Dissipation and diffusion by turbulence and irregular winds near 100 km
E layer kinetic energy viscous dissipation and transfer to potential energy by turbulence and irregular winds shear
Justus, C. G.↗
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Self-gravity and dissipation in polar rings
Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.
Dubinski, John↗
Tidal disruption of dissipative planetesimals
A self-consistent numerical model is developed for the tidal disruption of a solid planetesimal. The planetesimal is treated as a highly viscous, slightly compressible fluid whose disturbed parts are an inviscid, pressureless fluid undergoing distortion and disruption. The distortions were constrained to being symmetrical above and below the equatorial plane. The tidal potential is expanded in terms of Legendre polynomials, which eliminates the center of mass acceleration effects, permitting definition of equations of motion in a noninertial frame. Consideration is given to viscous dissipation and to characteristics of the solid-atmosphere boundary. The model is applied to sample cases in one, two and three dimensions.
Mizuno, H.↗
The dynamic fission instability and the origin of the Moon
A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.
Boss, A. P.↗
Decoupling the Role of Particle Inertia and Gravity on Particle Dispersion
Particle dispersion and the influence that particle momentum exchange has on the properties of a turbulent carrier flow in micro-gravity environments challenge present understanding and predictive schemes. The objective of this effort has been to develop and assess high-fidelity simulation tools for predicting particle transport within micro-gravity environments suspended in turbulent flows. The computational technique is based on Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations. The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian timescale of the turbulence and particle mass loadings up to one. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96(exp 3) collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier-Stokes equations using the point-force approximation in which 96(exp 3) particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviors. The spectrum of the fluid-particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid-particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of others.
Squires, Kyle D.↗
On neglect of nonlinear momentum terms in solar nebula accretion disk models
The standard model for accretion disks (e.g., Pringle, 1981; Lin and Papaloizou, 1985) parameterizes the radial eddy angular momentum flux which is quadratically nonlinear in velocity, solely by a viscous diffusion process which is linear in velocity. This paper shows that the eddy angular momentum flux, in addition to a gradient dissipative (viscous) flux, involves a countergradient accelerating flux. Therefore, the momentum parameterization in the standard model is in general unjustified. The formalism of the parameterization can be justified only by recognizing that the eddy viscosity used in the standard model is in fact a pseudoviscosity which includes the effects of countergradient fluxes, and which therefore may have a magnitude less than the eddy diffusivity K for mixing trace constituents in the disk.
Prinn, Ronald G.↗
Formation of the prelunar accretion disk
Considerations related to the angular momentum of the earth-moon system have led Ward and Cameron (1978) to the suggestion of a collisional origin of the moon. The required projectile would be about the mass of Mars (i.e., about 0.1 earth masses). The possibility has been considered that both the proto-earth and the projectile would be remnants of the formation of giant gaseous protoplanets. Processes of lunar formation studied take into account the viscous dissipation of an accretion disk. The present paper is concerned with the formation of the prelunar accretion disk. The hydrodynamics of a compressible viscous gas are simulated with the aid of the particle-in-cell method. The obtained results imply that the projectile is in an elliptical earth-crossing orbit.
Cameron, A. G. W.↗
Finite element analysis of nonisothermal polymer processing operations
A finite element formulation for the analysis of polymer processing is presented and its use in some typical situation including entry flow, transient Couette flow, and the Graetz (forced convection) problem is illustrated. The element formulations are constructed on the premise that momentum convection can be neglected (polymer melt flows typically have very low Reynolds' numbers), but that convective heat transfer may be significant (high Peclet numbers). Nonisothermal effects are considered important in polymer processing, due in part to the significant heating which may occur due to viscous dissipation, and also to the very strong influence of temperature on fluid viscosity. The flow is treated as Newtonian with the flow field being coupled to the heat transfer equation only through the viscous heat generation.
Douglas, C.↗
Mobile Lid Convection Beneath Enceladus' South Polar Terrain
Enceladus' south polar region has a large heat flux, 55-110 milliwatts per square meter (or higher), that is spatially associated with cryovolcanic and tectonic activity. Tidal dissipation and vigorous convection in the underlying ice shell are possible sources of heat; however, prior predictions of the heat flux carried by stagnant lid convection range from F(sub conv) ~15 to 30 milliwatts per square meter, too low to explain the observed heat flux. The high heat flux and increased cryovolcanic and tectonic activity suggest that near-surface ice in the region has become rheologically and mechanically weakened enough to permit convective plumes to reach close to the surface. If the yield strength of Enceladus' lithosphere is less than ~1-10 kPa, convection may instead occur in the mobile lid" regime, which is characterized by large heat fluxes and large horizontal velocities in the near-surface ice. I show that model ice shells with effective surface viscosities between 10(exp 16) and 10(exp 17) Pa s and basal viscosities between 10(exp 13) and 10(exp 15) Pa s have convective heat fluxes comparable to that observed by the Cassini Composite Infrared Spectrometer. If this style of convection is occurring, the south polar terrain should be spreading horizontally with v~1-10 millimeter per year and should be resurfaced in ~0.1-10 Ma. On the basis of Cassini imaging data, the south polar terrain is ~0.5 Ma old, consistent with the mobile lid hypothesis. Maxwell viscoelastic tidal dissipation in such ice shells is not capable of generating enough heat to balance convective heat transport. However, tidal heat may also be generated in the near-surface along faults as suggested by Nimmo et al. and/or viscous dissipation within the ice shell may occur by other processes not accounted for by the canonical Maxwell dissipation model.
Barr, Amy C.↗
Polar wander of an ice shell on Europa
The present consideration of a hypothesized ice shell around Europa, which is decoupled from the silicate core by a liquid water layer and possesses a spatially varying thermal equilibrium thickness profile, proceeds through the development of equations for variations in the inertia tensor of a body when second-harmonic-degree topography is added to the crustal base. Attention is given to a realistic model in which the shell and ocean are assumed to undergo reorientations as a single entity independently of the core, but subject to viscous dissipation within the shell. Shell friction is in this case noted to preclude polar wander, unless a low conductivity regolith increases the near-surface temperature by a few tens of degrees C; the ice beneath the regolith would then behave viscously on the time-scale of polar wander.
Ojakangas, Gregory W.↗
The evolution of the inner regions of viscous accretion disks surrounding neutron stars
The structure and evolution of the inner regions of an accretion disk around a neutron star have been investigated with respect to variations in the mass flow rate. In order to examine the sensitivity of the general response of the disk to the form of viscous dissipation, several theoretical constraints on disk evolution are proposed on the basis of current accretion disk theory. It is shown through a series of calculations that under certain circumstances nonlocal radial energy transfer can stabilize regions of the disk which appear to be unstable by local analysis. When viscous stress was scaled with the total pressure of the disk, global analysis was found to be consistent with local analysis, and instability was manifested in luminosity fluctuations and in bursts of less than 10 s. Analysis of the bursts in their limit cycles showed that the disk remained optically thick and geometrically thin throughout its evolution. Substantial agreement was found between the theoretical results and the available observational data.
Taam, R. E.↗
Neutron viscosity in accretion disks
Neutron viscosity is investigated as a possible mechanism for the dissipation of kinetic energy into luminosity in the innermost parts of accretion disks around compact objects. Simplified models are presented of the self-consistent, steady-state accretion flows in which viscosity is provided by neutron collisions with accreting ions. Ion temperatures are determined by balancing the heating of ions by viscous dissipation to their cooling by Coulomb collisions with the electrons, providing a self-consistent solution between neutron production and their impact on energy dissipation. The results indicate that neutrons can indeed provide the necessary dissipation to sustain the steady-state accretion of matter at rates of about 10 to the -8th solar mass/yr or less, and electron temperatures of about 100 keV-1 MeV. Neutrons thus present a promising way of modeling bright Galactic X-ray sources.
Guessoum, Nidhal↗
Surface Collisions Involving Particles and Moisture (SCIP'M)
Experiments were performed on the collision of a solid sphere with a nearly horizontal flat surface covered with a thin layer of viscous liquid. High-speed collisions were obtained by dropping the ball onto the surface from various heights, using gravitational acceleration. Low-speed collisions were obtained using pendulums with long strings or by launching the balls at low velocities in the reduced-gravity environment of parabolic flight. The sphere bounces only when the impact velocity exceeds a critical value. The coefficient of restitution (ratio of rebound velocity to impact velocity) increases with increasing impact velocity above the critical value, indicating the increasing relative importance of elastic deformation to viscous dissipation. The critical impact velocity increases, and the coefficient of restitution decreases, with increasing viscosity or thickness of the liquid layer and with decreasing density or size of the sphere. The ratio of the wet and dry coefficients is expressed as a function of the Stokes number (ratio of particle inertia and viscous forces), showing good agreement between theory and experiment. Similar experiments were performed with the flat surface inclined at various angles to the approaching sphere. A modified Stokes number, which is a measure of the ratio of inertia of the sphere in the normal direction to the viscous forces exerted by the fluid layer, was used for the analysis of oblique collisions. Even for these oblique collisions, it was found that no rebound of the ball was observed below a certain critical Stokes number. The coefficient of normal restitution, defined as a ratio of normal rebound velocity to normal approach velocity, was found to increase beyond the critical Stokes number and even out as it approaches the value for dry restitution at high Stokes numbers. It was also found that, for smooth spheres like steel, the normal restitution at the same modified Stokes number is independent of the angle of impact. The tangential coefficient of restitution, defined as the ratio of tangential rebound velocity to tangential approach velocity, is found to be nearly unity, except for very low approach velocities. Thus, as a first approximation, the theories that predict the coefficient of restitution for head-on wet collisions can be extended to predict the coefficient of normal restitution for oblique wet collisions. Additional experiments were performed with soft surfaces in which a porous cloth or sponge layer was placed over the hard, flat surface. In these experiments, the coefficient of restitution was found to decrease with increasing impact velocity, due to inelastic losses in the soft material. A model combining inelastic deformation and flow through porous media was developed to describe these findings.
Davis, Robert H.↗
Derivation of revised formulae for eddy viscous forces used in the ocean general circulation model
Presented is a re-derivation of the eddy viscous dissipation tensor commonly used in present oceanographic general circulation models. When isotropy is imposed, the currently-used form of the tensor fails to return to the laplacian operator. In this paper, the source of this error is identified in a consistent derivation of the tensor in both rectangular and earth spherical coordinates, and the correct form of the eddy viscous tensor is presented.
Chou, Ru Ling↗
A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma
A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.
Hesse, Michael↗
Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment
We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.
Lai, Dong↗
A SOLUTION FOR THE NONEQUILIBRIUM FLAT-PLATE BOUNDARY LAYER
Atom concentration in, and heat transfer from, a diatomic gas that is being dissociated by the heat of viscous dissipation in a flat plate boundary layer
DIATOMIC GAS↗
Very high temperature laminar flow of a gas through the entrance region of a cooled tube - Numerical calculations and experimental results.
The laminar flow equations in differential form are solved numerically on a digital computer for flow of a very high temperature gas through the entrance region of an externally cooled tube. The solution method is described and calculations are carried out in conjunction with experimental measurements. The agreement with experiment is good, with the result indicating relatively large energy and momentum losses in the highly cooled flows considered where the pressure is nearly uniform along the flow and the core flow becomes non-adiabatic a few diameters downstream of the inlet. The effects of a large range of Reynolds number and Mach number (viscous dissipation) are also investigated.
Back, L. H.↗