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At least 199 records · Page 11

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NASA NTRS2002

Waves in Turbulent Stably-Stratified Shear Flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It is found, however, that a continuous distribution of the phase angle is present in weakly and strongly stratified flow. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. It is found that a solution of the fully nonlinear viscous Navier-Stokes equations can be represented by the linearized inviscid solution. The projection yields a decomposition into vertical wave modes and horizontal vortical modes.

Jacobitz, F. G.↗

NASA NTRS2007

Assessment of Turbulent Shock-Boundary Layer Interaction Computations Using the OVERFLOW Code

The performance of two popular turbulence models, the Spalart-Allmaras model and Menter s SST model, and one relatively new model, Olsen & Coakley s Lag model, are evaluated using the OVERFLOWcode. Turbulent shock-boundary layer interaction predictions are evaluated with three different experimental datasets: a series of 2D compression ramps at Mach 2.87, a series of 2D compression ramps at Mach 2.94, and an axisymmetric coneflare at Mach 11. The experimental datasets include flows with no separation, moderate separation, and significant separation, and use several different experimental measurement techniques (including laser doppler velocimetry (LDV), pitot-probe measurement, inclined hot-wire probe measurement, preston tube skin friction measurement, and surface pressure measurement). Additionally, the OVERFLOW solutions are compared to the solutions of a second CFD code, DPLR. The predictions for weak shock-boundary layer interactions are in reasonable agreement with the experimental data. For strong shock-boundary layer interactions, all of the turbulence models overpredict the separation size and fail to predict the correct skin friction recovery distribution. In most cases, surface pressure predictions show too much upstream influence, however including the tunnel side-wall boundary layers in the computation improves the separation predictions.

Oliver, A. B.↗

NASA NTRS2009

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Barghouty, A. F.↗

NASA NTRS1994

Evaluation of turbulence models in the PARC code for transonic diffuser flows

Flows through a transonic diffuser were investigated with the PARC code using five turbulence models to determine the effects of turbulence model selection on flow prediction. Three of the turbulence models were algebraic models: Thomas (the standard algebraic turbulence model in PARC), Baldwin-Lomax, and Modified Mixing Length-Thomas (MMLT). The other two models were the low Reynolds number k-epsilon models of Chien and Speziale. Three diffuser flows, referred to as the no-shock, weak-shock, and strong-shock cases, were calculated with each model to conduct the evaluation. Pressure distributions, velocity profiles, locations of shocks, and maximum Mach numbers in the duct were the flow quantities compared. Overall, the Chien k-epsilon model was the most accurate of the five models when considering results obtained for all three cases. However, the MMLT model provided solutions as accurate as the Chien model for the no-shock and the weak-shock cases, at a substantially lower computational cost (measured in CPU time required to obtain converged solutions). The strong shock flow, which included a region of shock-induced flow separation, was only predicted well by the two k-epsilon models.

Georgiadis, N. J.↗

NASA NTRS1991

Optimal guidance law development for an advanced launch system

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

Calise, Anthony J.↗

NASA NTRS1991

The convergence rate of approximate solutions for nonlinear scalar conservation laws

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates.

Nessyahu, Haim↗

NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗

NASA NTRS1979

Stochastic modeling of the time-averaged equations for climate dynamics

Two analyses on climate dynamics are presented, both based on a simplified set of barotropic equations for representing large scale non-linear atmospheric circulation characteristics. The statistical properties of the set of equations were investigated for small values of a parameter k sub o, corresponding to the physical case of large zonal westerlies and relatively weak eddy motions. The effect of seasonal type forcing on the solution of these equations was also studied and some preliminary numerical results are presented.

Spreiter, J. R.↗

NASA NTRS1983

The existence of Hadley convective regimes of atmospheric motion

The solutions of the equations describing deep global convection on a rotating planet are discussed. The existence of generalized steady axisymmetric solutions is established. It is then shown that these are classical solutions when the heat source is sufficiently smooth. The solutions are shown to be unique when the heating is sufficiently weak and asymptotically stable when the shear is sufficiently small. Finally, the application of these results to earth's atmosphere is discussed, with eddy viscosity replacing molecular viscosity.

Dutton, J. A.↗

NASA NTRS1985

Theory of the current-driven ion cyclotron instability in the bottomside ionosphere

A comprehensive treatment of the theory of electrostatic ion cyclotron instability in the collisional bottomside ionosphere is given. The linear dispersion relations for the ion cyclotron instability (electron and ion collisions) are derived. Analytical solutions to the dispersion relation are obtained in three limits: collisionless; weakly collisional; and collisional. In addition, the linear dispersion relation is solved numerically, using parameters typical of the high-latitude bottomside ionosphere. It is pointed out that the linear growth rates in the bottomside collisional regime can be of the same order as the corresponding topside collisionless growth rates. A nonlinear saturation mechanism for the electrostatic ion cyclotron instability is proposed on the basis of Dupree's (1966) resonance broadening theory.

Satyanarayana, P.↗

NASA NTRS1999

Capabilities and Limitations of Radio Occultation Measurements for Ionosphere Monitoring

The paper: (1) describes the range of capabilities of GPS radio occultation missions in ionospheric research: (a) ionospheric profiling; (b) ionospheric imaging; (c) ionospheric data assimilation; and (d) measurement of scintillation. (2) Identify strengths and weaknesses of measurements: (a) coverage; (b) resolution; and (c) uniqueness of solution.

Hajj, G. A.↗

NASA NTRS1994

The hard X-ray emission spectra from accretion columns in intermediate polars

We consider the hard (greater than 2 keV) X-ray emission from accretion columns in an intermediate polar system, GK Per, using a simple settling solution. The rate of photon emission per logarithmic energy interval can be fitted with a power law, E(exp -gamma), with gamma approximately 2.0, in agreement with observations. This index is only weakly dependent on the mass accretion rate, dot-M, for dot-M in the range of a few times 10(exp 16-18) g/s. The peak energy of the photon spectra (after photoelectric absorption) is expected to be E(sub p) approximately (5 keV) gamma(exp -1/3) (N(sub H)/10(exp 23)/sq cm)(exp 1/3) where N(sub H) is the hydrogen column density along the line of sight. The observed spectra of GK Per and possibly of V1223 Sgr suggest N(sub H) approximately 10(exp 23)/sq cm. This large N(sub H) may be due to partially ionized preshock column material. Alternatively, we also consider absorption by the cool outer parts of an accretion disk. In this case the photoelectric absorption depth in the disk is a sensitive function of inclination. For GK Per the required inclination is approximately 83 deg. For mass accretion rates larger than a critical rate of approximately 10(exp 18) g/s, X-ray emission from the column accretion is significantly affected by radiation drag. Although the mass accretion rate increases dramatically during outbursts, the observed hard (greater than 2 keV) X-ray luminosity will not rise proportionately. The slope and peak energy of the outburst spectra are only weakly affected. We conclude that the observed X-ray spectra can be explained by this simple analytic solution and that the production of hard X-rays from the accretion shock at the magnetic poles in the intermediate polars is in general agreement with the observations. However, since the X-ray emission and absorption depend on the mass accretion rate in a complicated manner, observed hard X-ray luminosities (greater than 2 keV) are not a good indicator of the mass accretion rate in the X-ray emitting regions.

Yi, Insu↗

NASA NTRSDate not supplied

An exact solution of an augmented Burgers equation and amplitude-dependent acoustic propagation speed

Nonlinear sound propagation in the atmosphere is usually modeled using an augmented Burgers equation accounting for a weak nonlinearity and atmospheric absorption. Because the absorption includes the molecular vibrational relaxation, such a Burgers equation is more complex than the regular Burgers equation that only accounts for the thermoviscous dissipation in the absorption. Although an exact solution of the regular Burgers equation has long been derived using the Cole- Hopf transform, an exact solution of the augmented Burgers equation has not been derived previously. Thus, this paper presents an exact solution of the augmented Burgers equation. This novel solution is shown to be equivalent to the solution using the Cole-Hopf transform when the absorption only involves thermoviscous dissipation. It can also be reduced to the known solution of an N-wave when the absorption is ignored. The augmented Burgers equation is an approximation valid for weak nonlinearity. However, this assumption may not be accurate for acoustic signals propagating from the lower atmosphere and which are subsequently refracted downward from the upper atmosphere (e.g., stratosphere and thermosphere) due to the decreasing air density with increasing altitude [Lonzaga, et al., Geophysical Journal International, 200(3), pp.1347-1361]. Consequently, the current paper also discusses the effects of a strong nonlinearity that lead to an amplitude-dependent increase in signal propagation speed. For an impulsive signal such as a sonic boom, these effects cause a dispersion of the signal similar to the observed dispersion of acoustic signals from supersonic Concorde as well as from large explosions.

Joel B Lonzaga↗

NASA NTRS1991

Stretched three-dimensional plasma equilibria with field-aligned flow

A three-dimensional equilibrium theory for stretched plasma configurations, such as the earth's magnetotail, is extended to include the effects of field-aligned flow. The MHD equations for this case can be solved in a general way by reduction to a set of ordinary differential equations and an ordinary integral. The solutions represent lowest-order solutions of an asymptotic expansion of the MHD equations for small electric field and weak time dependence. Simplified equations are presented for two-dimensional equilibria and for incompressible flow. Possible magnetospheric applications include the configuration of the geotail near and beyond the termination of the closed field line region, the steady motion of a plasmoid (a plasma bubble severed from the earth) through the distant geotail, and configurations at the magnetopause, the interface between the magnetosphere and the shocked solar wind plasma. For illustration, solutions for the steady motion of a two-dimensional plasmoid through the distant magnetotail are presented.

Birn, J.↗

NASA NTRS1971

Dissipative effects on nonlinear waves in rotating fluids.

Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.

Leibovich, S.↗

NASA NTRS1972

An EPR investigation of the dynamic Jahn-Teller effect in SrCl2:y(2 plus) and SrCl2:Sc(2 plus)

EPR spectra have been observed for SrCl2:Y(2+) and SrCl2:Sc(2+) at liquid helium temperatures. At 1.2 K the spectra were dominated by anisotropic hyperfine patterns whose lineshapes and angular dependences were explained using second order solutions of the effective Hamiltonian for an isolated 2Eg state split by large random internal strains. Pronounced asymmetries in some of the strin produced lineshapes for Srcl2:Sc(2+) are shown to result from second order terms in the solution of the effective Hamiltonian. Coexisting with the anisotropic hyperfine patterns are weak nearly isotropic hyperfine patterns with typical lineshapes. Variations in the apparent intensity of lines in these weak hyperfine patterns as functions of the applied magnetic field direction and temperature imply that these lines result from averaging by vibronic relaxation of a portion of the anisotropic pattern. The effective Hamiltonian parameters for SrCl2:La(2+), SrCl2:y(2+), and SrCl2:SC(2+) are analyzed in terms of crystal field theory modified to include a dynamic Jahn-Teller effect.

Herrington, J. R.↗

NASA NTRS1974

Behaviour of ion velocity distributions for a simple collision model

Calculation of the ion velocity distributions for a weakly ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV/m. This shape persists for one to two hours after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fields. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.

St-Maurice, J.-P.↗

NASA NTRS1980

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. I - Pressure distribution

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.

Messiter, A. F.↗