenn Research Center, the structural design of the JIMO Heat Rejection Subsystem (HRS) is evaluated. An initial goal of this study was to perform sensitivity analyses to determine the relative importance of the input variables on the structural responses of the radiator panel. The desire was to let the sensitivity analysis information identify the important parameters. The probabilistic analysis methods illustrated here support this objective. The probabilistic structural performance evaluation of a HRS radiator sandwich panel was performed. The radiator panel structural performance was assessed in the presence of uncertainties in the loading, fabrication process variables, and material properties. The stress and displacement contours of the deterministic structural analysis at mean probability was performed and results presented. It is followed by a probabilistic evaluation to determine the effect of the primitive variables on the radiator panel structural performance. Based on uncertainties in material properties, structural geometry and loading, the results of the displacement and stress analysis are used as an input file for the probabilistic analysis of the panel. The sensitivity of the structural responses, such as maximum displacement and maximum tensile and compressive stresses of the facesheet in x and y directions and maximum VonMises stresses of the tube, to the loading and design variables is determined under the boundary condition where all edges of the radiator panel are pinned. Based on this study, design critical material and geometric parameters of the considered sandwich panel are identified.

Kuguoglu, Latife↗
NASA NTRS2006

The Load Capability of Piezoelectric Single Crystal Actuators

Piezoelectric lead magnesium niobate-lead titanate (PMN-PT) single crystal is one of the most promising materials for electromechanical device applications due to its high electrical field induced strain and high electromechanical coupling factor. PMN-PT single crystal-based multilayer stack actuators and multilayer stack-based flextensional actuators have exhibited high stroke and high displacement-voltage ratios. The actuation capabilities of these two actuators were evaluated using a newly developed method based upon a laser vibrometer system under various loading conditions. The measured displacements as a function of mechanical loads at different driving voltages indicate that the displacement response of the actuators is approximately constant under broad ranges of mechanical load. The load capabilities of these PMN-PT single crystal-based actuators and the advantages of the capability for applications will be discussed.

Xu, Tian-Bing↗
NASA NTRS2006

Thrust Stand for Electric Propulsion Performance Evaluation

An electric propulsion thrust stand capable of supporting testing of thrusters having a total mass of up to 125 kg and producing thrust levels between 100 microN to 1 N has been developed and tested. The design features a conventional hanging pendulum arm attached to a balance mechanism that converts horizontal deflections produced by the operating thruster into amplified vertical motion of a secondary arm. The level of amplification is changed through adjustment of the location of one of the pivot points linking the system. Response of the system depends on the relative magnitudes of the restoring moments applied by the displaced thruster mass and the twisting torsional pivots connecting the members of the balance mechanism. Displacement is measured using a non-contact, optical linear gap displacement transducer and balance oscillatory motion is attenuated using a passive, eddy-current damper. The thrust stand employs an automated leveling and thermal control system. Pools of liquid gallium are used to deliver power to the thruster without using solid wire connections, which can exert undesirable time-varying forces on the balance. These systems serve to eliminate sources of zero-drift that can occur as the stand thermally or mechanically shifts during the course of an experiment. An in-situ calibration rig allows for steady-state calibration before, during and after thruster operation. Thrust measurements were carried out on a cylindrical Hall thruster that produces mN-level thrust. The measurements were very repeatable, producing results that compare favorably with previously published performance data, but with considerably smaller uncertainty.

Polzin, Kurt A.↗
NASA NTRS2006

Kinematics of Strong Discontinuities

Synthetic Aperture Radar (SAR) provides a detailed view of the Arctic ice cover. When processed with the RADARSAT Geophysical Processor System (RGPS), it provides estimates of sea ice motion and deformation over large regions of the Arctic for extended periods of time. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. The RGPS deformation products are based on the assumption that the displacement and velocity are smooth functions of the spatial coordinates. However, if the dominant deformation of multiyear ice results from the opening, closing and shearing of leads, then the displacement and velocity can be discontinuous. This presentation discusses the kinematics associated with strong discontinuities that describe possible jumps in displacement or velocity. Ice motion from SAR data are analyzed using this framework. It is assumed that RGPS cells deform due to the presence of a lead. The lead orientation is calculated to optimally account for the observed deformation. It is shown that almost all observed deformation can be represented by lead opening and shearing. The procedure used to reprocess motion data to account for leads will be described and applied to regions of the Beaufort Sea. The procedure not only provides a new view of ice deformation, it can be used to obtain information about the presence of leads for initialization and/or validation of numerical simulations.

Peterson, K.↗
NASA NTRS2007

Nonlinear Theory and Breakdown

The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.

Smith, Frank↗