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Showing papers by "Ames Research Center published in 1981"


Journal ArticleDOI
TL;DR: The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one as mentioned in this paper, which readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum.

2,042 citations


Journal ArticleDOI
TL;DR: The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work and has an important effect on the application of implicit finite-difference schemes to vector processors.

1,232 citations


01 Sep 1981
TL;DR: In this article, the results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy in an incompressible fluid subjected to uniform deformation or rotation are compared with linear theory and experimental data.
Abstract: The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

993 citations


Journal ArticleDOI
TL;DR: Efficient, numerically stable, methods for the calculation of light-scattering intensity functions for concentrically coated spheres are discussed and are accurate for all refractive indices, for large and small particles, and for cores with any relative size.
Abstract: Efficient, numerically stable, methods for the calculation of light-scattering intensity functions for concentrically coated spheres are discussed. Earlier forms of these equations are subject to various numerical difficulties which give rise to significant errors, especially for thin absorbing shells. The present equations are accurate for all refractive indices, for large and small particles, and for cores with any relative size.

491 citations


Proceedings ArticleDOI
01 Jan 1981
TL;DR: In this paper, a second-order accurate method for solving viscous flow equations has been proposed that preserves conservation form, requires no block or scalar tridiagonal inversions, is simple and straightforward to program (estimated 10% modification for the update of many existing programs), and should easily adapt to current and future computer architectures.
Abstract: Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.

427 citations


Journal ArticleDOI
TL;DR: The climatic effects of these absorbing aeorosols are computed using a simple one-layer model, and the results suggest that heating rates in urban pollution layers may be of the order of 4 K/day.
Abstract: Recent measurements of the single-scattering albedo omega(0) of tropospheric aerosols indicate the presence of a strongly absorbing material which has tentatively been identified as graphitic carbon (soot). Theoretical calculations, based on several different models of the way in which soot might be mixed with other aerosol materials, show that a minimum of 20% soot by volume is necessary to achieve the observed urban value of omega(0) = 0.6. Rural values of the order of 0.8 can be accounted for with 1-5% soot by volume. These same values of omega can be produced by similar amounts of the iron oxide magnetite, which is shown to be virtually indistinguishable from soot by optical measurements performed on bulk samples. Calculations of phase functions for various mixtures of soot also indicate the difficulty of determining aerosol composition by optical scattering techniques. The climatic effects of these absorbing aeorosols are computed using a simple one-layer model, and the results suggest that heating rates in urban pollution layers may be of the order of 4 K/day.

404 citations


01 Mar 1981
TL;DR: In this paper, the general features of dynamic stall on oscillating airfoils are explained in terms of the vortex shedding phenomenon, and the important differences between static stall, light dynamic stall, and deep stall are described.
Abstract: The general features of dynamic stall on oscillating airfoils are explained in terms of the vortex shedding phenomenon, and the important differences between static stall, light dynamic stall, and deep stall are described. An overview of experimentation and prediction techniques is given.

399 citations


Journal ArticleDOI
01 Dec 1981-Icarus
TL;DR: In this paper, an analysis of the hydrodynamic aspects of the growth of protostellar disks from the accretion of a rotating gas cloud is presented, including the special case where the disk is very thin.

384 citations


Journal ArticleDOI
TL;DR: In this paper, an autoregressive (AR) model was used to analyze the optical light curve of the quasar 3C 273, and the best AR model was determined from sampled data and transformed to an MA for interpretation.
Abstract: Random process models phased in the time domain are used to analyze astrophysical time series data produced by random processes. A moving average (MA) model represents the data as a sequence of pulses occurring randomly in time, with random amplitudes. An autoregressive (AR) model represents the correlations in the process in terms of a linear function of past values. The best AR model is determined from sampled data and transformed to an MA for interpretation. The randomness of the pulse amplitudes is maximized by a FORTRAN algorithm which is relatively stable numerically. Results of test cases are given to study the effects of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the optical light curve of the quasar 3C 273 is given.

284 citations


Journal ArticleDOI
TL;DR: The hypothesis that with exercise, AVP release is a primary factor for fluid and electrolyte regulation as it is highly correlated with the plasma hyperosmolality produced by a net hypotonic plasma efflux is supported.
Abstract: Plasma volume (PV), renin activity (PRA), and osmotic (Osm), sodium (Na+), and arginine vasopressin (AVP) concentrations were measured in venous blood samples taken before and after three levels of cycle ergometer exercise (100, 175, and 225 W) in 15 young male volunteers. Plasma volume and solute concentrations changed significantly (P less than 0.05, denoted by *) with work intensity. The % delta PV was -3.7%* at 100 W, -8.8%* at 175 W, and -12.4%* at 225 W. Plasma Na+ concentration, Osm, and AVP increase were curvilinear with graded exercise and were significant only when work intensity exceeded 40% VO2max. PRA increase was linear and significant at all work levels. The % delta PV was significantly correlated with delta Osm (r = 0.99*) and delta Na+ (r = 0.89*) but had low correlations with delta AVP (r = 0.22, NS) and delta PRA (r = 0.12, NS). However, delta AVP was significantly correlated with delta Na+ (r = 0.86*) and delta Osm (r = 0.83*), whereas delta PRA had low correlations with delta Na+ (r = 0.33, NS), delta Osm (r = 0.29, NS), and delta AVP (r = 0.43, NS). The data support the hypothesis that a) with exercise, AVP release is a primary factor for fluid and electrolyte regulation as it is highly correlated with the plasma hyperosmolality produced by a net hypotonic plasma efflux; b) an exercise intensity greater than 40% VO2max is required to change plasma osmolality and, thus, stimulate significant AVP release; and c) the stimulation of the renin-angiotensin system is a more general stress response, which responds to increasing sympathetic nervous activity.

256 citations


Journal ArticleDOI
TL;DR: In this article, the free vibration of rotating beams is analyzed by means of a finite-element method of variable order, where the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series.
Abstract: The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.

Journal ArticleDOI
27 Aug 1981-Nature
TL;DR: Isotopic measurements of individual geothermal hydrocarbons that are, as a group, of higher molecular weight than methane are reported in this paper, and it is believed in light of this data that the principal source of hydro-carbons in four geothermal areas in western North America is the thermal decomposition of sedimentary or groundwater organic matter.
Abstract: Isotopic measurements of individual geothermal hydrocarbons that are, as a group, of higher molecular weight than methane are reported. It is believed in light of this data that the principal source of hydrocarbons in four geothermal areas in western North America is the thermal decomposition of sedimentary or groundwater organic matter.

Journal ArticleDOI
TL;DR: In this paper, the dynamic stall characteristics of eight airfoils have been investigated in sinusoidal pitch oscillations over a wide range of two-dimensional unsteady flow conditions.
Abstract: : The dynamic stall characteristics of eight airfoils have been investigated in sinusoidal pitch oscillations over a wide range of two-dimensional unsteady flow conditions. The results provide a unique comparison of the effects of section geometry in a simulated rotor environment. Important differences between the various airfoils were observed, particularly when the stall regimes were penetrated only slightly. Under these circumstances, the profiles that stall gradually from the trailing edge appear to offer an advantage. However, all of the airfoils tended increasingly toward leading-edge stall when both the severity of dynamic stall and the free-stream Mach number increased. In all cases, the parameters of the unsteady motion appear to be more important than airfoil geometry for configurations that are appropriate for helicopter rotors. (Author)

Journal ArticleDOI
Joseph Katz1
TL;DR: In this article, a discrete vortex method was used to analyze the separated non-steady flow about a cambered airfoil, where the chordwise location of the separation point was assumed to be known from experiments or flow-visualization data.
Abstract: A discrete vortex method was used to analyze the separated non-steady flow about a cambered airfoil. The foil flow modelling is based on the thin lifting-surface approach, where the chordwise location of the separation point is assumed to be known from experiments or flow-visualization data. Calculated results provided good agreement when compared with the post-stall aerodynamic data of two airfoils. Those airfoil sections differed in the extent of travel of the separation point with increasing angle of attack. Furthermore, the periodic wake shedding was analyzed and its time-dependent influence on the airfoil was investigated.

Journal ArticleDOI
TL;DR: In this paper, a three-layer general circulation model of the Martian atmosphere is described, and the assumptions governing the model are discussed; the simulated, zonally averaged circulation is found to have only limited sensitivity to differences between this model and an earlier generative model; this circulation compares reasonably well with observations.
Abstract: A three-layer general circulation model of the Martian atmosphere is described, and the assumptions governing the model are discussed. The simulated, zonally averaged circulation is found to have only limited sensitivity to differences between this model and an earlier general circulation model; this circulation compares reasonably well with observations. It is also found that the meridional mass flow produced by the seasonal condensation of CO2 in the winter polar region has a major influence on the circulation; owing to the weak influence of atmospheric heat transport, however, the mass flow is governed almost entirely by radiation. Quasi-barotropic stationary waves, which are forced kinematically by the topography and which resemble topographically forced terrestrial planetary waves, are generated by the model in the winter hemisphere region of strong eastward flow, while baroclinic stationary waves are thermally forced by topography in the tropics and summer subtropics. It is also concluded that transient baroclinically unstable waves, of somewhat lower dominant wavenumber than those found on the earth, are generated in winter midlatitudes; their amplitudes, wavenumbers, and phase speeds closely agree with what has been deduced from the Viking lander observations.

Proceedings ArticleDOI
01 Jun 1981
TL;DR: PAN AIR as mentioned in this paper is a computer program for predicting subsonic or supersonic linear potential flow about arbitrary configurations using linear source and quadratic doublet strength distributions.
Abstract: PAN AIR is a computer program for predicting subsonic or supersonic linear potential flow about arbitrary configurations. It uses linear source and quadratic doublet strength distributions. These higher-order distributions have been implemented in a manner that greatly reduces the numerical stability problems that have plagued earlier attempts to make surface paneling methods work successfully for supersonic flow. PAN AIR's problem-solving capability, numerical approach, modeling features, and program architecture are described. Numerical results are presented for a variety of geometries at supersonic Mach numbers.

Journal ArticleDOI
01 Oct 1981-Nature
TL;DR: Observations on fine structure, metabolic enzymes and stable isotope ratios of several species of Pogonophora from a wide range of habitats suggest that members of this enigmatic phylum of worm-like deep-sea animals use internal chemoauto -trophic bacteria as part of their nutrition, allowing them to exploit scarce nutrient and energy resources.
Abstract: Observations on fine structure, metabolic enzymes and stable isotope ratios of several species of Pogonophora from a wide range of habitats suggest that members of this enigmatic phylum of worm-like deep-sea animals use internal chemoauto -trophic bacteria as part of their nutrition, allowing them to exploit scarce nutrient and energy resources.

Journal ArticleDOI
TL;DR: In this paper, the authors characterized carbonaceous HF/HCl-resistant residues from the Allende meteorite by SEM/EDXA, X-ray diffraction, INAA, C, S, H, N, and noble gas analyses.

Journal ArticleDOI
01 Jun 1981
TL;DR: Theoretical studies in the intensity-borrowing sudden approximation of inner-valence-shell photoionization cross sections in N2 and CO are reported in this article, where the required ionic-state energies and spectroscopic amplitudes are obtained from appropriate Green's-function and configuration-interaction calculations, and previously devised Stieltjes-Tchebycheff moment-theory techniques are employed in determinations of corresponding continuum dipole transition moments in the static-exchange approximation.
Abstract: Theoretical studies in the intensity-borrowing sudden approximation are reported of inner-valence-shell photoionization cross sections in N2 and CO. The required ionic-state energies and spectroscopic amplitudes are obtained from appropriate Green's-function and configuration-interaction calculations, and previously devised Stieltjes-Tchebycheff moment-theory techniques are employed in determinations of corresponding continuum dipole transition moments in the static-exchange approximation. Comparisons are made of the Green's-function calculations in the two-particle-hole Tamm-Dancoff approximation with wavefunction results obtained from single-excitation and polarization configuration-interaction calculations. Detailed descriptions are given of the calculated spectroscopic intensity distributions and of the hole-particle configurational compositions of the corresponding inner-valence-shell ionic states. and comparisons are made with previously reported wavefunction studies in N2+ and CO+. Spectroscopic assignments are suggested on basis of the present calculations for the strong features observed recently in higher-resolution inner-valence-shell photoelectron spectra. The corresponding calculated partial-channel photoionization cross sections for the designated C2Σg+, F2Σg+, G2Σg+, and (2σg−1)2Σg+ bands in N2 and C2Σ+, D2Π, F2Σ+, G2Σ+, and (3σ−1)2Σ+ bands in CO are found to be in good quantitative accord with dipole (e, 2e), (e, e + ion), and synchrotron-radiation studies.

Journal ArticleDOI
TL;DR: The results of the configuration calculations of six singlet electronic states and one triplet electronic state of CO are presented in this paper, along with potential energy curves, spectroscopic constants, and electron transition moments.
Abstract: The results of the configuration calculations of six singlet electronic states and one triplet electronic state of CO are presented. The potential energy curves, spectroscopic constants, and electron transition moments are calculated, along with electronic dipole moment functions for three states. The self consistent field and configuration calculations used to obtain the electronic wave functions are described. The theoretical results are found to be in good agreement with the experimental measurements, and in the case of the dipole moment function calculations, preferable to them.

Journal ArticleDOI
20 Aug 1981-Nature
TL;DR: Voyager 1 images of Titan, when normalized to remove limb darkening, reveal an axially symmetric brightness pattern with significant north-south asymmetry, indicating that its production involves the atmosphere well below the unit optical depth level as mentioned in this paper.
Abstract: Voyager 1 images of Titan, when normalized to remove limb darkening, reveal an axially symmetric brightness pattern with significant north-south asymmetry. This interhemispheric contrast seems to be a response to seasonal solar heating variations resulting from Titan's inclined spin axis. The contrast significantly lags the solar forcing, indicating that its production involves the atmosphere well below the unit optical depth level. The contrast has a significant effect on Titan's disk-integrated brightness as seen from earth, and probably accounts for most of the observed long term variation, with solar UV variations accounting for the remainder.

Journal ArticleDOI
TL;DR: In this paper, the contribution of meteor residues to aerosol composition, the role of meteoric dust as condensation nuclei, and the effects of meteor debris on aerosol size distributions are quantified, and particle surface areas are estimated.
Abstract: Characterizations of meteoric dust height and size distributions are obtained using Hunten's calculations of meteor ablation and recondensation rates. The contribution of meteor residues to aerosol composition, the role of meteoric dust as condensation nuclei, and the effects of meteor debris on aerosol size distributions are quantified, and particle surface areas are estimated. The potential importance of heterogeneous chemistry for stratospheric trace gases is discussed. The interaction between H2SO4 vapor and meteor metal vapors is investigated. It is concluded that meteoric particles may dominate the natural stratospheric aerosols at small (less than .01 micron radius) and large (greater than 1 micron radius) sizes under normal conditions.

01 Jul 1981
TL;DR: In this paper, a method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented.
Abstract: A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.

01 Sep 1981
TL;DR: Problems in the transfer of information within the aviation system are discussed and particular attention is given to voice communication problems in both intracockpit and air/ground situations.
Abstract: Problems in the transfer of information within the aviation system are discussed. Particular attention is given to voice communication problems in both intracockpit and air/ground situations.

Journal ArticleDOI
TL;DR: In this paper, the Stieltjes-Tchebycheff moment method was used to calculate the total and partial-channel photoexcitation and ionization cross sections in carbon dioxide.
Abstract: Theoretical studies are reported of total and partial-channel photoexcitation and ionization cross sections in carbon dioxide. As in previously reported studies of discrete and continuum dipole spectra in diatomic (N2, CO, O2, F2) and polyatomic (H2O, H2CO, O3) molecules in this series, separated-channel static-exchange calculations of vertical-electronic transition energies and oscillator strengths and Stieltjes-Tchebycheff moment methods are employed in the development. Detailed comparisons are made of the static-exchange excitation and ionization spectra with photoabsorption, electron-impact excitation, and quantum-defect estimates of discrete transition energies and intensities, and with partial-channel photoionization cross sections obtained from fluorescence measurements and from tunable-source and (e,2e) photoelectron spectroscopy. The spectral characteristics of the various discrete series and continua are interpreted in terms of contributions from compact 2πu(π*), 5σg(σ*), and 4σu(σ*) virtual valence orbitals, and from more diffuse discrete and continuum Rydberg orbitals. The 2πu(π*) orbital is found to contribute to discrete excitation series, whereas the 5σg (σ*) and 4σu (σ*) orbitals generally appear in the photoionization continua as resonance-like diabatic valence features. Good agreement obtains between the calculated discrete excitation series and the results of a recent analysis of the available spectroscopic data. The calculated outer-valence-shell (1πg-1)X 2Πg, (1πu-1)A 2Πu, (3σu-1)B 2Σu+, and (4σg-1)C 2Σg+ partial-channel photoionization cross sections are in good accord with measured values, and clarify completely the origins of the various structures in the observed spectra. There is evidence, however, of coupling among scattering states associated with 1πg-1 and 1πu-1 ionic channels, giving rise to moderate disagreement with tunable-source photoelectron and fluorescence measurements over a portion of the spectrum. In the inner-valence-shell region, the calculated 2σu-1 and 3σg-1 cross sections are in qualitative accord with the observed many-electron spectral intensities, and provide a basis for quantitative interpretation when combined with appropriate intensity-borrowing calculations. The calculated carbon and oxygen K-edge cross sections are in good agreement with available cross sections obtained from electron-impact and photoabsorption measurements. It is of particular interest to find the oxygen K-edge (1σg-1, 1σu-1) cross section exhibits both the expected 5σg(σ*) and 4σu(σ*) resonance-like features. Finally, comparisons are made throughout of the discrete and continuum spectra in carbon dioxide with the results of previously reported studies in CO and O2, and the origins of the similarities and differences in the cross sections in these cases are clarified.

Journal ArticleDOI
01 Apr 1981
TL;DR: A model that encompasses all the levels of skill development outlined in the successive organizations of perception (SOP) theory is proposed, and preview is shown to demand no fundamental changes in structure or equalization and to allow the pilot to eliminate the effective time delays that accrue in the inversion of the controlled-element dynamics.
Abstract: A model of the human pilot is offered for pursuit tracking tasks; the model encompasses an existing model for compensatory tracking. The central hypothesis in the development of this model states that those primary structural elements in the compensatory model responsible for the pilot's equalization capabilities remain intact in the pursuit model. In this latter case, effective low-frequency inversion of the controlled-element dynamics occurs by feeding-forward derived input rate through the equalization dynamics, with low-frequency phase "droop" minimized. The sharp reduction in low-frequency phase lag beyond that associated with the disappearance of phase droop is seen to accompany relatively low-gain feedback of vehicle output. The results of some recent motion cue research are discussed and interpreted in terms of the compensatory-pursuit display dichotomy. Tracking with input preview is discussed in a qualitative way. In terms of the model, preview is shown to demand no fundamental changes in structure or equalization and to allow the pilot to eliminate the effective time delays that accrue in the inversion of the controlled-element dynamics. Precognitive behavior is discussed, and a model that encompasses all the levels of skill development outlined in the successive organizations of perception (SOP) theory is finally proposed.

01 Aug 1981
TL;DR: In this article, hot-wire anemometry was used to analyze the structure and geometry of rotary wing trailing vortices, and the detailed vortex structure is similar to that found for fixed wings and consists of four well defined regions, a viscous core, a turbulent mixing region, a merging region and an inviscid outer region.
Abstract: Hot-wire anemometry to analyze the structure and geometry of rotary wing trailing vortices is studied. Tests cover a range of aspect ratios and blade twist. For all configurations, measured vortex strength correlates well with maximum blade-bound circulation. Measurements of wake geometry are in agreement with classical data for high-aspect ratios. The detailed vortex structure is similar to that found for fixed wings and consists of four well defined regions--a viscous core, a turbulent mixing region, a merging region, and an inviscid outer region. A single set of empirical formulas for the entire set of test data is described.

Journal ArticleDOI
20 Aug 1981-Nature
TL;DR: The brightness structure within Cassini's division in Saturn's rings is explained in terms of perturbations produced by moonlets embedded within an optically thin disk of smaller ring particles.
Abstract: The brightness structure within Cassini's division in Saturn's rings is explained in terms of perturbations produced by moonlets embedded within an optically thin disk of smaller ring particles. The moonlets exert gravitational torques on neighboring ring particles and create gaps; diffusion acts to fill the gaps. A new explanation is offered for the inner edge of the Cassini division being located at the 2:1 resonance with Mimas.

Proceedings ArticleDOI
01 Jun 1981
TL;DR: A spray-on overcoat, with high catalytic efficiency, was used as a comparative basis for determining the HRSI surface catalytic performance through surface temperature measurement.
Abstract: A Space Shuttle experiment planned to measure the surface catalytic efficiency of the baseline high-temperature reusable surface insulation (HRSI) during earth entry is described A spray-on overcoat, with high catalytic efficiency, will be used as a comparative basis for determining the HRSI surface catalytic efficiency through surface temperature measurement Catalytic efficiency, as well as aerothermal response of the overcoat, was evaluated, using various models made of HRSI material in arc-plasma flow environments Agreement is obtained between the measured and computed heating rise of the coated surfaces Computed predictions for the flight case are presented

Journal ArticleDOI
20 Aug 1981-Nature
TL;DR: In the outer Cassini division of Saturn's rings, the spiral density wave driven by Iapetus is estimated to have a value of approximately 16 g/sq cm for the surface density in the region where the waves are seen as mentioned in this paper.
Abstract: Certain radial brightness variations in the outer Cassini division of Saturn's rings may be spiral density waves driven by Saturn's large moon Iapetus, in which case a value of approximately 16 g/sq cm for the surface density is calculated in the region where the waves are seen. The kinematic viscosity in the same region is approximately 170 sq cm/s and the vertical scale height of the ring is estimated to be a maximum of approximately 40 m.