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At least 73 records · Page 4
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NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS2008

Comparison of ALE and SPH Simulations of Vertical Drop Tests of a Composite Fuselage Section into Water

Simulation of multi-terrain impact has been identified as an important research area for improved prediction of rotorcraft crashworthiness within the NASA Subsonic Rotary Wing Aeronautics Program on Rotorcraft Crashworthiness. As part of this effort, two vertical drop tests were conducted of a 5-ft-diameter composite fuselage section into water. For the first test, the fuselage section was impacted in a baseline configuration without energy absorbers. For the second test, the fuselage section was retrofitted with a composite honeycomb energy absorber. Both tests were conducted at a nominal velocity of 25-ft/s. A detailed finite element model was developed to represent each test article and water impact was simulated using both Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) approaches in LS-DYNA, a nonlinear, explicit transient dynamic finite element code. Analytical predictions were correlated with experimental data for both test configurations. In addition, studies were performed to evaluate the influence of mesh density on test-analysis correlation.

Jackson, Karen E.↗
NASA NTRS1990

Direct simulation for the instability and breakup of laminar liquid jets

A direct numerical simulation method is described for predicting the deformation of laminar liquid jets. In the present nonlinear direct simulation, the convective term, which has been discarded in past linear analyses by Rayleigh and others, is included in the hydrodynamic equations. It is shown that only by maintaining full complexity of the nonlinear surface tension term accurate drop formation can be predicted. The continuity and momentum equations in the transient form are integrated on an adaptive grid, conforming the jet and surface wave shape. The equations, which are parabolic in time and elliptic in space, are solved by a TVD scheme with characteristic flux splitting. The results of the present work are discussed and compared with available measurements and other analyses. The comparison shows that among the predictions, the current 1-D direct simulation results agree best with the experimental data. Furthermore, the computer time requirements are much (an order of magnitude) smaller than those of previously reported multidimensional analyses.

Chuech, S. G.↗
NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗
NASA NTRS1993

The Kelvin-Helmholtz instability in photospheric flows - Effects of coronal heating and structure

A series of hydrodynamic numerical simulations has been used to investigate the nonlinear evolution of driven, subsonic velocity shears under a range of typical photospheric conditions. These calculations show that typical photospheric flows are susceptible to the Kelvin-Helmholtz instability (KHI), with rapid nonlinear growth times that are approximately half of a typical granule lifetime. The KHI produces vortical structures in intergranule lanes comparable to a typical fluxule radius; this is precisely the correct scale for maximum power transfer to the corona.

Karpen, Judith T.↗
NASA NTRS2002

Containerless Ripple Turbulence

One of the longest standing unsolved problems in physics relates to the behavior of fluids that are driven far from equilibrium such as occurs when they become turbulent due to fast flow through a grid or tidal motions. In turbulent flows the distribution of vortex energy as a function of the inverse length scale [or wavenumber 'k'] of motion is proportional to 1/k(sup 5/3) which is the celebrated law of Kolmogorov. Although this law gives a good description of the average motion, fluctuations around the average are huge. This stands in contrast with thermally activated motion where large fluctuations around thermal equilibrium are highly unfavorable. The problem of turbulence is the problem of understanding why large fluctuations are so prevalent which is also called the problem of 'intermittency'. Turbulence is a remarkable problem in that its solution sits simultaneously at the forefront of physics, mathematics, engineering and computer science. A recent conference [March 2002] on 'Statistical Hydrodynamics' organized by the Los Alamos Laboratory Center for Nonlinear Studies brought together researchers in all of these fields. Although turbulence is generally thought to be described by the Navier-Stokes Equations of fluid mechanics the solution as well as its existence has eluded researchers for over 100 years. In fact proof of the existence of such a solution qualifies for a 1 M$ millennium prize. As part of our NASA funded research we have proposed building a bridge between vortex turbulence and wave turbulence. The latter occurs when high amplitude waves of various wavelengths are allowed to mutually interact in a fluid. In particular we have proposed measuring the interaction of ripples [capillary waves] that run around on the surface of a fluid sphere suspended in a microgravity environment. The problem of ripple turbulence poses similar mathematical challenges to the problem of vortex turbulence. The waves can have a high amplitude and a strong nonlinear interaction. Furthermore, the steady state distribution of energy again follows a Kolmogorov scaling law; in this case the ripple energy is distributed according to 1/k (sup 7/4). Again, in parallel with vortex turbulence ripple turbulence exhibits intermittency. The problem of ripple turbulence presents an experimental opportunity to generate data in a controlled, benchmarked system. In particular the surface of a sphere is an ideal environment to study ripple turbulence. Waves run around the sphere and interact with each other, and the effect of walls is eliminated. In microgravity this state can be realized for over 2 decades of frequency. Wave turbulence is a physically relevant problem in its own right. It has been studied on the surface of liquid hydrogen and its application to Alfven waves in space is a source of debate. Of course, application of wave turbulence perspectives to ocean waves has been a major success. The experiment which we plan to run in microgravity is conceptually straightforward. Ripples are excited on the surface of a spherical drop of fluid and then their amplitude is recorded with appropriate photography. A key challenge is posed by the need to stably position a 10cm diameter sphere of water in microgravity. Two methods are being developed. Orbitec is using controlled puffs of air from at least 6 independent directions to provided the positioning force. This approach has actually succeeded to position and stabilize a 4cm sphere during a KC 135 segment. Guigne International is using the radiation pressure of high frequency sound. These transducers have been organized into a device in the shape of a dodecahedron. This apparatus 'SPACE DRUMS' has already been approved for use for combustion synthesis experiments on the International Space Station. A key opportunity presented by the ripple turbulence data is its use in driving the development of codes to simulate its properties.

Putterman, Seth↗
NASA NTRS2001

Nonlinearity Effects of Lateral Density Diffusion Coefficient on Gain-Guided VCSEL Performance

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. In this paper, we apply a hydrodynamic model developed from the semiconductor Bloch equations to numerically study the effects of nonlinearity in the diffusion coefficient on single mode operation and direct modulation of a gain-guided InGaAs/GaAs multiple quantum well laser, operating not too far from threshold. We found that a small diffusion coefficient is advantageous for lowering the threshold current and increasing the modulation bandwidth. Most importantly, the effects of nonlinearity in the coefficient can be approximately reproduced by replacing the coefficient with an effective constant diffusion coefficient, which corresponds roughly to the half height density of the density distribution.

Li, Jian-Zhong↗
NASA NTRS1986

Unstable transition properties of the driven magnetohydrodynamic sheet pinch

The unstable transition behavior of a bounded current-carrying two-dimensional magnetofluid is explored, using the hydrodynamic theory developed for parallel shear flows as a guide. Nonlinear excitation of the higher wavenumbers results in the development of electric current sheets of finite extent, as well as the formation of 'attraction currents' centered at the magnetic O-points. A secondary instability mechanism, the dynamic tearing of the electric current sheet, is also observed. This dynamic tearing leads to sawtoothlike temporal oscillations in certain global quantities. The long-time state of the system resembles a nonlinearly saturated state with significant excitation of many wavenumbers. Some features of this state can be understood by means of a Landau nonlinear stability theory based on certain assumptions about the perturbation energy balance.

Dahlburg, R. B.↗
NASA NTRS2008

Tide Corrections for Coastal Altimetry: Status and Prospects

Knowledge of global oceanic tides has markedly advanced over the last two decades, in no small part because of the near-global measurements provided by satellite altimeters, and especially the long and precise Topex/Poseidon time series e.g. [2]. Satellite altimetry in turn places very severe demands on the accuracy of tidal models. The reason is clear: tides are by far the largest contributor to the variance of sea-surface elevation, so any study of non-tidal ocean signals requires removal of this dominant tidal component. Efforts toward improving models for altimetric tide corrections have understandably focused on deep-water, open-ocean regions. These efforts have produced models thought to be generally accurate to about 2 cm rms. Corresponding tide predictions in shelf and near-coastal regions, however, are far less accurate. This paper discusses the status of our current abilities to provide near-global tidal predictions in shelf and near-coastal waters, highlights some of the difficulties that must be overcome, and attempts to divine a path toward some degree of progress. There are, of course, many groups worldwide who model tides over fairly localized shallow-water regions, and such work is extremely valuable for any altimeter study limited to those regions, but this paper considers the more global models necessary for the general user. There have indeed been efforts to patch local and global models together, but such work is difficult to maintain over many updates and can often encounter problems of proprietary or political nature. Such a path, however, might yet prove the most fruitful, and there are now new plans afoot to try again. As is well known, tides in shallow waters tend to be large, possibly nonlinear, and high wavenumber. The short spatial scales mean that current mapping capabilities with (multiple) nadir-oriented altimeters often yield inadequate coverage. This necessitates added reliance on numerical hydrodynamic models and data assimilation, which in turn necessitates very accurate bathymetry with high spatial resolution. Nonlinearity means that many additional compound tides and overtides must be accounted for in our predictions, which increases the degree of modeling effort and increases the amounts of data required to disentangle closely aliased tides.

Ray, Richard D.↗
NASA NTRS1994

Nonlinear evolution of tidally distorted accretion disks: Two-dimensional simulations

According to a previously published linear analysis, the tidal distortion of accretion disks in binary star systems produces a local hydrodynamic instability to m = 1 internal waves, which may have arbitrarily small wavelengths in the absence of viscosity. The instability is three-dimensional and approximately incrompressible. To explore the nonlinear outcome of this instability, we develop a shearing-sheet approximation on scales comparable to the disk thickness. The large-scale azimuthal variation of the disk is represented by varying the local metric with time (local orbital phase). The hydrodynamic equations can then be posed two-dimensionally on local meridional planes. We solve these equations with a second-order gasdynamical code based on the Total-Variation-Diminishing scheme. Our simulations confirm the predicted linear growth rate. The modes saturate chaotically at velocities scaling as the product of the linear growth rate and the wavelength. If the wavelength is small compared with the disk thickness, the modes remain nearly incompressible even when nonlinear. The two-dimensional power spectrum of velocities after saturation is roughly isotropic and extends over a broad range of scales in an approximately power-law fashion. We measure the heating rate associated with the nonlinear dissipation of the modes. The dissipation implies a secular torque on the disk and a return of angular momentum to the secondary star via the tidal potential. The estimated torque is somewhat larger than the tidal torque produced by maximal disk viscosity (alpha approximately 1). At least in these two-dimensional simulations, however, there is no significant angular momentum flux within the disk.

Ryu, Dongsu↗
NASA NTRS1993

The stability of cosmic-ray-dominated shocks - A secondary instability

Previous studies in one spatial dimension showed that the precursors of cosmic-ray-dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray-dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent.

Ryu, Dongsu↗
NASA NTRS2007

Hydrodynamic Force on a Cylinder Oscillating at Low Frequency

The hydrodynamic force on a cylinder oscillating transversely to its axis is a nonlinear function of the displacement amplitude x0. We report measurements and numerical calculations of the force at frequencies low enough that delta > R, where delta is the viscous penetration length and R is the cylinder radius. For small amplitudes, the numerically calculated Fourier transform of the force per unit length, F(sub small), agrees with Stokes' analytical calculation. For larger amplitudes, the force per unit length found by both calculation and measurement is F = F(sub small)C (x(sub 0)/delta,R/delta). The complex function C depends only weakly on R/delta, indicating that x0/delta is more appropriate as a scaling variable than the Keulegan-Carpenter number KC = pi*x(sub 0)/R. The measurements used a torsion oscillator driven at frequencies from 1 to 12 Hz while immersed in dense xenon. The oscillator comprised cylinders with an effective radius of R = 13.4 micron and oscillation amplitudes as large as x(sub 0)/delta = 4 (corresponding to KC as large as 71). The calculations used similar conditions except that the amplitudes were as large as x0/delta = 28.

Berg, Robert F.↗
NASA NTRS1983

Flare loop radiative hydrodynamics. IV - Dynamic evolution of unstable semiempirical loop models

The evolution of the unstable solar atmosphere into the nonlinear phase, in response to various perturbations, is followed. The initial dynamic evolution of the atmosphere follows the predictions of linear stability analysis. In the nonlinear phase, rapid changes are confined to the transition region; these changes are manifested as a propagation of the transition region through the plasma, i.e., chromospheric evaporation or condensation. Global evolution therefore proceeds on the coronal conductive time scale. The rate of propagation of the transition region is determined by the imbalance between the energy supplied by thermal conduction from the corona and radiative cooling within the transition region itself. Flow velocities in the lower corona during evaporation or condensation are, in the cases studied, of order 3 km/s. The observed dynamic evolution is consistent with the existence of relatively long-lived coronal loops whose brightnesses vary on the evaporative time scale.

An, C.-H.↗
NASA NTRS1981

Galaxy formation in an intergalactic medium dominated by explosions

The evolution of galaxies in an intergalactic medium dominated by explosions of star systems is considered analogously to star formation by nonlinearly interacting processes in the interstellar medium. Conditions for the existence of a hydrodynamic instability by which galaxy formation leads to more galaxy formation due to the propagation of the energy released at the death of massive stars are examined, and it is shown that such an explosive amplification is possible at redshifts less than about 5 and stellar system masses between 10 to the 8th and 10 to the 12th solar masses. Explosions before a redshift of about 5 are found to lead primarily to the formation of massive stars rather than galaxies, while those at a redshift close to 5 will result in objects of normal galactic scale. The model also predicts a dusty interstellar medium preventing the detection of objects of redshift greater than 3, numbers and luminosities of protogalaxies comparable to present observations, unvirialized groups of galaxies lying on two-dimensional surfaces, and a significant number of black holes in the mass range 1000-10,000 solar masses.

Ostriker, J. P.↗
NASA NTRS1996

[Kelvin-Helmholtz instability in protostellar jets]

NASA grant NAG 5 2866, funded by the Astrophysics Theory Program, enabled the study the Kelvin-Helmholtz instability in protostellar jets. In collaboration with co-investigator Philip Hardee, the PI derived the analytic dispersion relation for the instability in including a cooling term in the energy equation which was modeled as one of two different power laws. Numerical solutions to this dispersion relation over a wide range of perturbation frequencies, and for a variety of parameter values characterizing the jet (such as Mach number, and density ratio) were found It was found that the growth rates and wavelengths associated with unstable roots of the dispersion relation in cooling jets are significantly different than those associated with adiabatic jets, which have been studied previously. In collaboration with graduate student Jianjun Xu (funded as a research associate under this grant), hydrodynamical simulations were used to follow the growth of the instability into the nonlinear regime. It was found that asymmetric surface waves lead to large amplitude, sinusoidal distortions of the jet, and ultimately to disruption Asymmetric body waves, on the other hand, result in the formation of shocks in the jet beam in the nonlinear regime. In cooling jets, these shocks lead to the formation of dense knots and filaments of gas within the jet. For sufficiently high perturbation frequencies, however, the jet cannot respond and it remains symmetric. Applying these results to observed systems, such as the Herbig-Haro jets HH34, HH111 and HH47 which have been observed with the Hubble Space Telescope, we predicted that some of the asymmetric structures observed in these systems could be attributed to the K-H modes, but that perturbations on timescales associated with the inner disk (about 1 year) would be too rapid to cause disruption. Moreover, it was discovered that weak shock 'spurs' in the ambient gas produced by ripples in the jet surface due to nonlinear, modes of surface and/or body waves could accelerate the ambient gas to low velocity. This latter effect represents a new mechanism by which supersonic jets can accelerate low velocity outflows.

Stone, James↗
NASA NTRS1977

A multiscale numerical study into the cascade of kinetic energy leading to severe local storms

The cascade of kinetic energy from macro- through mesoscales is studied on the basis of a nested grid system used to solve a set of nonlinear differential equations. The kinetic energy cascade and the concentration of vorticity through the hydrodynamic spectrum provide a means for predicting the location and intensity of severe weather from large-scale data sets. A mechanism described by the surface pressure tendency equation proves to be important in explaining how initial middle-tropospheric mass-momentum imbalances alter the low-level pressure field.

Paine, D. A.↗
NASA NTRS1990

Development of Renormalization Group Analysis of Turbulence

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

L M Smith↗