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NASA NTRS1989

Boundary value problems in magnetohydrodynamics (and fluid dynamics). I - Radiation boundary condition

In view of the difficulties that emerge in numerical simulations of time-dependent phenomena involving MHD waves due to waves' artificial reflection at numerical boundaries, where time-dependent magnetic fields outside those boundaries are unknown, a method previously developed for the determination of radiative boundary conditions is generalized for the treatment of isothermal MHD waves. The illustrative problem thus treated is that of the magnetic braking of a rigidly rotating disk which is embedded in a differentially-rotating fluid. The analytic results obtained are compared with those from numerical simulations with and without the present boundary treatment.

Vanajakshi, T. C.↗

NASA NTRS1978

A well posed boundary value problem in transonic gas dynamics

A boundary value problem for the Tricomi equation was studied in connection with transonic gas dynamics. The transformed equation delta u plus 1/3Y u sub Y equals 0 in canonical coordinates was considered in the complex domain of two independent complex variables. A boundary value problem was then set by prescribing the real part of the solution on the boundary of the real unit circle. The Dirichlet problem in the upper unit semicircle with vanishing values of the solution at Y = 0 was solved explicitly in terms of the hypergeometric function for the more general Euler-Poisson-Darboux equation. An explicit representation of the solution was also given for a mixed Dirichlet and Neumann problem for the same equation and domain.

Sanz, J. M.↗

NASA NTRS2016

The Open-Ocean Sensible Heat Flux and Its Significance for Arctic Boundary Layer Mixing During Early Fall

The increasing ice-free area during late summer has transformed the Arctic to a climate system with more dynamic boundary layer (BL) clouds and seasonal sea ice growth. The open-ocean sensible heat flux, a crucial mechanism of excessive ocean heat loss to the atmosphere during the fall freeze season, is speculated to play an important role in the recently observed cloud cover increase and BL instability. However, lack of observations and understanding of the resilience of the proposed mechanisms, especially in relation to meteorological and interannual variability, has left a poorly constrained BL parameterization scheme in Arctic climate models. In this study, we use multiyear Japanese cruise-ship observations from RV Mirai over the open Arctic Ocean to characterize the surface sensible heat flux (SSHF) during early fall and investigate its contribution to BL turbulence. It is found that mixing by SSHF is favored during episodes of high surface wind speed and is also influenced by the prevailing cloud regime. The deepest BLs and maximum ocean-atmosphere temperature difference are observed during cold air advection (associated with the stratocumulus regime), yet, contrary to previous speculation, the efficiency of sensible heat exchange is low. On the other hand, the SSHF contributes significantly to BL mixing during the uplift (low pressure) followed by the highly stable (stratus) regime. Overall, it can explain 10 of the open ocean BL height variability, whereas cloud-driven (moisture and radiative) mechanisms appear to be the other dominant source of convective turbulence. Nevertheless, there is strong interannual variability in the relationship between the SSHF and the BL height which can be intensified by the changing occurrence of Arctic climate patterns, such as positive surface wind speed anomalies and more frequent conditions of uplift. This study highlights the need for comprehensive BL observations like the RV Mirai for better understanding and predicting the dynamic nature of the Arctic climate.

boundary layer↗

NASA NTRS1993

Cost-effective test methods for Shuttle payloads

Techniques are discussed for deriving constrained vibration mode shapes for space shuttle payloads using unconstrained or free-boundary dynamic properties. Application of the residual flexibility method requires measurement of a set of free boundary modes plus the residual flexibility of the payload-to-orbiter interfaces. The mass-additive approach involves the measurement of unconstrained modes and frequencies of a payload with large masses attached to the interfaces. In either case, the orbiter interfaces of the test-verified payload model are analytically constrained to provide the mode shapes for the shuttle-constrained configuration. Use of these methods or a hybrid combination of them for structures to which they are applicable allows the difficulty and expense associated with development and verification of fixed-base test fixtures to be avoided.

Tinker, Michael L.↗

NASA NTRS1993

Cost-effective test methods for Shuttle payloads

Techniques are discussed for deriving constrained vibration mode shapes for Space Shuttle payloads using unconstrained or free-boundary dynamic properties. Application of the residual flexibility method requires measurement of a set of free-boundary modes plus the residual flexibility of the payload-to-orbiter interfaces. The mass-additive approach involves the measurement of unconstrained modes and frequencies of a payload with large masses attached to the interfaces. In either case, the orbiter interfaces of the test-verified payload model are analytically constrained to provide the mode shapes for the Shuttle-constrained configuration. Use of these methods or a hybrid combination of them for structures to which they are applicable allows the difficult and expense associated with development and verification of fixed-base test fixtures to be avoided.

Tinker, Michael L.↗

NASA NTRSDate not supplied

Can Tracked Great Frigatebirds (Fregata minor) be Used to Measure the Dynamics of the Planetary Boundary Layer Height?

Observing the dynamics of the planetary boundary layer (PBL) will require creative combinations of space-based and in-situ measurements. Animals fitted with biologgers have been used to gather data and parameterize physical models in various settings and may be a useful addition to the suite of space-based measurements that NASA is considering. For example, great frigatebirds (Fregata minor) generally fly below 700m but have been shown to routinely climb up to 2,000 meters during the day, occasionally reaching heights over 4,000 meters. This suggests that they may be tracking boundary layer height dynamics as they soar and glide on air currents with little energetic cost. We show here that the high-altitude climbing heights of great frigatebirds carrying GPS/accelerometer biologgers (e-obs GmbH Bird Solar 15g) at Palmrya Atoll, Pacific Ocean, are consistent with the long-term climatology (2006-2019) of the local planetary boundary layer height, and that these soaring heights can be reliably extracted from the tag data. Additional study is needed to determine how well movement data from tracked birds can constrain PBL height, but this work demonstrates the potential for animal-borne sensors to complement space-based measurements. Biologging data were contributed by the USGS and the Nature Conservancy's Palmyra Bluewater Research (PBR) study and analyzed as part of NASA’s Internet of Animals project.

Planetary Boundary Layer Height↗

NASA NTRS1989

A general dynamic model of flexible robot arms for control

Hamilton's principle is used to derive the dynamic model for a large class of flexible robot arms. The resultant dynamic model consists of a system of partial differential-integral equations and the dynamic boundary conditions associated with it. Some properties of the model are observed, and its application to control is discussed. This model represents an infinite-dimensional nonlinear dynamic system and yet can be turned into a finite-dimensional system that could be obtained by modal expansion, if it is desired. This provides more flexibility for control purposes as well as for the analysis of the system.

Ding, X.↗

NASA NTRS2002

Modeling Disturbance Dynamics in Transitional and Turbulent Boundary Layers

The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced across the boundary layer by the solid boundary. In addition, the dominating dynamics in the disturbance kinetic energy equation is governed by the energy production, pressure-transport and viscous diffusion - also in contrast to the fully turbulent regime. For the disturbance dissipation rate, a dynamic balance exists between the destruction and diffusion of dissipation.

Grosch, C. E.↗

NASA NTRS1995

Accretion disk boundary layers in cataclysmic variables. 1: Optically thick boundary layers

We develop numerical models of accretions disks in cataclysmic variables (CVs), including and emphasizing the boundary layer region where the accretion disk meets the accreting white dwarf. We confine ourselves to solutions where the boundary layer region is vertically optically thick, and find that these solutions share several common features. The angular and radial velocities of the accreting material drop rapidly in a dynamical boundary layer, which has a radial width approximately 1%-3% of the white dwarf radius. The energy dissipated in this region diffuses through the inner part of the disk and is radiated from the disk surface in a thermal boundary layer, which has a radial width comparable to the disk thickness, approximately 5%-15% of the white dwarf radius. We examine the dependence of the boundary layer structure on the mass accretion rate, the white dwarf mass and rotation rate, and the viscosity parameter alpha. We delineate the boundary between optically thick and optically thin boundary layer solutions as a function of these parameters and suggest that by means of a careful comparison with observations it may be possible to estimate alpha in CVs. We derive an expression for the total boundary layer luminosities as a function of the parameters and show that it agrees well with the luminosites of our numerical solutions. Finally, we calcuate simple blackbody continuum spectra of the boundary layer and disk emission for our solutions and compare these to soft X-ray, EUV, and He II emission-line observations of CVs. We show that, through such comparisons, it may be possible to determine the rotation rates of the accreting stars in CVs, and perhaps also the white dwarf masses and the accretion rates. The spectra are quite insensitive to alpha, so the uncertainty in this parameter does not affect such comparisons.

Popham, Robert↗

NASA NTRS1997

Advection in Accretion Disk Boundary Layers

Recent numerical simulations of accretion disk boundary layers have shown qualitatively the importance tance of advected energy in the inner region of the disk. In this short paper we present quantitative results of advective boundary layers in the optically thick regime. Numerical results are obtained for various systems, by means of a one-dimensional time-dependent numerical code. At high accretion mass rates, dot-M approx. = 10(exp -4) solar mass/yr, or low values of the viscosity parameter, alpha approx. = 0.001-0.01 (characteristic of FU Orionis systems and some symbiotic stars), the optical thickness in the inner part of the disk becomes very large (tau much greater than 1). The disk, unable to cool efficiently, becomes geometrically thick (H/r approx. = 0.5). The energy dissipated in the dynamical boundary layer is radiated outward to larger radii and advected into the star. The boundary-layer luminosity is only a fraction of its expected value; the rest of the energy is advected into the star. The fraction of the advected energy is zeta = L(sub adv)/L(sub acc) approx. = 0.1 in symbiotic stars (accretion onto a low-mass main-sequence star) and zeta approx. = 0.2 in FU Ori systems (accretion onto a pre-main sequence star).

Godon, Patrick↗

NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗

NASA NTRS1983

Development of a distributed-parameter mathematical model for simulation of cryogenic wind tunnels

A one-dimensional distributed-parameter dynamic model of a cryogenic wind tunnel was developed which accounts for internal and external heat transfer, viscous momentum losses, and slotted-test-section dynamics. Boundary conditions imposed by liquid-nitrogen injection, gas venting, and the tunnel fan were included. A time-dependent numerical solution to the resultant set of partial differential equations was obtained on a CDC CYBER 203 vector-processing digital computer at a usable computational rate. Preliminary computational studies were performed by using parameters of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Studies were performed by using parameters from the National Transonic Facility (NTF). The NTF wind-tunnel model was used in the design of control loops for Mach number, total temperature, and total pressure and for determining interactions between the control loops. It was employed in the application of optimal linear-regulator theory and eigenvalue-placement techniques to develop Mach number control laws.

Tripp, J. S.↗

NASA NTRS1987

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Revenaugh, Justin↗

NASA NTRS1993

Active control of asymmetric conical flow using spinning and rotatory oscillations

The effectiveness of active control on asymmetric flows around circular cones is investigated computationally using cone spinning and rotatory oscillation around its axis. The investigation uses the time-accurate solution of the unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, flux-difference splitting, finite-volume scheme. The present solutions are obtained under the locally-conical-flow assumption in order to understand the flow physics using very fine grids for reasonable flow resolution at low computational cost. For all the computational solutions, a grid of 241 x 81 x 2 points in the wrap-around, normal and axial directions, respectively, is used. The grid is spinning or oscillating rigidly with the cone according to its motion and the kinematical and dynamical boundary conditions are modified accordingly. The computational applications include the effects of uniform spinning rates and periodic rotatory oscillations at different amplitudes and frequencies on the flow asymmetry.

Kandil, Osama A.↗

NASA NTRS1996

Perspectives of the 1st IACG Campaign: Preliminary Results

The activities and aims of the Inter-Agency Consultative Group (IACG) for space science are reported on. The principle aim is to enhance the scientific return among the members through the coordination of their fleets of current and future spacecraft. The four current campaigns are: magnetotail energy flow and nonlinear dynamics; boundaries in the collisionless plasma; solar events and their manifestations in interplanetary space and geoscience, and solar sources of heliospheric structure observed out of the ecliptic. The first of these campaigns and its implementation are reviewed.

Greem, James L.↗

NASA NTRS2001

Large Scale Deformation of the Western US Cordillera

Destructive earthquakes occur throughout the western US Cordillera (WUSC), not just within the San Andreas fault zone. But because we do not understand the present-day large-scale deformations of the crust throughout the WUSC, our ability to assess the potential for seismic hazards in this region remains severely limited. To address this problem, we are using a large collection of Global Positioning System (GPS) networks which spans the WUSC to precisely quantify present-day large-scale crustal deformations in a single uniform reference frame. Our work can roughly be divided into an analysis of the GPS observations to infer the deformation field across and within the entire plate boundary zone and an investigation of the implications of this deformation field regarding plate boundary dynamics.

Bennett, Richard A.↗

NASA NTRS2002

Large Scale Deformation of the Western U.S. Cordillera

The overall objective of the work that was conducted was to understand the present-day large-scale deformations of the crust throughout the western United States and in so doing to improve our ability to assess the potential for seismic hazards in this region. To address this problem, we used a large collection of Global Positioning System (GPS) networks which spans the region to precisely quantify present-day large-scale crustal deformations in a single uniform reference frame. Our results can roughly be divided into an analysis of the GPS observations to infer the deformation field across and within the entire plate boundary zone and an investigation of the implications of this deformation field regarding plate boundary dynamics.

Bennett, Richard A.↗

NASA NTRS2002

Large Scale Deformation of the Western U.S. Cordillera

Over the past couple of years, with support from NASA, we used a large collection of data from GPS, VLBI, SLR, and DORIS networks which span the Western U.S. Cordillera (WUSC) to precisely quantify present-day large-scale crustal deformations in a single uniform reference frame. Our work was roughly divided into an analysis of these space geodetic observations to infer the deformation field across and within the entire plate boundary zone, and an investigation of the implications of this deformation field regarding plate boundary dynamics. Following the determination of the first generation WUSC velocity solution, we placed high priority on the dissemination of the velocity estimates. With in-kind support from the Smithsonian Astrophysical Observatory, we constructed a web-site which allows anyone to access the data, and to determine their own velocity reference frame.

Bennett, Richard A.↗