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NASA NTRS2001

Perception of tilt (somatogravic illusion) in response to sustained linear acceleration during space flight

During the 1998 Neurolab mission (STS-90), four astronauts were exposed to interaural and head vertical (dorsoventral) linear accelerations of 0.5 g and 1 g during constant velocity rotation on a centrifuge, both on Earth and during orbital space flight. Subjects were oriented either left-ear-out or right-ear-out (Gy centrifugation), or lay supine along the centrifuge arm with their head off-axis (Gz centrifugation). Pre-flight centrifugation, producing linear accelerations of 0.5 g and 1 g along the Gy (interaural) axis, induced illusions of roll-tilt of 20 degrees and 34 degrees for gravito-inertial acceleration (GIA) vector tilts of 27 degrees and 45 degrees , respectively. Pre-flight 0.5 g and 1 g Gz (head dorsoventral) centrifugation generated perceptions of backward pitch of 5 degrees and 15 degrees , respectively. In the absence of gravity during space flight, the same centrifugation generated a GIA that was equivalent to the centripetal acceleration and aligned with the Gy or Gz axes. Perception of tilt was underestimated relative to this new GIA orientation during early in-flight Gy centrifugation, but was close to the GIA after 16 days in orbit, when subjects reported that they felt as if they were 'lying on side'. During the course of the mission, inflight roll-tilt perception during Gy centrifugation increased from 45 degrees to 83 degrees at 1 g and from 42 degrees to 48 degrees at 0.5 g. Subjects felt 'upside-down' during in-flight Gz centrifugation from the first in-flight test session, which reflected the new GIA orientation along the head dorsoventral axis. The different levels of in-flight tilt perception during 0.5 g and 1 g Gy centrifugation suggests that other non-vestibular inputs, including an internal estimate of the body vertical and somatic sensation, were utilized in generating tilt perception. Interpretation of data by a weighted sum of body vertical and somatic vectors, with an estimate of the GIA from the otoliths, suggests that perception weights the sense of the body vertical more heavily early in-flight, that this weighting falls during adaptation to microgravity, and that the decreased reliance on the body vertical persists early post-flight, generating an exaggerated sense of tilt. Since graviceptors respond to linear acceleration and not to head tilt in orbit, it has been proposed that adaptation to weightlessness entails reinterpretation of otolith activity, causing tilt to be perceived as translation. Since linear acceleration during in-flight centrifugation was always perceived as tilt, not translation, the findings do not support this hypothesis.

STS-90 Shuttle Project↗

DOE OSTI2024

Determining the tilt of the Raman laser beam using an optical method for atom gravimeters

The tilt of a Raman laser beam is a major systematic error in precision gravity measurement using atom interferometry. The conventional approach to evaluating this tilt error involves modulating the direction of the Raman laser beam and conducting time-consuming gravity measurements to identify the error minimum. In this work, we demonstrate a method to expediently determine the tilt of the Raman laser beam by transforming the tilt angle measurement into characterization of parallelism, which integrates the optical method of aligning the laser direction, commonly used in freely falling corner-cube gravimeters, into an atom gravimeter. A position-sensing detector (PSD) is utilized to quantitatively characterize the parallelism between the test beam and the reference beam, thus measuring the tilt precisely and rapidly. After carefully positioning the PSD and calibrating the relationship between the distance measured by the PSD and the tilt angle measured by the tiltmeter, we achieved a statistical uncertainty of less than 30 µrad in the tilt measurement. Furthermore, we compared the results obtained through this optical method with those from the conventional tilt modulation method for gravity measurement. The comparison validates that our optical method can achieve tilt determination with an accuracy level of better than 200 µrad, corresponding to a systematic error of 20 µGal in g measurement. This work has practical implications for real-world applications of atom gravimeters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2000

Transient cardio-respiratory responses to visually induced tilt illusions

Although the orthostatic cardio-respiratory response is primarily mediated by the baroreflex, studies have shown that vestibular cues also contribute in both humans and animals. We have demonstrated a visually mediated response to illusory tilt in some human subjects. Blood pressure, heart and respiration rate, and lung volume were monitored in 16 supine human subjects during two types of visual stimulation, and compared with responses to real passive whole body tilt from supine to head 80 degrees upright. Visual tilt stimuli consisted of either a static scene from an overhead mirror or constant velocity scene motion along different body axes generated by an ultra-wide dome projection system. Visual vertical cues were initially aligned with the longitudinal body axis. Subjective tilt and self-motion were reported verbally. Although significant changes in cardio-respiratory parameters to illusory tilts could not be demonstrated for the entire group, several subjects showed significant transient decreases in mean blood pressure resembling their initial response to passive head-up tilt. Changes in pulse pressure and a slight elevation in heart rate were noted. These transient responses are consistent with the hypothesis that visual-vestibular input contributes to the initial cardiovascular adjustment to a change in posture in humans. On average the static scene elicited perceived tilt without rotation. Dome scene pitch and yaw elicited perceived tilt and rotation, and dome roll motion elicited perceived rotation without tilt. A significant correlation between the magnitude of physiological and subjective reports could not be demonstrated.

NASA Center JSC↗

NASA NTRS2006

Tilt and Translation Motion Perception during Off Vertical Axis Rotation

The effect of stimulus frequency on tilt and translation motion perception was studied during constant velocity off-vertical axis rotation (OVAR), and compared to the effect of stimulus frequency on eye movements. Fourteen healthy subjects were rotated in darkness about their longitudinal axis 10deg and 20deg off-vertical at 0.125 Hz, and 20deg offvertical at 0.5 Hz. Oculomotor responses were recorded using videography, and perceived motion was evaluated using verbal reports and a joystick with four degrees of freedom (pitch and roll tilt, mediallateral and anteriorposterior translation). During the lower frequency OVAR, subjects reported the perception of progressing along the edge of a cone. During higher frequency OVAR, subjects reported the perception of progressing along the edge of an upright cylinder. The modulation of both tilt recorded from the joystick and ocular torsion significantly increased as the tilt angle increased from 10deg to 20deg at 0.125 Hz, and then decreased at 0.5 Hz. Both tilt perception and torsion slightly lagged head orientation at 0.125 Hz. The phase lag of torsion increased at 0.5 Hz, while the phase of tilt perception did not change as a function of frequency. The amplitude of both translation perception recorded from the joystick and horizontal eye movements was negligible at 0.125 Hz and increased as a function of stimulus frequency. While the phase lead of horizontal eye movements decreased at 0.5 Hz, the phase of translation perception did not vary with stimulus frequency and was similar to the phase of tilt perception during all conditions. During dynamic linear acceleration in the absence of other sensory input (canal, vision) a change in stimulus frequency alone elicits similar changes in the amplitude of both self motion perception and eye movements. However, in contrast to the eye movements, the phase of both perceived tilt and translation motion is not altered by stimulus frequency. We conclude that the neural processing to distinguish tilt and translation linear acceleration stimuli differs between eye movements and motion perception.

Wood, Scott J.↗

NASA NTRS2009

Effects of Frequency and Motion Paradigm on Perception of Tilt and Translation During Periodic Linear Acceleration

Previous studies have demonstrated an effect of frequency on the gain of tilt and translation perception. Results from different motion paradigms are often combined to extend the stimulus frequency range. For example, Off-Vertical Axis Rotation (OVAR) and Variable Radius Centrifugation (VRC) are useful to test low frequencies of linear acceleration at amplitudes that would require impractical sled lengths. The purpose of this study was to compare roll-tilt and lateral translation motion perception in 12 healthy subjects across four paradigms: OVAR, VRC, sled translation and rotation about an earth-horizontal axis. Subjects were oscillated in darkness at six frequencies from 0.01875 to 0.6 Hz (peak acceleration equivalent to 10 deg, less for sled motion below 0.15 Hz). Subjects verbally described the amplitude of perceived tilt and translation, and used a joystick to indicate the direction of motion. Consistent with previous reports, tilt perception gain decreased as a function of stimulus frequency in the motion paradigms without concordant canal tilt cues (OVAR, VRC and Sled). Translation perception gain was negligible at low stimulus frequencies and increased at higher frequencies. There were no significant differences between the phase of tilt and translation, nor did the phase significantly vary across stimulus frequency. There were differences in perception gain across the different paradigms. Paradigms that included actual tilt stimuli had the larger tilt gains, and paradigms that included actual translation stimuli had larger translation gains. In addition, the frequency at which there was a crossover of tilt and translation gains appeared to vary across motion paradigm between 0.15 and 0.3 Hz. Since the linear acceleration in the head lateral plane was equivalent across paradigms, differences in gain may be attributable to the presence of linear accelerations in orthogonal directions and/or cognitive aspects based on the expected motion paths.

Beaton, K. H.↗

NASA NTRS2011

Influence of Vibrotactile Feedback on Controlling Tilt Motion After Spaceflight

We hypothesize that adaptive changes in how inertial cues from the vestibular system are integrated with other sensory information leads to perceptual disturbances and impaired manual control following transitions between gravity environments. The primary goals of this ongoing post-flight investigation are to quantify decrements in manual control of tilt motion following short-duration spaceflight and to evaluate vibrotactile feedback of tilt as a sensorimotor countermeasure. METHODS. Data is currently being collected on 9 astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation (216 deg/s, <20 cm radius) in a darkened room is utilized to elicit otolith reflexes in the lateral plane without concordant canal or visual cues. A Tilt-Translation Sled (TTS) is capable of synchronizing pitch tilt with fore-aft translation to align the resultant gravitoinertial vector with the longitudinal body axis, thereby eliciting canal reflexes without concordant otolith or visual cues. A simple 4 tactor system was implemented to provide feedback when tilt position exceeded predetermined levels in either device. Closed-loop nulling tasks are performed during random tilt steps or sum-of-sines (TTS only) with and without vibrotactile feedback of chair position. RESULTS. On landing day the manual control performance without vibrotactile feedback was reduced by >30% based on the gain or the amount of tilt disturbance successfully nulled. Manual control performance tended to return to baseline levels within 1-2 days following landing. Root-mean-square position error and tilt velocity were significantly reduced with vibrotactile feedback. CONCLUSIONS. These preliminary results are consistent with our hypothesis that adaptive changes in vestibular processing corresponds to reduced manual control performance following G-transitions. A simple vibrotactile prosthesis improves the ability to null out tilt motion within a limited range of motion disturbances.

Wood, S. J.↗

NASA NTRS2004

Effects of Vestibular Loss on Orthostatic Responses to Tilts in the Pitch Plane

The purpose of this study was to determine the extent to which vestibular loss might impair orthostatic responses to passive tilts in the pitch plane in human subjects. Data were obtained from six subjects having chronic bilateral vestibular loss and six healthy individuals matched for age, gender, and body mass index. Vestibular loss was assessed with a comprehensive battery including dynamic posturography, vestibulo-ocular and optokinetic reflexes, vestibular evoked myogenic potentials, and ocular counterrolling. Head up tilt tests were conducted using a motorized two-axis table that allowed subjects to be tilted in the pitch plane from either a supine or prone body orientation at a slow rate (8 deg/s). The sessions consisted of three tilts, each consisting of20 min rest in a horizontal position, tilt to 80 deg upright for 10 min, and then return to the horizontal position for 5 min. The tilts were performed in darkness (supine and prone) or in light (supine only). Background music was used to mask auditory orientation cues. Autonomic measurements included beat-to-beat recordings of blood pressure (Finapres), heart rate (ECG), cerebral blood flow velocity in the middle cerebral artery (transcranial Doppler), end tidal CO2, respiratory rate and volume (Respritrace), and stroke volume (impedance cardiography). For both patients and control subjects, cerebral blood flow appeared to exhibit the most rapid adjustment following transient changes in posture. Outside of a greater cerebral hypoperfusion in patients during the later stages of tilt, responses did not differ dramatically between the vestibular loss and control subjects, or between tilts performed in light and dark room conditions. Thus, with the 'exception of cerebrovascular regulation, we conclude that orthostatic responses during slow postural tilts are not substantially impaired in humans following chronic loss of vestibular function, a result that might reflect compensation by nonvisual graviceptor inputs (e.g., somatosensory) or other circulatory reflex mechanisms.

Wood, Scott J.↗

DOE OSTI2024

Effect of feed-rod tilting on friction surfacing of steel

During the friction surfacing process, the forge-axial force, rotation rate, and traverse speed of the consumable feed-rod play crucial roles in determining the deposition rate and layer morphology. Although some researchers have studied the enhancement of deposition by introducing a backward tilt relative to the traverse direction, there has been limited investigation into the effects of other tilt orientations. Therefore, this study aims to provide a more comprehensive understanding of feed-rod tilting in friction surfacing. In this investigation, the consumable feed-rod undergoes tilting in four distinct directions: forward, backward, advancing side, and retreating side, each tested at two different tilt angles (1.5° and 3.0°). The results reveal that the feed-rod tilting can influence the deposition dynamics by altering the location and area of the rubbing interface situated between the feed-rod and the substrate. Moreover, the feed-rod tilting can significantly enhance the bond width, deposition rate, and deposition efficiency. The enhancement in deposition efficiency signifies a successful reduction in flash formation. Furthermore, a distinct layered microstructure is evident within each deposition layer, regardless of tilt conditions, indicating the unique deposition process inherent to friction surfacing. Finally, the innovative approach proposed in this study not only offers a straightforward and feasible means to improve deposition rate and efficiency but also expands the potential for constructing more intricate geometries or authentic surfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Magneto-optical Evidence of the Tilting Effect in Coupled Weyl Bands

Theories have revealed the universality of the band tilting effect in topological Weyl semimetals (WSMs) and its implications for the material physical properties. However, the experimental identification of tilted Weyl bands remains less explored. Here, we report the magneto-optical evidence of the tilting effect in WSM niobium phosphide. Specifically, we observe Landau level transitions with rich features that are well reproduced within a model of coupled tilted Weyl points. Our analysis indicates that the tilting effect relaxes the selection rules and leads to transitions that would otherwise be forbidden in the non-tilt case. Additionally, we observe unconventional interband transitions with flat and negative magnetic field dispersions, highlighting the importance of coupling between Weyl points. Our results not only emphasize the significance of the tilting effect in the optical responses of WSMs but also demonstrate magneto-optics as an effective tool for probing the tilting effect in electronic band structures.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Pair momentum dependence of a tilted source in heavy-ion collisions

In noncentral heavy-ion collisions, the particle-emitting source can be tilted away from the beam direction, an effect that becomes particularly significant at collision energies of a few GeV and lower. This phenomenon, manifest itself in many observables such as directed flow, polarization, and vorticity, is therefore important to investigate. Here, in this paper, we study the consistency between the tilt extracted directly from the freeze-out distribution of pions and the tilt parameter obtained using the azimuthally sensitive femtoscopy (asHBT) method. Using the Ultrarelativistic Quantum Molecular Dynamics model, we demonstrate a strong dependence of the tilt parameter extracted with asHBT on the momentum of the particle pair. Considering the experimental challenges in accessing low particle momenta—where the tilt parameter extracted with asHBT closely matches the tilt of the freeze-out distribution of pions—we propose an exponential extrapolation method to obtain the tilt of the entire freeze-out distribution. This approach aims to enhance the accuracy of experimental measurements of tilt in noncentral heavy-ion collisions.

particle correlations & fluctuations↗

DOE OSTI2024

Slant, Fan, and Narrow: The Response of Stellar Streams to a Tilting Galactic Disk

Stellar streams are sensitive tracers of the gravitational potential, which is typically assumed to be static in the inner Galaxy. However, massive mergers like Gaia-Sausage-Enceladus can impart torques on the stellar disk of the Milky Way that result in the disk tilting at rates of up to 10°–20° Gyr –1 . Here, we demonstrate the effects of disk tilting on the morphology and kinematics of stellar streams. Through a series of numerical experiments, we find that streams with nearby apocenters (r apo ≲ 20 kpc) are sensitive to disk tilting, with the primary effect being changes to the stream's on-sky track and width. Interestingly, disk tilting can produce both more diffuse streams and more narrow streams, depending on the orbital inclination of the progenitor and the direction in which the disk is tilting. Our model of Pal 5's tidal tails for a tilting rate of 15° Gyr –1 is in excellent agreement with the observed stream's track and width, and reproduces the extreme narrowing of the trailing tail. We also find that failure to account for a tilting disk can bias constraints on shape parameters of the Milky Way's local dark matter distribution at the level of 5%–10%, with the direction of the bias changing for different streams. Disk tilting could therefore explain discrepancies in the Milky Way's dark matter halo shape inferred using different streams.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2010

Motion Perception and Manual Control Performance During Passive Tilt and Translation Following Space Flight

This joint ESA-NASA study is examining changes in motion perception following Space Shuttle flights and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data has been collected on 5 astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation (216 deg/s) combined with body translation (12-22 cm, peak-to-peak) is utilized to elicit roll-tilt perception (equivalent to 20 deg, peak-to-peak). A forward-backward moving sled (24-390 cm, peak-to-peak) with or without chair tilting in pitch is utilized to elicit pitch tilt perception (equivalent to 20 deg, peak-to-peak). These combinations are elicited at 0.15, 0.3, and 0.6 Hz for evaluating the effect of motion frequency on tilt-translation ambiguity. In both devices, a closed-loop nulling task is also performed during pseudorandom motion with and without vibrotactile feedback of tilt. All tests are performed in complete darkness. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for translation motion perception to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. The results of this study indicate that post-flight recovery of motion perception and manual control performance is complete within 8 days following short-duration space missions. Vibrotactile feedback of tilt improves manual control performance both before and after flight.

Clement, Gilles↗

NASA NTRS2022

A Dynamo Simulation Generating Saturn-Like Small Magnetic Dipole Tilts

Abstract Among planetary dynamos, the magnetic field of Saturn stands out in its exceptional level of axisymmetry. One of its peculiar features is that the magnetic dipole mode is tilted with respect to the planetary rotation axis by only ≈0.007° or less. Numerical dynamo simulations performed in this context have had great difficulty in producing such small dipole tilt angles without introducing ad hoc ingredients such as a latitudinally varying heat flux pattern in the outer layers or stably stratified layers (SSLs). Here we present a numerical dynamo simulation that generates a highly axisymmetric dynamo with a dipole tilt of about ≈0.0008° on average. The model consists of a deep dynamo layer and an overlying low-conductivity layer but without any SSLs. We highlight a novel mechanism where strong differential rotation generated in the atmospheric layer penetrates into the dynamo region, helping to maintain a very small magnetic dipole tilt. Plain Language Summary Saturn's dipole-dominant magnetic field exhibits a very peculiar feature: the dipole component of the planetary magnetic field is tilted by less than ≈0.007° with respect to the planetary spin axis. Numerical simulations performed in this context suggest that if a spatial heat-flux variation is imposed, along with a stably stratified region, on top of an active dynamo layer, then small dipole tilt values can be realized. Here we present a model where extremely small dipole tilt values can be achieved without these ad hoc ingredients. Our simulations demonstrate that dynamo theory allows extremely small dipole tilt values in a relatively simple model configuration.

Rakesh Kumar Yadav↗

NASA NTRS1983

Speed benefits of tilt-rotor designs for LHX

The merits of an advanced helicopter and a tilt rotor aircraft for light utility, scout, and attack roles in combat missions envisioned for the year 2000 and beyond were compared. It is demonstrated that speed has increasing value for 11 different mission classes broadly encompassing the intended LHX roles. Helicopter speeds beyond 250 knots are judged to have lower military worth. Since the tilt rotor concept offers a different cost speed relationship than that of helicopters, assessment of a tilt rotor LHX variant was warranted. The technical parameters of an advanced tilt rotor are stablished. Parameters of representative missions are identified, computed relative value of the tilt rotor LHX are compared to the baseline helicopter, a first-order life cycle estimate for the tilt rotor LHX is established, military worth of the alternative design is computed and the results are evaluated. It is suggested that the tilt rotor is the solution with the greatest capability for meeting the uncertainties of future needs.

Mcdaniel, R. L.↗

NASA NTRS1985

Effects of exercise-heat acclimation on fluid, electrolyte, and endocrine responses during tilt and +Gz acceleration in women and men

Two aspects of prolonged endurance training were investigated: (1) the effects of exercise-heat acclimation (on a cycle ergometer at 40 C, 42 rh) on orthostatic tolerance (70 deg head-up tilt) and on a +Gz (head-to-foot) acceleration tolerance of male and female subjects; and (2) comparison of their fluid-electrolyte shifts and hormonal (plasma epinephdrine, norepinephrine, renin, and vasopressin) responses during tilting and centrifugation. The adaptive responses during the 12 d, 2-h acclimation did not alter acceleration tolerance of either men or women, or the women's tilt tolerance, but did increase men's tilt tolerance from 30.4 min before to 58.3 min after acclimation. The patterns of fluid, electrolyte, and protein shifts at tolerance in acceleration and tilting tests were virtually the same in men and women. On the other hand, the hormonal plasma epinephrine, norepinephrine, renin, and vasopressin resonses displayed different shift patterns during acceleration and tilting. It is concluded that the responses to tilting cannot be used to predict responses to acceleration. Future experiments for relating the orthostatic and the acceleration tolerances, and the practical questions of the training regimens for future astronauts are discussed.

Greenleaf, J. E.↗

NASA NTRS1985

A strategy for advancing tilt-rotor technology

Tilt-rotor technology has many features which make it a very promising development in aviation which might have application to a wide variety of transportation and logistics situations. However, aside from military applications and rather specialized industrial applications, little is known regarding the potential of tilt-rotor for commercial transportation and hence it is difficult to plan a development program which would gain support and be likely to produce a stream of significant benefits. The purpose is to attempt to provide some of this information in a manner that would be useful for preparing a strategy for development of tilt-rotor aircraft technology. Specifically, the objectives were: to identify promising paths of development and deployment of tilt-rotor aircraft technology in the air transportation system considering both benefits and disbenefits, and to identify any particular groups that are likely to benefit significantly and propose plans for gaining their support of research and development of this technology. Potential advantages of the tilt-rotor technology in the context of air transportation as a door-to-door system were identified, and then promising paths of development of such tilt-rotor systems were analyzed. These then lead to recommendations for specific studies, information dissemination and development of awareness of the tilt-rotor among specific transport-related groups.

Morlok, Edward K.↗

NASA NTRS1989

The effects of dipole tilt on magnetotail structure and dynamics

A three-dimensional time-dependent global magnetohydrodynamic (MHD) model of the interaction between the solar wind and the earth's magnetosphere has been used to study the effects of dipole tilt on the structure and dynamics of the magnetotail. The location of the tail neutral sheet shifts in the north-south direction following changes in the dipole tilt. When the northern edge of the geomagnetic dipole is tilted toward the sun (positive tilt), it is above the geocentric solar magnetosphere (GSM) equator, while for negative tilt, it is below. The neutral sheet forms an arc across the tail in the y-z plane for nonzero tilt. For positive tilt, the neutral sheet rises above the GSM equatorial plane near the noon-midnight meridian and returns to the equator near the magnetopause. The position and shape of the neutral sheet result from the requirement that the earthward magnetic flux equals the tailward flux and can be well explained by a simple analytical model.

Walker, Raymond J.↗

NASA NTRS1991

Vertical tilts of tropospheric waves - Observations and theory

Two methods are used to investigate the vertical tilts of planetary waves as functions of zonal wavenumber and frequency. The vertical tilts are computed by cross-spectral analysis of the geopotential heights at different pressures. In the midlatitude troposphere, the eastward-moving waves had a westward tilt with height, as expected, but the westward-moving waves with frequencies higher than 0.2/d showed statistically significant eastward vertical tilts. For a free Rossby wave, this implies that the Eliassen-Palm flux is downward along with its energy propagation. A downward energy propagation suggests an upper-level source of these waves. It is proposed that the eastward-tilting waves were forced by the nonlinear interaction of stationary waves and baroclinically unstable cyclone-scale waves. The predicted vertical tilt and phase speed were consistent with the observations. In addition, simulations of a general circulation model were analyzed. In the control run, eastward-tilting waves disappeared when the sources of stationary waves were removed. This is consistent with the present theory.

Ebisuzaki, Wesley↗