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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

A Layered Debris Disk around M Star TWA 7 in Scattered Light

We have obtained Hubble Space Telescope (HST) coronagraphic observations of the circumstellar disk around M star TWA 7 using the Space Telescope Imaging Spectrograph (STIS) instrument in visible light. Together with archival observations, including HST/NICMOS using the F160W filter and Very Large Telescope/SPHERE at the H-band in polarized light, we investigate the system in scattered light. By studying this nearly face-on system using geometric disk models and Henyey–Greenstein phase functions, we report a new discovery of a tertiary ring and a clump. We identify a layered architecture: three rings, a spiral, and an ≈150 au 2 elliptical clump. The most extended ring peaks at 28 au, and the other components are on its outskirts. Our point-source detection-limit calculations demonstrate the necessity of disk modeling in imaging fainter planets. Morphologically, we witness a clockwise spiral motion, and the motion pattern is consistent with both solid body motion and local Keplerian motion; we also observe underdensity regions for the secondary ring that might result from mean-motion resonance or moving shadows: both call for re-observations to determine their nature. Comparing multi-instrument observations, we obtain blue STIS-NICMOS color, a STIS-SPHERE radial distribution peak difference for the tertiary ring, and a high SPHERE-NICMOS polarization fraction; these aspects indicate that TWA 7 could retain small dust particles. By viewing the debris disk around M star TWA 7 at a nearly face-on vantage point, our study allows for the understanding of such disks in scattered light in both system architecture and dust property.

Debris disks↗
DOE OSTI2021

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Aging of galaxies along the morphological sequence, marked by bulge growth and disk quenching

Aims: We revisit the color bimodality of galaxies using the extensive EFIGI morphological classification of nearby galaxies. Methods: The galaxy profiles from the Sloan Digital Sky Survey (SDSS) gri images were decomposed as a bulge and a disk by controlled profile modeling with the Euclid SourceXtractor++ software. The spectral energy distributions from our resulting gri SDSS photometry complemented with Galaxy Evolution Explorer (GALEX) NUV photometry were fitted with the ZPEG software and PEGASE.2 templates in order to estimate the stellar masses and specific star formation rates (sSFR) of whole galaxies as well as their bulge and disk components. Results: The absolute NUV-r color versus stellar mass diagram shows a continuous relationship between the present sSFR of galaxies and their stellar mass, which spans all morphological types of the Hubble sequence monotonously. Irregular galaxies to intermediate-type Sab spirals make up the “Blue Cloud” across 4 orders of magnitude in stellar mass but a narrow range of sSFR. This mass build-up of spiral galaxies requires major mergers, in agreement with their frequently perturbed isophotes. At high mass, the Blue Cloud leads to the “Green Plain”, dominated by S0a and Sa early-type spirals. It was formerly called the “Green Valley”, due to its low density, but we rename it because of its wide stretch and nearly flat density over ~2 mag in NUV-r color (hence sSFR), despite a limited range of stellar mass (1 order of magnitude). The Green Plain links up the “Red Sequence”, containing all lenticular and elliptical galaxies with a 2 order of magnitude mass interval, and systematically higher masses for the ellipticals. We confirm that the Green Plain cannot be studied using u - r optical colors because it is overlayed by the Red Sequence, hence NUV data are necessary. Galaxies across the Green Plain undergo a marked growth by a factor 2 to 3 in their bulge-to-total mass ratio and a systematic profile change from pseudo to classical bulges, as well as a significant reddening due to star formation fading in their disks. The Green Plain is also characterized by a maximum stellar mass of 10 11.7 M ⊙ beyond which only elliptical galaxies exist, hence supporting the scenario of ellipticals partly forming by major mergers of massive disk galaxies. Conclusions: The EFIGI attributes indicate that dynamical processes (spiral arms and isophote distortions) contribute to the scatter of the Main Sequence of star-forming galaxies (Blue Cloud), via the enhancement of star formation (flocculence, HII regions). The significant bulge growth across the Green Plain confirms that it is a transition region, and excludes a predominantly quick transit due to rapid quenching. The high frequency of bars for all spirals as well as the stronger spiral arms and flocculence in the knee of the Green Plain suggest that internal dynamics, likely triggered by flybys or (mainly minor) mergers, may be the key to the bulge growth of massive disk galaxies, which is a marker of the aging of galaxies from star forming to quiescence. The Hubble sequence can then be considered as an inverse sequence of galaxy physical evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Dissolution of Additively Manufactured Mo Disks and Structures for Accelerator Based Production of Mo-99

The press-and-sinter approach for production of Mo targets has been successfully tested and demonstrated. The main advantage of this process is that it uses readily available technology and tools that have been tuned for production of various metal and metal oxide targets. However, certain target design specifications, such as dimensional accuracy of the diameter and thickness of the disks, are required for proper fit into a target holder and therefore place strict tolerances on sintered Mo disks intended for accelerator production. Furthermore, having a target composed of multiple disks poses certain challenges for post-irradiation processing, where there is a potential for spillage of individual disks during the manipulation for dissolution inside a processing hot cell. Additive manufacturing (AM), also referred to as 3D printing, provides capabilities to design and build a single-piece Mo target that provides the opportunity for better geometry for optimized production of Mo-99, improved cooling capability, and safer post-irradiation handling. A drawback of AM Mo structures is roughness of finished surfaces, which could reduce the effectiveness of gas cooling systems. Process development for AM Mo structures using selective laser melting is described in work by Gibson and Lowden. For post-irradiation processing, it is important to look at the dissolution behavior of AM Mo structures in comparison to readily dissolved press-and-sinter Mo targets. The dissolution behavior of press-and-sinter targets has been well documented in our previous reports. In this report, we discuss results of dissolution experiments conducted with AM Mo disks and structures (provided by Oak Ridge National Laboratory [ORNL]) in 50% hydrogen peroxide (H 2 O 2 ).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Characterize the Rings in Protoplanetary Disks Formed by an Eccentric Instability [Slides]

Typical long-term time evolution of gas surface density in a disk undergoing eccentric mode instability (EMI). In a disk with no initial substructures or external perturbers, EMI generates a growing one arm spiral (top right). After EMI saturates, the disk continues to evolve with a long-lived coherent eccentric pattern. If the disk has strong wave damping, the disk is then left with circular rings. Synthesized dust continuum images of some EMI simulations from this IC project show some characteristics similar to the actual PPD images.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Testing of Helium Cooled Metal Molybdenum Disk Target System

NorthStar Medical Radioisotopes LLC is planning to produce the important medical radioisotope molybdenum-99 (Mo-99) through a photonuclear reaction on molybdenum-100 (Mo-100). In this approach, multiple thin disks of enriched molybdenum metal will be bombarded with a 40-MeV electron beam. Because enriched Mo-100 is expensive, we intend to use as much beam power as possible to achieve maximum production yield and minimize the size of the target. This requirement leads to very high beam power density (heat deposition in the target), which sets challenging requirements for cooling. Together with scientists at Los Alamos National Laboratory, a team at Argonne National Laboratory has developed and demonstrated a cooling approach using pressurized helium, which allows for efficient heat removal. One of the challenges in this approach is the management of the heat load on the target window. The target window separates the high-pressure helium atmosphere inside the target from the vacuum in the beamline, so it is constantly under stress from differential pressure. Also, the window is cooled only by the helium gas flow from one side, making the window design challenging. High heat deposition in the target disks also imposes a strict requirement on performance of the helium cooling system and thickness of the target disks. The target disks are produced from metal powder via a press-and-sinter process. The resulting disks do not possess as high a tensile strength as solid molybdenum and might not survive the vibration from the high-velocity helium coolant and the high thermal stress from beam heating.

42 ENGINEERING↗
DOE OSTI2020

Probing UV-sensitive Pathways for CN and HCN Formation in Protoplanetary Disks with the Hubble Space Telescope

The UV radiation field is a critical regulator of gas-phase chemistry in surface layers of disks around young stars. In an effort to understand the relationship between photocatalyzing UV radiation fields and gas emission observed at infrared and submillimeter wavelengths, we present an analysis of new and archival Hubble Space Telescope (HST), Spitzer, ALMA, IRAM, and SMA data for five targets in the Lupus cloud complex and 14 systems in Taurus-Auriga. The HST spectra were used to measure Lyα and far-UV (FUV) continuum fluxes reaching the disk surface, which are responsible for dissociating relevant molecular species (e.g., HCN, N{sub 2}). Semi-forbidden C ii] λ2325 and UV-fluorescent H{sub 2} emission were also measured to constrain inner disk populations of C{sup +} and vibrationally excited H{sub 2}. We find a significant positive correlation between 14 μm HCN emission and fluxes from the FUV continuum and C ii] λ2325, consistent with model predictions requiring N{sub 2} photodissociation and carbon ionization to trigger the main CN/HCN formation pathways. We also report significant negative correlations between submillimeter CN emission and both C ii] and FUV continuum fluxes, implying that CN is also more readily dissociated in disks with stronger FUV irradiation. No clear relationships are detected between either CN or HCN and Lyα or UV-H{sub 2} emission. This is attributed to the spatial stratification of the various molecular species, which span several vertical layers and radii across the inner and outer disk. We expect that future observations with the James Webb Space Telescope will build on this work by enabling more sensitive IR surveys than were possible with Spitzer.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Three New Late-type Stellar Companions to Very Dusty WISE Debris Disks Identified with SPHERE Imaging

Debris disk stars are good targets for high-contrast imaging searches for planetary systems, since debris disks have been shown to have a tentative correlation with giant planets. We selected 20 stars identified as debris disk hosts by the WISE mission, with particularly high levels of warm dust. We observed these with the VLT/SPHERE high-contrast imaging instrument with the goal of finding planets and imaging the disks in scattered light. Our survey reaches a median 5σ sensitivity of 10.4 M {sub J} at 25 au and 5.9 M {sub J} at 100 au. We identified three new stellar companions (HD 18378B, HD 19257B, and HD 133778B): two are mid-M-type stars and one is a late-K or early-M star. Three additional stars have very widely separated stellar companions (all at >2000 au) identified in the Gaia catalog. The stars hosting the three SPHERE-identified companions are all older (≳700 Myr), with one having recently left the main sequence and one a giant star. We infer that the high volumes of dust observed around these stars has been caused by a recent collision between the planets and planetesimal belts in the system, although for the most evolved star, mass loss could also be responsible for the infrared excess. Future mid-infrared spectroscopy or polarimetric imaging may allow the positions and spatial extent of these dust belts to be constrained, thereby providing evidence as to the true cause of the elevated levels of dust around these old systems. None of the disks in this survey is resolved in scattered light.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

The Rarity of Very Red Trans-Neptunian Objects in the Scattered Disk

We investigate the origins of the photometrically very red (VR) and less red (LR) trans-Neptunian objects (TNOs). We first reanalyze the data set of Marsset et al. and find that in addition to the known color–inclination correlation in hot TNOs, a similar trend exists for color–eccentricity. We show that VR TNOs are sharply constrained to eccentricities <0.42 and inclinations <21°, leading to a paucity of VR scattered disk and distant mean motion resonance objects. We then interpret these findings using N-body simulations accounting for Neptune’s outward migration into a massless particles disk and find that these observations are best reproduced with an LR-to-VR color transition line between ∼38 and 42 au in the primordial disk, separating the objects’ formation locations. For an initial surface density profile (Σ ∝ 1/r {sup 2}), a color transition around 38 au is needed to explain the high abundance of VR plutinos, but it creates too many VR scattered disk objects, while a transition line around 42 au seems to better reproduce the scattered disk colors but creates virtually no VR plutinos. Our simulations furthermore show that the rarity of VR particles at high eccentricity is possibly due to the absence of sweeping higher-order MMRs, and secular resonances, beyond 42 au. Inspecting individual populations, we show that the majority of VR SDOs originate as objects trapped in Neptune’s second- and third-order MMRs. These then evolve due to diffusion, scattering, Kozai–Lidov cycles, and secular resonances into their current orbits. Future unbiased color surveys are crucial to better constrain the TNOs dynamical origins.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Seeking Echoes of Circumstellar Disks in Kepler Light Curves

Light echoes of flares on active stars offer the opportunity for direct detection of circumstellar dust. We revisit the problem of identifying faint echoes in postflare light curves, focusing on debris disks from ongoing planet formation. Starting with simulations, we develop an algorithm for estimating the radial extent and total mass from disk echo profiles. We apply this algorithm to light curves from over 2100 stars observed by NASA’s Kepler mission, selected for multiple short-lived flares in either the long-cadence or short-cadence data sets. While flux uncertainties in light curves from individual stars preclude useful mass limits on circumstellar disks, catalog-averaged light curves yield constraints on disk mass that are comparable to estimates from known debris disks. The average mass in micron- to millimeter-sized dust around the Kepler stars cannot exceed 10% of an Earth mass in exo-Kuiper belts or 10% of a lunar mass in the terrestrial zone. We group stars according to IR excess, based on WISE W1–W3 color, as an indicator for the presence of circumstellar dust. The mass limits are greater for stars with strong IR excess, a hint that echoes are lurking not far beneath the noise in postflare light curves. With increased sensitivity, echo detection will let time-domain astronomy complement spectroscopic and direct-imaging studies in mapping how, when, and where planets form.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Observational Signatures of Planets in Protoplanetary Disks: Temperature Structures in Spiral Arms

High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with β cooling to a vertically stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3%–3% inside the planet radius but always < 0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic PdV work, which introduces a ~10%–20% perturbation within a factor of ~2 from the planet’s orbital radius. We devise an empirical fit of the spiral amplitude Δ(T)=(M{sub p}/M{sub th}){sup c}(f{sub PdV}e{sup -t{sub a}{sub r}{sub m}/t{sub c}}+f{sub rad}) to take into account both effects. Where cooling is slow, we find also that temperature perturbations from buoyancy spirals—a strictly 3D, nonisothermal phenomenon—become nearly as strong as those from Lindblad spirals, which are amenable to 2D and isothermal studies. Our findings may help explain observed thermal features in disks like TW Hydrae and CQ Tauri, and underscore that 3D effects have a qualitatively important effect on disk structure.

42 ENGINEERING↗
DOE OSTI2021

Circumbinary Disk Accretion into Spinning Black Hole Binaries

Supermassive black hole binaries are likely to accrete interstellar gas through a circumbinary disk. Shortly before merger, the inner portions of this circumbinary disk are subject to general relativistic effects. To study this regime, we approximate the spacetime metric of close orbiting black holes by superimposing two boosted Kerr–Schild terms. After demonstrating the quality of this approximation, we carry out very long-term general relativistic magnetohydrodynamic simulations of the circumbinary disk. We consider black holes with spin dimensionless parameters of magnitude 0.9, in one simulation parallel to the orbital angular momentum of the binary, but in another anti-parallel. These are contrasted with spinless simulations. We find that, for a fixed surface mass density in the inner circumbinary disk, aligned spins of this magnitude approximately reduce the mass accretion rate by 14% and counter-aligned spins increase it by 45%, leaving many other disk properties unchanged.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Role of Strong Magnetic Fields in Stabilizing Highly Luminous Thin Disks

Abstract We present and analyze a set of three-dimensional, global, general relativistic radiation magnetohydrodynamic simulations of thin, radiation-pressure-dominated accretion disks surrounding a nonrotating, stellar-mass black hole. The simulations are initialized using the Shakura–Sunyaev model with a mass accretion rate of M ̇ = 3 L Edd / c 2 (corresponding to L = 0.17 L Edd ). Our previous work demonstrated that such disks are thermally unstable when accretion is driven by an α -viscosity. In the present work, we test the hypothesis that strong magnetic fields can both drive accretion through magnetorotational instability and restore stability to such disks. We test four initial magnetic field configurations: (1) a zero-net-flux case with a single, radially extended set of magnetic field loops (dipole), (2) a zero-net-flux case with two radially extended sets of magnetic field loops of opposite polarity stacked vertically (quadrupole), (3) a zero-net-flux case with multiple radially concentric rings of alternating polarity (multiloop), and (4) a net-flux, vertical magnetic field configuration (vertical). In all cases, the fields are initially weak, with a gas-to-magnetic pressure ratio ≳100. Based on the results of these simulations, we find that the dipole and multiloop configurations remain thermally unstable like their α -viscosity counterpart, in our case collapsing vertically on the local thermal timescale and never fully recovering. The vertical case, on the other hand, stabilizes and remains so for the duration of our tests (many thermal timescales). The quadrupole case is intermediate, showing signs of both stability and instability. The key stabilizing factor is the ability of specific field configurations to build up and sustain strong, P mag ≳ 0.5 P tot , toroidal fields near the midplane of the disk. We discuss the reasons why certain configurations are able to do this effectively and others are not. We then compare our stable simulations to the standard Shakura–Sunyaev disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Contracting and Expanding Binary Black Holes in 3D Low-mass AGN Disks: The Importance of Separation

LIGO/Virgo has detected several binary black hole (BBH) merger events that may have originated in the accretion disks of active galactic nuclei (AGNs). These events require individual black hole masses that fall within the pair instability supernova mass gap, and therefore these black holes may have been grown from hierarchical mergers. AGN disks are a prime environment for hierarchical mergers and thus a potential location for the progenitors of BBH gravitational wave events. Understanding how a BBH embedded in an AGN disk interacts with the surrounding environment is thus crucial for determining whether this interaction can lead to its merger. However, there are few high-fidelity simulations of this process, and almost all are two-dimensional. We present the results from 3D, high-resolution, local shearing-box simulations of an embedded BBH interacting with an AGN disk. In these first simulations of their kind, we focus on determining the mass accretion rate and the orbital evolution rate at different BBH separations. We find that circular, equal-mass BBHs with separations greater than 10% of their Hill radius contract while accreting at a super-Eddington rate. At smaller separations, however, our 3D simulations find that BBHs expand their orbits. This result suggests that it may be difficult for an AGN disk to push a BBH to merger, but we discuss several mechanisms, including MHD turbulence and radiative and mechanical feedback, which could alleviate this difficulty.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Semi-analytical Model for Stellar Evolution in AGN Disks

Disks of gas accreting onto supermassive black holes may host numerous stellar-mass objects, formed within the disk or captured from a nuclear star cluster. We present a simplified model of stellar evolution in these dense environments, which exhibits exceptional agreement with full stellar evolution calculations at a minuscule fraction of the cost. Although the model presented here is limited to stars burning hydrogen in their cores, it is sufficient to determine the evolutionary fate of disk-embedded stars: whether they proceed to later stages of nuclear burning and leave behind a compact remnant, reach a quasi-steady state where mass loss and accretion balance one another, or whether accretion proceeds faster than stellar structure can adjust, causing a runaway. We highlight how various disk parameters and phenomena such as gap opening affect stellar evolution outcomes. We also highlight how our model can accommodate time-varying conditions, such as those experienced by a star on an eccentric orbit, and can couple to N -body integrations. This model will enable more detailed studies of stellar populations and their interaction with accretion disks than have previously been possible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An Electron-scattering Time Delay in Black Hole Accretion Disks

Abstract Universal to black hole X-ray binaries, the high-frequency soft lag gets longer during the hard-to-intermediate state transition, evolving from ≲1 to ∼10 ms. The soft lag production mechanism is thermal disk reprocessing of nonthermal coronal irradiation. X-ray reverberation models account for the light-travel time delay external to the disk, but assume instantaneous reprocessing of the irradiation inside the electron-scattering-dominated disk atmosphere. We model this neglected scattering time delay as a random walk within an α -disk atmosphere, with approximate opacities. To explain soft lag trends, we consider a limiting case of the scattering time delay that we dub the thermalization time delay, t th ; this is the time for irradiation to scatter its way down to the effective photosphere, where it gets thermalized, and then scatter its way back out. We demonstrate that t th plausibly evolves from being inconsequential for low mass accretion rates m ̇ characteristic of the hard state, to rivaling or exceeding the light-travel time delay for m ̇ characteristic of the intermediate state. However, our crude model confines t th to a narrow annulus near peak accretion power dissipation, so cannot yet explain in detail the anomalously long-duration soft lags associated with larger disk radii. We call for time-dependent models with accurate opacities to assess the potential relevance of a scattering delay.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Fragmentation in Gravitationally Unstable Collapsar Disks and Subsolar Neutron Star Mergers

Abstract Although stable neutron stars (NSs) can in principle exist down to massesM ns ≈ 0.1M ⊙ , standard models of stellar core-collapse predict a robust lower limitM ns ≳ 1.2M ⊙ , roughly commensurate with the Chandrasekhar massM Ch of the progenitor’s iron core (electron fractionY e ≈ 0.5). However, this limit may be circumvented in sufficiently dense neutron-rich environments (Y e < 0.5) for which M Ch ∝ Y e 2 is reduced to ≲1M ⊙ . Such physical conditions could arise in the black hole accretion disks formed from the collapse of rapidly rotating stars (“collapsars”), as a result of gravitational instabilities and cooling-induced fragmentation, similar to models for planet formation in protostellar disks. We confirm that the conditions to form subsolar-mass NS (ssNS) may be marginally satisfied in the outer regions of massive neutrino-cooled collapsar disks. If the disk fragments into multiple ssNSs, their subsequent coalescence offers a channel for precipitating subsolar mass LIGO/Virgo gravitational-wave mergers that does not implicate primordial black holes. The model makes several additional predictions: (1) ∼Hz frequency Doppler modulation of the ssNS-merger gravitational-wave signals due to the binary’s orbital motion in the disk; (2) at least one additional gravitational-wave event (coincident within ≲hours), from the coalescence of the ssNS-merger remnant(s) with the central black hole; (3) an associated gamma-ray burst and supernova counterpart, the latter boosted in energy and enriched withr-process elements from the NS merger(s) embedded within the exploding stellar envelope (“kilonovae inside a supernova”).

Astronomy & Astrophysics↗
NASA NTRS1975

Turbulent flow between a rotating disk and a parallel wall

A scalar effective viscosity method is used to calculate the incompressible flow in the gap between two infinite, parallel smooth disks, one of them rotating and the other stationary. The flow is calculated for two values of the gap Reynolds number omega(s squared)/nu, namely 296 and 2852, where omega is the disk angular velocity, s the gap width, and nu the kinematic viscosity of the fluid; and over a range of radial Reynolds number omega(r squared)/nu from 0 to 10 million, where r is the radius from the axis of rotation. A numerical shooting technique is used to match the two boundary-layer flows arising on the disk and wall. Gradual transition is assumed for radial Reynolds numbers from 160,000 to 250,000. The results are in good agreement with Daily and Nece's measurements of velocity profiles and disk friction drag for enclosed rotating disks, and at sufficiently large radius the local skin friction approaches that of turbulent Couette flow.

Cooper, P.↗