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At least 127 records · Page 7

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NASA NTRS1984

Effect of boundary layers on solid walls in three-dimensional subsonic wind tunnels

A solution for the tunnel wall boundary layer effects for three-dimensional subsonic tunnels is presented. The model potentials are represented with simple singularities placed on the centerline of the tunnel and Laplace's equation in cylindrical coordinates is solved for either the conventional homogeneous slotted-wall boundary condition, the solid-wall viscous boundary condition, or a combination of them. The most pronounced wall boundary layer effect is on solid blockage for completely closed wind tunnels. Boundary layers on the wall reduce the blockage from the solid-wall, no-boundary-layer case in a manner similar to opening slots in a solid wall. Additionally, for solid-wall tunnel configurations, the streamline curvature interference factor is reduced by a significant amount, whereas the lift interference factor at the model station does not depend on the boundary layer parameter. For combination wall configurations, the slot effect of the horizontal walls dominates the viscous effect of the solid sidewalls.

Adcock, J. B.↗

NASA NTRS1985

Interface shape in Czochralski grown crystals - Effect of conduction and radiation

A sequential modular computational scheme has been proposed for the calculation of temperature profiles in the melt and crystal including the melt-crystal interface shape and the crystal pulling rate for a fixed crystal radius. The heat transfer in the melt is assumed to occur by conduction only. The shape of melt-gas meniscus, described by Laplace-Young equation, is incorporated in the model and its effects on interface shape and pulling rate are examined. Further, the model incorporates the detailed radiation interaction among the various surfaces in the puller using the Gebhart enclosure theory which accounts for both direct and reflected radiation. The effects of various process parameters on the interface shape and the pulling rate have been investigated. The results of this study indicate that the shape of the melt-gas meniscus has a significant effect on the pulling rate and the interface shape in conformity with earlier studies. Further, it is shown that a simple radiation model (Stefan's model) is inadequate to model the radiation heat exchange in the Czochralski puller apparatus and the detailed Gebhart analysis is necessary for accurate calculation of both the temperature profile in the crystal as well as the interface shape.

Srivastava, R. K.↗

NASA NTRS1987

The behavior of surface tension on steady-state rotating fluids in the low gravity environments

The effect of surface tension on steady-state rotating fluids in a low gravity environment is studied. All the values of the physical parameters used in these calculations, except in the low gravity environments, are based on the measurements carried out by Leslie (1985) in the low gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating the pressure drop across an interface to the radii of curvature which has been applied to a low gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes non-zero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.

Hung, R. J.↗

NASA NTRS1985

The relations between the linear and bilinear atmospheric tidal fields in geometric height and in log-pressure coordinates

Theoretical models of planetary-atmosphere tidal fields are examined analytically, comparing models based on geometric-height coordinates with those employing log-pressure coordinates. The relationship between the linearized meteorological variables in the two systems is explored for classical tidal theory and its reduction to the Laplace tidal equation, and it is shown that identical horizontal and vertical equations are obtained. Also considered are the tidal zonal-mean bilinear flux convergences and their Eliassen-Palm formulations. Numerical results for problems involving the earth and Mars atmospheres are presented in graphs and discussed.

Zurek, Richard W.↗

NASA NTRS1987

A two-dimensional radial outflow model of plasma at Jupiter

An analytic solution illustrating the behavior of incompressible irrotational plasma outflow in two dimensions is given for application to the Jovian magnetosphere. Plasma is assumed to emanate from the Alfven surface and is channeled downtail by the confining magnetopause surface. Conformal transformation methods are used to map this complex magnetotail geometry into a rectangular box for which the solution to Laplace's equation is expressed in simple form. The model suggests that a dipole layer is formed on the dawn side in the vicinity of the Alfven surface where the flow bifurcates into clockwise and counterclockwise motion. An electric field discontinuity of this type fixed in local time may be able to account for several anomalous spin-periodic phenomena, namely, the modulation of Io-independent radio emissions and the injection of energetic electrons into interplanetary space.

Barbosa, D. D.↗

NASA NTRS1988

The self-consistent dynamic pole tide in non-global oceans

The dynamic pole tide is determined by solving Laplace tide equations which take into account the presence of continents in oceans, oceanic self-gravitation and loading, and mantle elasticity. Dynamical effects are found to be only mild. It is shown that the dynamical pole tide contributes about one day more to the Chandler period than a static pole tide would, and dissipates wobble energy at a very weak rate. It is noted that, depending on the wobble period predicted for an oceanless elastic earth, mantle anelasticity at low frequencies may nevertheless contribute negligibly to the Chandler period.

Dickman, S. R.↗

NASA NTRS1989

Variability of quasi-stationary planetary waves

The results of the analysis of nonzonal perturbations (m = 1, 2, 3) of the geopotential field at a 30 mb level are presented. A long period modulation of the harmonics' amplitude is discovered. Calculations of eigenfunctions and eigennumbers of the Laplace tidal equation are carried out for a real latitudinal wind profile. The observed first zonal harmonic in different years is caused by the same mode. Thus, the difference in the wave amplitudes could not be accounted for by the difference in stratospheric zonal circulation in different years and should be related to tropospheric processes.

Krivolutsky, A. A.↗

NASA NTRS1989

Precise solution for a finite set of spherical coefficients from equiangular gridded data

An important goal of geodesy is to determine the anomalous potential and its derivatives outside of the earth. Representing the surface anomalies by a series of spherical harmonics is useful since it is then possible to do a term by term solution of Laplace's equation and upward continuation. The problem of finding such a spherical harmonic series for anomaly values given on an equiangular surface grid is addressed. (This is a first step toward the more complicated problem of finding a function such that locally averaged values fit a grid of mean anomalies.) Three approaches to this fitting problem are discussed and compared: the discrete Fourier technique, the discrete integral technique, and a new approach. The peculiar nature of the equiangular grid, with its increasing density of (noisy) data toward the poles, causes each method to exhibit a different type of difficulty. The new method is shown to be practical as well as precise since the numerical conditioning problems which appear can be successfully handled by such well-known techniques as a (simple) Kalman filter.

Zucker, Paul A.↗

NASA NTRS1990

Hypercluster parallel processing library user's manual

This User's Manual describes the Hypercluster Parallel Processing Library, composed of FORTRAN-callable subroutines which enable a FORTRAN programmer to manipulate and transfer information throughout the Hypercluster at NASA Lewis Research Center. Each subroutine and its parameters are described in detail. A simple heat flow application using Laplace's equation is included to demonstrate the use of some of the library's subroutines. The manual can be used initially as an introduction to the parallel features provided by the library. Thereafter it can be used as a reference when programming an application.

Quealy, Angela↗

NASA NTRS1990

Inhomogeneous electric field effects in a linear RF quadruple trap

The exact potential corresponding to confining fields inside a linear rf quadrupole particle trap of finite length is presented. The analytic expressions for the trapping potential is derived by introducing a linear trap employing a relatively simple cylindrical geometry and solving Laplace's equation for the trap electrodes. The finite length of linear traps results in field distortion near the trap ends. An exact analytic determination of the fields is useful because the profile of the trapped ion cloud is highly dependent on the fields confining it. It is shown that near the ends of the trap, the effective potential arising from the rf fields acts to propel particles out of the trap, and further, that the addition of a dc bias generates an inhomogeneous in the trap that influences the particles both perpendicularly to and along the trap's long axis.

Melborne, R. K.↗

NASA NTRS1989

A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.

Dickman, S. R.↗

NASA NTRS1990

Eigenfrequencies and horizontal structure of divergent barotropic instability originating in tropical latitudes

A systematic investigation of eigenfunctions of the generalized Laplace tidal equation, for the case of tropical-latitude monotonic mean zonal wind profiles with a single narrow reversed vorticity gradient region, has revealed that, in the limit of low planetary zonal wavenumber, the barotropic instability modes bifurcate into weakly divergent modes of hemispheric scale, on the one hand, and on the other strongly divergent 'internal' modes trapped about the source region. These latter disturbances penetrate into the deep tropics as a Kelvin wave-type phenomenon not previously seen in this context. These results suggest that hemispheric barotropic instability need not be purely nondivergent, and that the growth of weakly divergent modes is preferred.

Dunkerton, Timothy J.↗

NASA NTRS1989

Construction of surface pressure field from scatterometer wind field

An account of the construction of surface pressure fields from Seasat-A satellite scatterometer (SASS) winds as carried out by different methods, and the comparison of these pressure fields with those derived from in situ ship observations is presented. On the assumption that the pressure adjusts itself instantaneously to the motion field, it may be computed by various methods. One of these makes use of planetary boundary theory, and of the possible techniques in this category a two-layer iterative scheme admitting of the parametrization of diabatic and baroclinic effects and of secondary flow was chosen. A second method involves the assumption of zero two-dimensional divergence, leading to a Laplace's equation (the balance equation) in pressure, with the wind field serving as a forcing function. This method does not accommodate adiabatic or baroclinic effects, and requires a knowledge of the pressure at all boundary points. Two comparison fields are used for validation: the conventional operational analyses of the US National Meteorological Center (NMC), and the special analyses of the Gulf of Alaska Experiment (GOASEX), which were done by hand. The results of the computations were as follows: (1) The pressure fields, as computed from the SASS winds alone, closely approximated the NMC fields in regions where reasonable in situ coverage was available (typically, one or two mb differences over most of the chart, three to four mb in extreme cases); (2) In some cases the SASS-derived pressure fields displayed high-resolution phenomena not detected by the NMC fields, but evident in the GOASEX data; and, (3) As expected, the pressure fields derived from the balance equation were much smoother and less well resolved than the SASS-derived or NMC fields. The divergence as measured from the SASS winds is smaller than, but of the same order of magnitude as, the vorticity.

Wurtele, Morton G.↗

NASA NTRS1991

Analytic potential in a linear radio-frequency quadrupole trap with cylindrical electrodes

An analytical expression is derived for a radio-frequency ion trap of novel configuration consisting of a four-sectored hollow cylinder enclosed between two end caps. The cylindrical geometry of the sectored trap provides shielding against the buildup of charge and also makes it possible to calculate the potential within the trap by solving Laplace's equation for given boundary conditions. Equations are presented for calculating the time-averaged potential generated by the RF fields, the end-cap potential, and the potential arising from the application of a dc bias on two of the four electrode sectors. It is shown that, near the ends of this trap, the effective potential arising from the RF fields acts to propel ions out of the trap and that the addition of a dc bias on two neighboring sectors generates an inhomogeneous field in the trap which produces a force on the ions along the trap's long axis in a direction dependent on the sign of the bias.

Melbourne, R. K.↗

NASA NTRS1992

Ion collection from a plasma by a pinhole

Ion focusing by a biased pinhole is studied numerically. Laplace's equation is solved in 3-D for cylindrical symmetry on a constant grid to determine the potential field produced by a biased pinhole in a dielectric material. Focusing factors are studied for ions of uniform incident velocity with a 3-D Maxwellian distribution superimposed. Ion currents to the pinhole are found by particle tracking. The focusing factor of positive ions as a function of initial velocity, temperature, injection radius, and hole size is reported. For a typical Space Station Freedom environment (oxygen ions having a 4.5 eV ram energy, 0.1 eV temperature, and a -140 V biased pinhole), a focusing factor of 13.35 is found for a 1.5 mm radius pinhole.

Snyder, David B.↗

NASA NTRS1990

The pole tide in deep oceans

The fluid-dynamical theory of the pole tide is examined by describing the oceanic response to the Chandler wobble and assessing its implications for mantle anelasticity and low-frequency ocean dynamics. The Laplace tide equations accounting for bottom friction are given, and a spherical harmonic approach is delineated in which the time-independent portion of the tide height is expanded. Pole-tide height and related inertia products are linearly proportional to wobble amplitude, and the final equations are modified to account for mantle elasticity and oceanic loading. Results for pole tide effects are given for various earth models with attention to the role of boundary constraints. A dynamic effect is identified which lengthens the Chandler period by about 1 day more than static lengthening, a contribution that suggests a vigorous low-frequency response. The values derived are shown to agree with previous models that do not incorporate the effects of the pole tide.

Dickman, S. R.↗

NASA NTRS1992

Antarctic marine gravity field from high-density satellite altimetry

High-density (about 2-km profile spacing) Geosat/GM altimetry profiles were obtained for Antarctic waters (6-deg S to 72 deg S) and converted to vertical gravity gradient, using Laplace's equation to directly calculate gravity gradient from vertical deflection grids and Fourier analysis to construct gravity anomalies from two vertical deflection grids. The resultant gravity grids have resolution and accuracy comparable to shipboard gravity profiles. The obtained gravity maps display many interesting and previously uncharted features, such as a propagating rift wake and a large 'leaky transform' along the Pacific-Antarctic Rise.

Sandwell, David T.↗

NASA NTRS1991

Global ocean tide mapping using TOPEX/Poseidon altimetry

The investigation's main goals are to produce accurate tidal maps of the main diurnal, semidiurnal, and long-period tidal components in the world's deep oceans. This will be done by the application of statistical estimation techniques to long time series of altimeter data provided by the TOPEX/POSEIDON mission, with additional information provided by satellite tracking data. In the prelaunch phase, we will use in our simulations and preliminary work data supplied by previous oceanographic missions, such as Seasat and Geosat. These results will be of scientific interest in themselves. The investigation will also be concerned with the estimation of new values, and their uncertainties, for tidal currents and for the physical parameters appearing in the Laplace tidal equations, such as bottom friction coefficients and eddy viscosity coefficients. This will be done by incorporating the altimetry-derived charts of vertical tides as boundary conditions in the integration of those equations. The methodology of the tidal representation will include the use of appropriate series expansions such as ocean-basin normal modes and spherical harmonics. The results of the investigation will be space-determined tidal models of coverage and accuracy superior to that of the present numerical models of the ocean tides, with the concomitant benefits to oceanography and associated disciplinary fields.

Sanchez, Braulio V.↗