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NASA NTRS1959

Charts and Tables for Estimating the Stability of the Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

The minimum critical Reynolds numbers for the similar solutions of the compressible laminar boundary layer computed by Cohen and Reshotko and also for the Falkner and Skan solutions as recomputed by Smith have been calculated by Lin's rapid approximate method for two-dimensional disturbances. These results enable the stability of the compressible laminar boundary layer with heat transfer and pressure gradient to be easily estimated after the behavior of the boundary layer has been computed by the approximate method of Cohen and Reshotko. The previously reported unusual result (NACA Technical Note 4037) that a highly cooled stagnation point flow is more unstable than a highly cooled flat-plate flow is again encountered. Moreover, this result is found to be part of the more general result that a favorable pressure gradient is destabilizing for very cool walls when the Mach number is less than that for complete stability. The minimum critical Reynolds numbers for these wall temperature ratios are, however, all larger than any value of the laminar-boundary-layer Reynolds number likely to be encountered. For Mach numbers greater than those for which complete stability occurs a favorable pressure gradient is stabilizing, even for very cool walls.

Tetervin, Neal↗

NASA NTRS1982

A nonlocal theory of an electrostatic sinusoidal density drift instability

The stability of space plasmas in which the macroscopic variables vary in the direction x perpendicular to the magnetic field is usually studied by means of the local approximation, in which the fluctuating potential is assumed to be independent of x. To remove this approximation, a nonlocal problem is studied in which the background density, and hence the fluctuating potentials, are periodic in x. From the linear Vlasov/Poisson equations, a set of coupled, linear, homogeneous, algebraic equations relating the Fourier amplitudes of the eigensolution is derived. The equations are solved numerically and a hierarchy of exact eigenmodes characterized by different growth rates and spatial structures is found. At points where the density gradient is locally zero, the mode amplitude is generally several orders of magnitude lower than the peak amplitude. The dependence of these solutions on the parameters which define the background density perturbation is studied and a correspondence between these nonlocal results and those obtained with the local approximation is demonstrated.

Thomsen, M. F.↗

NASA NTRS1976

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2

The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.

Peters, B. C., Jr.↗

NASA NTRS1978

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.

Peters, B. C., Jr.↗

NASA NTRS1991

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Korte, John J.↗

DOE OSTI2023

Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Drag force to all orders in gradients

We study the energy loss of a heavy quark slowly moving through an evolving strongly coupled plasma. We use the linearized fluid/gravity correspondence to describe small perturbations of the medium flow with general spacetime dependence. This all order linearized hydrodynamics results in a drag force exerted on a heavy quark even when it is at rest with the fluid element. We show how the general contribution to the drag force can be derived order by order in the medium velocity gradients and provide explicit results valid up to the third order. We then obtain an approximate semi-analytic result for the drag force to all orders in the gradient expansion but linearized in the medium velocity. Thus, the effects of a class of hydrodynamic gradients on the drag force are re-summed, giving further insight into the dissipative properties of strongly coupled plasmas. The all order result allows us to study the drag force in the non-hydrodynamic regime of linear medium perturbations that vary rapidly in space and time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗

DOE OSTI2024

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science↗

NASA NTRS1979

Covariance analyses of satellite-derived mesoscale wind fields

Statistical structure functions have been computed independently for nine satellite-derived mesoscale wind fields that were obtained on two different days. Small cumulus clouds were tracked at 5 min intervals, but since these clouds occurred primarily in the warm sectors of midlatitude cyclones the results cannot be considered representative of the circulations within cyclones in general. The field structure varied considerably with time and was especially affected if mesoscale features were observed. The wind fields on the 2 days studied were highly anisotropic with large gradients in structure occurring approximately normal to the mean flow. Structure function calculations for the combined set of satellite winds were used to estimate random error present in the fields. It is concluded for these data that the random error in vector winds derived from cumulus cloud tracking using high-frequency satellite data is less than 1.75 m/s. Spatial correlation functions were also computed for the nine data sets. Normalized correlation functions were considerably different for u and v components and decreased rapidly as data point separation increased for both components. The correlation functions for transverse and longitudinal components decreased less rapidly as data point separation increased.

Maddox, R. A.↗

NASA NTRS1989

New contributions to transit-time damping in multidimensional systems

The existence of two previously unrecognized contributions to transit-time damping in systems of more than one dimension is demonstrated and discussed. It is shown that these contributions cannot be treated by one-dimensional analyses unless it is assumed that the gradient of the field perpendicular to itself always vanishes. Such an assumption is unjustified in general and the new contributions can dominate damping by fast particles in more general situations. Analytic expressions obtained using a Born approximation are found to be in excellent agreement with numerical test-particle calculations of transit-time damping for a variety of field configurations. These configurations include those of a resonance layer and of a spherical wave packet, which approximates a collapsing wave packet in a strongly turbulent plasma. It is found that the fractional power absorption can be strongly enhanced in non-slablike field configurations.

Robinson, P. A.↗

NASA NTRS2006

Small-Scale Gravity Waves in ER-2 MMS/MTP Wind and Temperature Measurements during CRYSTAL-FACE

Lower stratospheric wind and temperature measurements made from NASA's high-altitude ER-2 research aircraft during the CRYSTAL-FACE campaign in July 2002 were analyzed to retrieve information on small scale gravity waves (GWs) at the aircraft's flight level (typically approximately 20 km altitude). For a given flight segment, the S-transform (a Gaussian wavelet transform) was used to search for and identify small horizontal scale GW events, and to estimate their apparent horizontal wavelengths. The horizontal propagation directions of the events were determined using the Stokes parameter method combined with the cross S-transform analysis. The vertical temperature gradient was used to determine the vertical wavelengths of the events. GW momentum fluxes were calculated from the cross S-transform. Other wave parameters such as intrinsic frequencies were calculated using the GW dispersion relation. More than 100GW events were identified. They were generally high frequency waves with vertical wavelength of approximately 5 km and horizontal wavelength generally shorter than 20 km. Their intrinsic propagation directions were predominantly toward the east, whereas their ground-based propagation directions were primarily toward the west. Among the events, approximately 20% of them had very short horizontal wavelength, very high intrinsic frequency, and relatively small momentum fluxes, and thus they were likely trapped in the lower stratosphere. Using the estimated GW parameters and the background winds and stabilities from the NCAR/NCEP reanalysis data, we were able to trace the sources of the events using a simple reverse ray-tracing. More than 70% of the events were traced back to convective sources in the troposphere, and the sources were generally located upstream of the locations of the events observed at the aircraft level. Finally, a probability density function of the reversible cooling rate due to GWs was obtained in this study, which may be useful for cirrus cloud models.

Wang, L.↗

DOE OSTI2024

On the Departure from Monin–Obukhov Surface Similarity and Transition to the Convective Mixed Layer

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients Φ for wind speed and air temperature generally align with Monin–Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in Φ to first-order approximation, yielding improved similarity from approximately 0.05z i to above 0.3z i , where z i is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin–Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1 z i .

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1983

Latitudinal and field-aligned cosmic ray gradients 2 to 5 AU Voyagers 1 and 2 and IMP 8

Results are presented showing that the contemporary picture of a relatively small heliocentric radial gradient is generally correct. They emphasize that such a gradient should really be thought of in terms of field-aligned structures since the cosmic ray populations tend to 'corotate' locally with the interplanetary field structure. Nonuniform latitudinal gradients of approximately 2 to 5 percent/deg in structures lasting 10 to 30 days are identified unambiguously. Additional evidence is seen for somewhat smaller latitudinal gradients often north to south and probably mixed with small field-aligned gradients of less than 1 percent/AU that persist for several solar rotations. It is suggested that these smallest ephemeral latitudinal gradients manifest themselves by affecting the degree of irregularity in diurnal variations of high latitude neutron monitors.

Roelof, E. C.↗

NASA NTRS2001

Mean Ages of Stratospheric Air Derived From in Situ Observations of CO2, CH4, and N2O

Accurate mean ages for stratospheric air have been derived from a spatially and temporally comprehensive set of in situ observations of CO2, CH4, and N2O obtained from 1992 to 1998 from the NASA ER-2 aircraft and balloon flights. Errors associated with the tropospheric CO2 seasonal cycle and interannual variations in the CO2 growth rate are less than 0.5 year throughout the stratosphere and less than 0.3 year for air older than 2 years (N2O less than 275 ppbv), indicating that the age spectra are broad enough to attenuate these influences over the time period covered by these observations. The distribution of mean age with latitude and altitude provides detailed, quantitative information about the general circulation of the stratosphere. At 20 km, sharp meridional gradients in the mean age are observed across the subtropics. Between 20 and 30 km, the average difference in mean age between the tropics and midlatitudes is approximately 2 years, with slightly smaller differences at higher and lower altitudes. The mean age in the midlatitude middle stratosphere (approx. 25-32 km) is relatively constant with respect to altitude at 5 plus or minus 0.5 years. Comparison with earlier balloon observations of CO2 dating back to the 1970s indicates that the mean age of air in this region has remained within 11 year of its current value over the last 25 years. A climatology of mean age is derived from the observed compact relationship between mean age and N2O. These characteristics of the distribution of mean age in the stratosphere will serve as critically needed diagnostics for models of stratospheric transport.

Andrews, A. E.↗

NASA NTRS1971

An analysis and comparison of several trajectory optimization methods

The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.

Lewallen, J. M.↗

NASA NTRS2014

Seasonal Evolution of Saturn's Polar Temperatures and Composition

The seasonal evolution of Saturn's polar atmospheric temperatures and hydrocarbon composition is derived from a decade of Cassini Composite Infrared Spectrometer (CIRS) 7-16 micrometers thermal infrared spectroscopy. We construct a near-continuous record of atmospheric variability poleward of 60 deg from northern winter/southern summer (2004, Ls = 293 deg) through the equinox (2009, Ls= 0 deg) to northern spring/southern autumn (2014, Ls = 56 deg). The hot tropospheric polar cyclones that are entrained by pro-grade jets within 2-3 deg of each pole, and the hexagonal shape of the north polar belt, are both persistent features throughout the decade of observations. The hexagon vertices rotated westward by approx. equal to 30 deg longitude between March 2007 and April 2013, confirming that they are not stationary in the Voyager-defined System III longitude system as previously thought. Tropospheric temperature contrasts between the cool polar zones (near 80-85 deg) and warm polar belts (near 75-80 deg) have varied in both hemispheres, resulting in changes to the vertical wind shear on the zonal jets in the upper troposphere and lower stratosphere. The extended region of south polar stratospheric emission has cooled dramatically poleward of the sharp temperature gradient near 75 deg S (by approximately -5 K/yr), coinciding with a depletion in the abundances of acetylene (0030 +/- 0.005 ppm/yr) and ethane (0.35 +/- 0.1 ppm/yr), and suggestive of stratospheric upwelling with vertical wind speeds of w approx. equal to +0.1 mm/s. The upwelling appears most intense within 5 deg latitude of the south pole. This is mirrored by a general warming of the northern polar stratosphere (+5 K/yr) and an enhancement in acetylene (0.030 +/- 0.003 ppm/yr) and ethane (0.45 +/- 0.1 ppm/yr) abundances that appears to be most intense poleward of 75 deg N, suggesting subsidence at w approx. equal to -0.15 mm/ s. However, the sharp gradient in stratospheric emission expected to form near 75 deg N by northern summer solstice (2017, Ls = 90 deg) has not yet been observed, so we continue to await the development of a northern summer stratospheric vortex. The peak stratospheric warming in the north occurs at lower pressure levels (p less than 1 mbar) than the peak stratospheric cooling in the south (p greater than 1 mbar). Vertical motions are derived from both the temperature field (using the measured rates of temperature change and the deviations from the expectations of radiative equilibrium models) and hydrocarbon distributions (solving the continuity equation). Vertical velocities tend towards zero in the upper troposphere where seasonal temperature contrasts are smaller, except within the tropospheric polar cyclones where w approx. equal to +0.02 mm/s. North polar minima in tropospheric and stratospheric temperatures were detected in 2008-2010 (lagging one season, or 6-8 years, behind winter solstice); south polar maxima appear to have occurred before the start of the Cassini observations (1-2 years after summer solstice), consistent with the expectations of radiative climate models. The influence of dynamics implies that the coldest winter temperatures occur in the 75-80 deg region in the stratosphere, and in the cool polar zones in the troposphere, rather than at the poles themselves. In addition to vertical motions, we propose that the UV-absorbent polar stratospheric aerosols entrained within Saturn's vortices contribute significantly to the radiative budget at the poles, adding to the localized enhancement in the south polar cooling and north polar warming poleward of +/-75 deg.

polar temperatures↗

NASA NTRS1980

Structure and circulation of the Venus atmosphere

The Pioneer Venus data relevant to the dynamics and thermodynamics of the atmosphere is summarized and interpreted. On the day side there is a thermosphere in which temperatures increase with height to an exospheric temperature of about 300 K. On the night side there is a cryosphere in which temperatures decrease with height to an exospheric temperature of about 100 K. The atmosphere is stratified stably from the highest altitudes down to about 28 km except for a layer in the clouds between about 50 and 55 km which is nearly adiabatic. Horizontal thermal contrasts are approximately 1 to 2% in the deep atmosphere and 100% in the upper atmosphere. The temperatures generally decrease with latitude at and below the clouds on constant pressure surfaces. Above the clouds there is a reversed zonally averaged latitudinal temperature gradient. The dominant circulation of the atmosphere above the lowest one or two scale heights is a zonal retrograde motion with 100 m/s winds at 60 km altitude. There is also a superrotation at altitudes of 150 km and above.

Schubert, G.↗