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At least 145 records · Page 8
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NASA NTRS2014

Resonant Tidal Excitation of Internal Waves in the Earth's Fluid Core

It has long been speculated that there is a stably stratified layer below the core-mantle boundary, and two recent studies have improved the constraints on the parameters describing this stratification. Here we consider the dynamical implications of this layer using a simplified model. We first show that the stratification in this surface layer has sensitive control over the rate at which tidal energy is transferred to the core. We then show that when the stratification parameters from the recent studies are used in this model, a resonant configuration arrives whereby tidal forces perform elevated rates of work in exciting core flow. Specifically, the internal wave speed derived from the two independent studies (150 and 155 m/s) are in remarkable agreement with the speed (152 m/s) required for excitation of the primary normal mode of oscillation as calculated from full solutions of the Laplace Tidal Equations applied to a reduced-gravity idealized model representing the stratified layer. In evaluating this agreement it is noteworthy that the idealized model assumed may be regarded as the most reduced representation of the stratified dynamics of the layer, in that there are no non-essential dynamical terms in the governing equations assumed. While it is certainly possible that a more realistic treatment may require additional dynamical terms or coupling, it is also clear that this reduced representation includes no freedom for coercing the correlation described. This suggests that one must accept either (1) that tidal forces resonantly excite core flow and this is predicted by a simple model or (2) that either the independent estimates or the dynamical model does not accurately portray the core surface layer and there has simply been an unlikely coincidence between three estimates of a stratification parameter which would otherwise have a broad plausible range.

Geodynamo↗
NASA NTRS2023

Capacitive Micro-Gravity Fluid Mass Gauge

Measuring fluid mass in micro gravity, where fluid behavior is dominated by fluid properties, is a challenging problem. To address this problem engineers at NASA are developing a capacitance-based, mass-fraction gauge for vessels containing two-phase fluids. The vessel volume is enclosed with an array of electrodes, and a unique set of capacitance measurements of the enclosed volume are made between the electrodes. The capacitance measurements are scaled with appropriate weighting factors derived from Laplace's Equation to compensate for the highly non-uniform electric fields inside the measurement volume and achieve a greater level of mass fraction accuracy.

Mark A Nurge↗
NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of the limitations of the technique can be obtained by simulating the inspection process. Time domain finite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

thermography↗
NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of thelimitations of the technique can be obtained by simulating the inspection process. Time domainfinite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

Thermography↗
NASA NTRS1985

Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble

A direct and convenient method is presented for deriving expressions which equate any thermodynamic state function to averages of specific dynamical functions and their fluctuations over the classical microcanonical distribution. Specific expressions are obtained for a variety of thermodynamic quantities. The effect of various entropy definitions on the results are assessed, and the latter are compared to previous work in the literature. The derived formulas are applied to the analysis of molecular-dynamics computer simulations.

Pearson, E. M.↗
NASA NTRS1982

An analytic approach to two-fixed-impulse transfers between Keplerian orbits

Solutions are obtained for the two-impulse transfer of a vehicle between arbitrary inclined orbits in an inverse-square force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.

Jezewski, D. J.↗
NASA NTRS1988

Parameter estimation technique for boundary value problems by spline collocation method

A parameter-estimation technique for boundary-integral equations of the second kind is developed. The output least-squares identification technique using the spline collocation method is considered. The convergence analysis for the numerical method is discussed. The results are applied to boundary parameter estimations for two-dimensional Laplace and Helmholtz equations.

Kojima, Fumio↗
NASA NTRS1974

U.S. National Congress of Applied Mechanics, 7th, University of Colorado, Boulder, Colo., June 3-7, 1974, Proceedings

A series of experimental, theoretical, and review papers dealing with various aspects of applied mechanics, including structural analysis, mathematical methods, and fluid dynamics. Some of the topics covered are: the direct formulation of two-dimensional mechanics problems, the mechanical aspects of athletics, Laplace's tidal equations, cochlear mechanics, dynamic constitutive equations, optical techniques for the determination of displacement and strain fields, chemical and biochemical problems involving nonlinear diffusion processes, thermal stresses, the rotating rod viscometer, finite-element methods in plasticity, ships of minimum resistance, and wide-band random vibration of structures. Individual items are announced in this issue.

Source record↗
NASA NTRS1978

Open ocean tide modelling

Two trends evident in global tidal modelling since the first GEOP conference in 1972 are described. The first centers on the incorporation of terms for ocean loading and gravitational self attraction into Laplace's tidal equations. The second centers on a better understanding of the problem of near resonant modelling and the need for realistic maps of tidal elevation for use by geodesists and geophysicists. Although new models still show significant differences, especially in the South Atlantic, there are significant similarities in many of the world's oceans. This allows suggestions to be made for future locations for bottom pressure gauge measurements. Where available, estimates of M2 tidal dissipation from the new models are significantly lower than estimates from previous models.

Parke, M. E.↗
NASA NTRS1978

The inverse problem: Ocean tides derived from earth tide observations

Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.

Kuo, J. T.↗
NASA NTRS1979

M2, S2, K1 models of the global ocean tide

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.

Parke, M. E.↗
NASA NTRS1986

Modelling the pole tide and its effect on the earth's rotation

The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.

Carton, J. A.↗
NASA NTRS1989

New estimates of oceanic tidal energy dissipation from satellite altimetry

As a novel approach to computing the flux of tidal power into shelf areas, tidal maps of an oceanic area near the Patagonian Shelf are derived from 11 months of altimetry records from the GEOSAT satellite. Power fluxes are computed from the maps through Laplace's tidal equations. Flux vectors for M2 clearly show a convergence on to the southern portion of the shelf sea and their total is nearly twice the loss computed by Miller for that area. A decrease of 'quality factor' with frequency from M2 to S2 is in keeping with Webb's hypothesis of shelf resonances at frequencies a little higher than the tidal band.

Cartwright, David E.↗
NASA NTRS1991

Research on diabatic initialization

The objective was to contribute to the improvement of the analyses of irrotational wind and moisture fields in the trophics through advancement in the technique of initialization by incorporating diabatic effects. Significant accomplishments made during the period May 1990 to April 1991 in the following areas are presented: (1) estimation of the uncertainty of daily synoptic analyses in the tropics; (2) normal modes of Laplace's tidal equations for zonal wavenumber zero; and (3) tropical initialization to ameliorate the spin-up problem of precipitation forecasts. The focus of current research and plans for next year are also presented.

Kasahara, Akira↗
NASA NTRS1993

Gravitational tides in the outer planets. I - Implications of classical tidal theory. II - Interior calculations and estimation of the tidal dissipation factor

Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.

Ioannou, Petros J.↗
NASA NTRS1977

Unsteady subsonic and supersonic potential aerodynamics for complex configurations

A recently developed general theory for unsteady compressible potential fluid dynamics for complex-configuration aircraft is reviewed. The method is based on a combination of the following techniques: Green's function method (to transform the differential equation into an integral differential-delay equation), finite element method (to transform the equation into a set of differential-delay equations in time), and the Laplace transform method (to transform the differential-delay equations into algebraic equations).

Morino, L.↗