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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Ground-based detectability of terrestrial and Jovian extrasolar planets: observations of CM Draconis at Lick Observatory

The detection of terrestrial-sized extrasolar planets from the ground has been thought to be virtually impossible due to atmospheric scintillation limits. However, we show that this is not the case especially selected (but nevertheless main sequence) stars, namely small eclipsing binaries. For the smallest of these systems, CM Draconis, several months to a few years of photometric observations with 1-m-class telescopes will be sufficient to detect the transits of any short-period planets of sizes > or = 1.5 Earth radii (RE), using cross-correlation analysis with moderately good photometry. Somewhat larger telescopes will be needed to extend this detectability to terrestrial planets in larger eclipsing binary systems. (We arbitrarily define "terrestrial planets" herein as those whose disc areas are closer to that of Earth's than Neptune's i.e., less than about 2.78 RE.) As a "spin-off" of such observations, we will also be able to detect the presence of Jovian-mass planets without transits using the timing of the eclipse minima. Eclipse minima will drift in time as the binary system is offset by a sufficiently massive planet (i.e., one Jupiter mass) about the binary/giant-planet barycenter, causing a periodic variation in the light travel time to the observer. We present here an outline of present observations taking place at the University of California Lick Observatory using the Crossley 0.9-m telescope in collaboration with other observatories (in South Korea, Crete, France, Canary Islands, and New York) to detect or constrain the existence of terrestrial planets around main sequence eclipsing binary star systems, starting with CM Draconis. We demonstrate the applicability of photometric data to the general detection of gas giant planets via eclipse minima timings in many other small-mass eclipsing binary systems as well.

NASA Program Exobiology↗
NASA NTRS1996

A matched filter method for ground-based sub-noise detection of terrestrial extrasolar planets in eclipsing binaries: application to CM Draconis

The photometric detection of extrasolar planets by transits in eclipsing binary systems can be significantly improved by cross-correlating the observational light curves with synthetic models of possible planetary transit features, essentially a matched filter approach. We demonstrate the utility and application of this transit detection algorithm for ground-based detections of terrestrial-sized (Earth-to-Neptune radii) extrasolar planets in the dwarf M-star eclipsing binary system CM Draconis. Preliminary photometric observational data of this system demonstrate that the observational noise is well characterized as white and Gaussian at the observational time steps required for precision photometric measurements. Depending on planet formation scenarios, terrestrial-sized planets may form quite close to this low-luminosity system. We demonstrate, for example, that planets as small as 1.4 Earth radii with periods on the order of a few months in the CM Draconis system could be detected at the 99.9% confidence level in less than a year using 1-m class telescopes from the ground. This result contradicts commonly held assumptions limiting present ground-based efforts to, at best, detections of gas giant planets after several years of observation. This method can be readily extended to a number of other larger star systems with the utilization of larger telescopes and longer observing times. Its extension to spacecraft observations should also allow the determination of the presence of terrestrial-sized planets in nearly 100 other known eclipsing binary systems.

NASA Discipline Number 52-10↗
NASA NTRS2000

Ventilation-perfusion matching in long-term microgravity

We studied the ventilation-perfusion matching pattern in normal gravity (1 G) and short- and long-duration microgravity (microG) using the cardiogenic oscillations in the sulfur hexaflouride (SF(6)) and CO(2) concentration signals during the phase III portion of vital capacity single-breath washout experiments. The signal power of the cardiogenic concentration variations was assessed by spectral analysis, and the phase angle between the oscillations of the two simultaneously expired gases was obtained through cross-correlation. For CO(2), a significant reduction of cardiogenic power was observed in microG, with respect to 1 G, but the reduction was smaller and more variable in the case of SF(6). A shift from an in-phase condition in 1 G to an out-of-phase condition was found for both short- and long-duration microG. We conclude that, although the distribution of ventilation and perfusion becomes more homogeneous in microG, significant inhomogeneities persist and that areas of high perfusion become associated with areas of relatively lower ventilation. In addition, these modifications seem to remain constant during long-term exposure to microG.

Mir Project↗
NASA NTRS2002

Distant Cluster Hunting: A Comparison of X-Ray and Optical Cluster Detection Techniques and Catalogs from the ROSAT Optical X-Ray Survey - II

We present and analyze the optical and X-ray catalogs of moderate-redshift cluster candidates from the ROSA TOptical X-Ray Survey, or ROXS. The survey covers the sky area contained in the fields of view of 23 deep archival ROSA T PSPC pointings, 4.8 square degrees. The cross-correlated cluster catalogs were con- structed by comparing two independent catalogs extracted from the optical and X-ray bandpasses, using a matched-filter technique for the optical data and a wavelet technique for the X-ray data. We cross-identified cluster candidates in each catalog. As reported in Paper 1, the matched-filter technique found optical counter- parts for at least 60% (26 out of 43) of the X-ray cluster candidates; the estimated redshifts from the matched filter algorithm agree with at least 7 of 1 1 spectroscopic confirmations (Az 5 0.10). The matched filter technique. with an imaging sensitivity of ml N 23, identified approximately 3 times the number of candidates (155 candidates, 142 with a detection confidence >3 u) found in the X-ray survey of nearly the same area. There are 57 X-ray candidates, 43 of which are unobscured by scattered light or bright stars in the optical images. Twenty-six of these have fairly secure optical counterparts. We find that the matched filter algorithm, when applied to images with galaxy flux sensitivities of mI N 23, is fairly well-matched to discovering z 5 1 clusters detected by wavelets in ROSAT PSPC exposures of 8000-60,000 s. The difference in the spurious fractions between the optical and X-ray (30%) and IO%, respectively) cannot account for the difference in source number. In Paper I, we compared the optical and X-ray cluster luminosity functions and we found that the luminosity functions are consistent if the relationship between X-ray and optical luminosities is steep (Lx o( L&f). Here, in Paper 11, we present the cluster catalogs and a numerical simulation of the ROXS. We also present color-magnitude plots for several of the cluster candidates, and examine the prominence of the red sequence in each. We find that the X-ray clusters in our survey do not all have a prominent red sequence. We conclude that while the red sequence may be a distinct feature in the color-magnitude plots for virialized massive clusters, it may be less distinct in lower mass clusters of galaxies at even moderate redshifts. Multiple, complementary methods of selecting and defining clusters may be essential, particularly at high redshift where all methods start to run into completeness limits, incomplete understanding of physical evolution, and projection effects.

Donahue, Megan↗
NASA NTRS2004

A Method of Estimating Low Turbulence Levels in Near Real Time Using Laser Anemometry

Laser anemometry was used to make two independent measurements of the flow velocity by capturing individual Doppler signals with high-speed digitizing boards. The two independent measurements were cross-correlated to reduce the contribution of photo detector shot noise on the frequency determination and subsequently on the turbulence estimate. In addition, criteria were developed to eliminate "bad" Doppler bursts from the data set, which then allowed reasonable low turbulence estimates to be made. The laser anemometer measurements were obtained at the inlet of an annular cascade and at the exit of a flow calibration nozzle and were compared with hot-wire data.

Goldman, Louis J.↗
NASA NTRS1998

Auditory cues for orientation and postural control in sighted and congenitally blind people

This study assessed whether stationary auditory information could affect body and head sway (as does visual and haptic information) in sighted and congenitally blind people. Two speakers, one placed adjacent to each ear, significantly stabilized center-of-foot-pressure sway in a tandem Romberg stance, while neither a single speaker in front of subjects nor a head-mounted sonar device reduced center-of-pressure sway. Center-of-pressure sway was reduced to the same level in the two-speaker condition for sighted and blind subjects. Both groups also evidenced reduced head sway in the two-speaker condition, although blind subjects' head sway was significantly larger than that of sighted subjects. The advantage of the two-speaker condition was probably attributable to the nature of distance compared with directional auditory information. The results rule out a deficit model of spatial hearing in blind people and are consistent with one version of a compensation model. Analysis of maximum cross-correlations between center-of-pressure and head sway, and associated time lags suggest that blind and sighted people may use different sensorimotor strategies to achieve stability.

NASA Discipline Neuroscience↗
NASA NTRS1998

Cardiogenic oscillation phase relationships during single-breath tests performed in microgravity

We studied the phase relationships of the cardiogenic oscillations in the phase III portion of single-breath washouts (SBW) in normal gravity (1 G) and in sustained microgravity (microG). The SBW consisted of a vital capacity inspiration of 5% He-1.25% sulfurhexafluoride-balance O2, preceded at residual volume by a 150-ml Ar bolus. Pairs of gas signals, all of which still showed cardiogenic oscillations, were cross-correlated, and their phase difference was expressed as an angle. Phase relationships between inspired gases (e.g., He) and resident gas (n2) showed no change from 1 G (211 +/- 9 degrees) to microG (163 +/- 7 degrees). Ar bolus and He were unaltered between 1 G (173 +/- 15 degrees) and microG (211 +/- 25 degrees), showing that airway closure in microG remains in regions of high specific ventilation and suggesting that airway closure results from lung regions reaching low regional volume near residual volume. In contrast, CO2 reversed phase with He between 1 G (332 +/- 6 degrees) and microG (263 +/- 27 degrees), strongly suggesting that, in microG, areas of high ventilation are associated with high ventilation-perfusion ratio (VA/Q). This widening of the range of VA/Q in microG may explain previous measurements (G.K. Prisk, A.R. Elliott, H.J.B. Guy, J.M. Kosonen, and J.B. West J. Appl. Physiol. 79: 1290-1298, 1995) of an overall unaltered range of VA/Q in microG, despite more homogeneous distributions of both ventilation and perfusion.

Non-NASA Center↗
NASA NTRS1996

The barberplaid illusion: plaid motion is biased by elongated apertures

The perceived direction of motion of plaids windowed by elongated spatial Gaussians is biased toward the window's long axis. The bias increases as the relative angle between the plaid motion and the long axis of the window increases, peaks at a relative angle of approximately 45 deg, and then decreases. The bias increases as the window is made narrower (at fixed height) and decreases as the component spatial frequency increases (at fixed aperture size). We examine several models of human motion processing (cross-correlation, motion-energy, intersection-of-constraints, and vector-sum), and show that none of these standard models can predict our data. We conclude that spatial integration of motion signals plays a crucial role in plaid motion perception and that current models must be explicitly expanded to include such spatial interactions.

NASA Center ARC↗
NASA NTRS2004

Bima Array Detections of HCN in Comets Linear (C/2002 T7) and Neat (C/2001 Q4)

We present interferometric detections of HCN in comets LINEAR (C/2002 T7) and NEAT (C/2001 Q4) with the Berkeley-Illinois-Maryland Association (BIMA) Array in its D-configuration cross-correlation mode. We detected the HCN J = 1 - 0 emission line in both comets. With a 25".4 x 20".3 synthesized beam around Comet LINEAR, we found a total beam averaged HCN column density (assuming a rotation temperature of 146 K) of < N(sub T) > = 2.1(11)x 10(sup 13) cm(exp -2), and a HCN production rate of Q(HCN)=2.8(15)x 10(sup 27) s(exp -1). With a 21".3 x 17".5 synthesized beam around Comet NEAT, we found a total beam averaged HCN column density (assuming a rotation temperature of 107 K) of < N(sub T) > = 5.7(30) x 10(sup l2) cm(exp -2), and a HCN production rate of Q(HCN)=8.3(44) x 10(sup 26) s(exp -l) giving a production rate of HCN relative to H2O of approximately 0.09(5)%. The production rates relative to H2O and spatial extent of HCN are similar to previous comet observations.

Friedel, D. N.↗
NASA NTRS1997

Reduction of ETS-VI Laser Communication Equipment Optical-Downlink Telemetry Collected During GOLD

Free-space laser communications experiments were conducted between the laser communication equipment (LCE) on board the Japanese Engineering Test Satellite VI (ETS-VI) and the ground station located at the Table Mountain Facility (TMF) during late 1995 and early 1996. This article describes the on-line data reduction process used to decode LCE telemetry (called E2) downlinked on the optical carrier during the Ground/Orbiter Lasercomm Demonstration (GOLD) experiments. The LCE has the capability of transmitting real-time sensor and status information at 128 kbps by modulating the onboard diode laser. The optical downlink was detected on the ground, bit synchronized, and the resulting data stream stored on a data recorder. The recorded data were subsequently decoded by on-line data processing that included cross-correlation of the known telemetry data format and the downlink data stream. Signals obtained from the processing can be useful not only in evaluating the characteristics of the LCE but also in understanding uplink and downlink signal quality.

Toyoshima, M.↗
NASA NTRS2001

Density Fluctuation in Asymmetric Nozzle Plumes and Correlation with Far Field Noise

A comparative experimental study of air density fluctuations in the unheated plumes of a circular, 4-tabbed-circular, chevron-circular and 10-lobed rectangular nozzles was performed at a fixed Mach number of 0.95 using a recently developed Rayleigh scattering based technique. Subsequently, the flow density fluctuations are cross-correlated with the far field sound pressure fluctuations to determine sources for acoustics emission. The nearly identical noise spectra from the baseline circular and the chevron nozzles are found to be in agreement with the similarity in spreading, turbulence fluctuations, and flow-sound correlations measured in the plumes. The lobed nozzle produced the least low frequency noise, in agreement with the weakest overall density fluctuations and flow-sound correlation. The tabbed nozzle took an intermediate position in the hierarchy of noise generation, intensity of turbulent fluctuation and flow-sound correlation. Some of the features in the 4-tabbed nozzle are found to be explainable in terms of splitting of the jet in a central large core and 4 side jetlets.

Panda, J.↗
NASA NTRS1989

Psychology of computer use: IX. A menu of self-administered microcomputer-based neurotoxicology tests

This study examined the feasibility of repeated self-administration of a newly developed battery of mental acuity tests which may have application in screening for fitness-for-duty or for persons who may be exposed to environmental stress, toxic agents, or disease. 16 subjects self-administered 18 microcomputer-based tests (13 new, 5 "core"), without proctors, over 10 sessions. The hardware performed well throughout the study and the tests appeared to be easily self-administered. Stabilities and reliabilities of the tests from the "core" battery were comparable to those obtained previously under more controlled experimental conditions. Eight of the new tests exceeded minimum criteria for metric and practical requirements and can be recommended as additions to the menu. Although the average retest reliability was high, cross-correlations between tests were low, implying factorial diversity. The menu can be used to form batteries with flexible total testing time which are likely to tap different mental processes and functions.

NASA Discipline Neuroscience↗
NASA NTRS2005

Full-Field Measurements of Self-Excited Oscillations in Momentum-Dominated Helium Jets

Flow structure of momentum-dominated helium jets discharged vertically into ambient air was investigated using a high-speed rainbow schlieren deflectometry (RSD) apparatus operated at up to 2000 Hz. The operating parameters, i.e., Reynolds number and Richardson number were varied independently to examine the self-excited, flow oscillatory behavior over a range of experimental conditions. Measurements revealed highly periodic oscillations in the laminar region at a unique frequency as well as high regularity in the flow transition and initial turbulent regions. The buoyancy was shown to affect the oscillation frequency and the distance from the jet exit to the flow transition plane. Instantaneous helium concentration contours across the field of view revealed changes in the jet flow structure and the evolution of the vortical structures during an oscillation cycle. A cross-correlation technique was applied to track the vortices and to find their convection velocity. Time-traces of helium concentration at different axial locations provided detailed information about the oscillating flow.

Yildirim, B. S.↗
NASA NTRS2004

Concentration Measurements in Self-Excited, Momentum-Dominated Helium Jets

Flow structure of momentum-dominated pure helium jets discharged vertically into ambient air was investigated using high-speed rainbow schlieren deflectometry (RSD) technique. Effects of the operating parameters, i.e., Reynolds number (Re) and Richardson number (Ri), on the oscillatory behavior of the flow were examined over a range of experimental conditions. To seek the individual effect of these parameters, one of them was fixed and the other was varied with certain constraints. Measurements revealed highly periodic oscillations in the laminar region as well as high regularity in transition and turbulent regions. Maximum spectral power profiles at different axial locations indicated the oscillation amplitude increasing until the breakdown of the jet in the turbulent regime. The transition from the laminar to turbulent flow was also investigated. Fast Fourier transform analysis performed in the transition regime showed that the flow oscillates at a unique frequency, which was the same in the upstream laminar flow region. Measured deflection angle data were used in Abel inversion algorithm to construct the helium concentration fields. Instantaneous helium concentration contours revealed changes in the flow structure and evolution of vortical structures during an oscillation cycle. Temporal evolution plots of helium concentration at different axial location showed repeatable oscillations at all axial and radial locations up to the turbulent regime. A cross-correlation technique, applied to find the spatial displacements of the vortical structures, provided correlation coefficient peaks between consecutive schlieren images. Results show that the vortical structure convected and accelerated only in the axial direction.

Yildirim, Bekir Sedat↗
NASA NTRS2005

Fuzzy Logic Particle Tracking

A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements, and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle-tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus the velocity. Combining these two techniques makes use of the higher spatial resolution available from the particle tracking. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two-staged velocimetric technique can measure particle velocities with high spatial resolution over a broad range of seeding densities.

Source record↗
NASA NTRS2005

Spatial Extent of a Deep Moonquake Nest: A Preliminary Report of Reexamination

Deep moonquakes, occurring at depths about halfway to the center of the Moon, were discovered during the Apollo lunar landing missions, 1969-1972. Their near-monthly occurrence with nearly identical waveforms at any given seismic station suggests that they are strongly influenced by tides, caused by the Earth and the Sun, acting on certain limited regions of the deep lunar interior. However, much about them is unknown, why they are restricted to certain depths and to limited source regions (nests), and what they tell us about the nature of the material and dynamics of the interior of the Moon. A piece of information helpful to decipher their true nature is the spatial extent and distribution of their hypocenters. The occurrence of nearly identical waveforms suggests groups of hypocenters appear in close proximity to one another, but can we tell how closely they are located and how they are distributed? The Apollo PSE (Passive Seismic Experiment) data from all stations of the seismic network were received in real time at a common receiving station on Earth in digital form. This provided extremely high inter-station timing accuracy not achievable for most earthquake data on Earth at that time. We took advantage of this to compute relative locations of waveform-matched events, and concluded that deep moonquake foci in the A1 moonquake nest were concentrated on a nearly horizontal plane of less than 1 km in diameter. This earlier study was based on deep moonquake events visually identified on seismograms. A recent reanalysis of earlier unidentified seismic events fully utilizing the high capability of present-day computers expanded the list of positively identified deep moonquakes by more than a factor of five. The new list contains many events that are not visually matched in waveforms, yet correlated at a significant level when cross-correlated with a computer. Thus it became imperative to reexamine the spatial distribution of deep moonquake hypocenters including the newly identified events. Additional information is included in the original extended abstract.

Nakamura, Yosio↗
NASA NTRS2005

Jet-Intracluster Medium Interactions of the Head Tail Radio Galaxy 3C 129

The 50 ksec XMM observations of the galaxy cluster 3C 129 were taken as scheduled, and the data are of good quality. We analyzed the data in the following way. After standard cleaning, we flat-fielded the XMM surface brightness maps. Combining the data from the EPIC MOS and PN Camera CCDs, we performed a cross-correlation analysis of the X-ray surface brightness distribution with the 1.4 GHz VLA radio map. We found evidence for cavities in the X-ray emitting Intra-Cluster Medium (ICM) associated with the radio tail of the head-tail radio galaxy 3C 129. This discovery is very interesting as it excludes the presence of a large fraction of thermal plasma in the radio tail. Together with the observation of an apparent pressure mismatch between the radio plasma and the ICM, and an upper limit on the magnetic field inside the radio tail (from the radio spectral indices map) the observation implies that the tail pressure is dominated either by low-energy electrons/positrons, or, by relativistic protons. Furthermore, we studied the energy spectrum of an X-ray "hot-spot" associated with the head of the radio galaxy 3C 129. It seems likely that the X-ray hot-spot originates from shocked gas in front of the radio galaxy. , The analysis turned out to be much more difficult than anticipated. The main reason is the lack of a comprehensive, publicly available background model that is key for the analysis of extended sources. Small groups like our do not have the man-power to come up with a background model themselves. We used the model from Read & Ponman (A&A 409, 395, 2003). However, the background subtracted X-ray surface brightness maps show a bright ring in the outer 20% of the camera. We tried to get rid of this ring and contacted the XMM helpdesk and Read & Ponman, the authors of the background paper. However, up to this day, we did not entirely succeed to remove the brightness enhancement at the outer parts of the camera. Unfortunately, our results are somewhat sensitive to the uncertainty, as the radio galaxy 3C 129 is very large and occupies a rather large fraction of the XMM field of view. We are now working on a paper describing the results. The paper will include a detailed discussion of the uncertainties associated with the non- perfect background subtraction.

Krawczynski, Henric S. W.↗
NASA NTRS2002

Tip-Clearance Vortex Characterized With Three-Dimensional Digital Particle Image Velocimetry

An optical measurement technique known as Three-Dimensional Digital Particle Image Velocimetry (3-D DPIV) was used to characterize the tip clearance flow in NASA Glenn Research Center's low-speed axial compressor. 3-D DPIV is a technique in which a stereoscopic imaging system consisting of two cross-correlation cameras is used to record particles entrained in a flow as a laser light sheet is pulsed at two instances in time. Although 3-D DPIV has been used elsewhere, this is the first time it has been used to measure compressor tip clearance flows. In-house modifications of the DPIV system include the use of effective seeding technology and a novel system to perform a priori calibrations at all five measurement planes, greatly reducing facility run time. Computational fluid dynamics predictions, which are used to guide design changes toward improving the efficiency and operating range of turbomachinery, can be verified and improved by comparison with 3-D DPIV measurements of the actual tip clearance flow. This measurement campaign dealt with the characterization of the tip clearance vortex in the first stage of a four-stage axial compressor. The tip clearance vortex is formed in compressors operating with a clearance gap between the moving rotor blade tips and the stationary casing when a leakage flow, forced from the pressure side of the blade over the blade tip, forms a vortical structure on the suction side of the blade. 3-D DPIV is ideally suited to measure the clearance vortex for two reasons: (1) this technique captures the entire blade passage flow at one instant in time, so that wandering of the vortex during the measurement does not smear out velocity gradients in the flow field, and (2) the spanwise component of velocity changes sign across the vortex core, providing a more accurate measurement of the vortex location than was available with previous two-dimensional measurement approaches. These two attributes of the data will enable computational fluid dynamics researchers to validate their predictions to a level of accuracy not previously attainable. In an effort to understand the effects of this flow phenomenon on the operation of the low speed axial compressor, data were acquired at two mass flow coefficients: 0.395 (design operating point) and 0.35 (operating point just above stall). In order to identify the spatial extent, location, and magnitude of the tip clearance vortex for each mass flow condition, data were acquired at five equally spaced spanwise locations, from 90- to 100-percent span. The data presented shows a cross section of the tip clearance vortex at 94-percent span and a mass flow coefficient of 0.395, where the color contours represent the radial velocity component. The blue (flow towards the hub) and red (flow towards the casing) regions illustrate the extent of the tip clearance vortex. The interface between the blue and red regions delineates the location of the vortex core.

John, W. Trevor↗