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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Schlesinger, R. E.↗
DOE OSTI2025

Assessing the fidelity of shallow-water carbonates as records of the Ni isotope composition of surface seawater

Nickel is a bioessential metal that is used in enzymes important to the C, N, and O cycles, and changes in its marine abundance and bioavailability may have affected the evolutionary trajectory of early life. Changes over time in the Ni isotope composition (δ 60 Ni) of surface seawater, which reflects biological demand for Ni, could allow for the reconstruction of the dynamics of Ni demand over Earth’s history, but this approach would require geologic records of surface seawater. Here, we investigate the fidelity of shallow-water carbonates as a record of the Ni isotope composition of surface seawater by determining how Ni is first partitioned into natural carbonates and then how post-depositional processes influence the Ni signal. Our samples come from the Great Bahama Bank, which is a well-studied, modern carbonate platform often used to study ancient platforms. We found that Ni is fractionated from seawater upon incorporation into carbonates capturing shallow (<18 cm), recent deposition (0.1 ‰–0.4 ‰ lighter than seawater). Variation among these [Ni] and δ 60 Ni values may be controlled by variation in mineral proportions. Meteoric diagenesis shifts δ 60 Ni to lower values, which we attribute to isotopically light meteoric fluids. In contrast, carbonates that experienced sediment-buffered marine diagenesis with respect to Ca isotopes and Sr/Ca ratios do not appear to differ in δ 60 Ni values from sediments generally representative of their initial deposition. The sensitivity of δ 60 Ni to diagenetic reset in these samples appears comparable to the sensitivities of Ca isotopes and Sr/Ca ratios, to first order. Thus, in general, carbonates that experienced sediment-buffered marine diagenesis with respect to these elements may hold the most promise as a record of the δ 60 Ni of coeval surface seawater. Additionally, we use our results to infer that the fraction of Ni removed from seawater into carbonates is less than 10 % of the total Ni output from the global oceans and incorporation of this Ni sink into global biogeochemical models will only have a minor impact on the modeled modern Ni budget.

Great Bahama Bank carbonates↗
NASA NTRS1988

Semi-Lagrangian integration of a grid-point shallow water model on the sphere

This paper describes a semi-Lagrangian technique for integrating the equations of motion on the global domain. The technique uses an auxiliary spherical coordinate system at each near-polar gridpoint of the latitude-longitude grid; the auxiliary system is obtained by a rotation such that the new equator passes through the gridpoint in question and the new coordinate directions coincide with those of the original system at that point. The technique was applied to the shallow water equations, incorporating a semiimplicit treatment of the adjustment terms on a C-grid, with two-time levels. A five day integration was successfully carried out for a situation involving strong cross-polar flow. No filtering or diffusion was required to maintain stability over a five day period.

Mcdonald, A.↗
NASA NTRS1984

Modeling of SAR signatures of shallow water ocean topography

A hydrodynamic/electromagnetic model was developed to explain and quantify the relationship between the SEASAT synthetic aperture radar (SAR) observed signatures and the bottom topography of the ocean in the English Channel region of the North Sea. The model uses environmental data and radar system parameters as inputs and predicts SAR-observed backscatter changes over topographic changes in the ocean floor. The model results compare favorably with the actual SEASAT SAR observed backscatter values. The developed model is valid for only relatively shallow water areas (i.e., less than 50 meters in depth) and suggests that for bottom features to be visible on SAR imagery, a moderate to high velocity current and a moderate wind must be present.

Shuchman, R. A.↗
NASA NTRS1986

Geostrophic adjustment in a shallow-water numerical model as it relates to thermospheric dynamics

The theory of geostrophic adjustment and its application to the dynamics of the high latitude thermosphere have been discussed in previous papers based on a linearized treatment of the fluid dynamical equations. However, a linearized treatment is only valid for small Rossby numbers given by Ro = V/fL, where V is the wind speed, f is the local value of the Coriolis parameter, and L is a characteristic horizontal scale for the flow. For typical values in the auroral zone, the approximation is not reasonable for wind speeds greater than 25 m/s or so. A shallow-water (one layer) model was developed that includes the spherical geometry and full nonlinear dynamics in the momentum equations in order to isolate the effects of the nonlinearities on the adjustment process. A belt of accelerated winds between 60 deg and 70 deg latitude was used as the initial condition. The adjustment process was found to proceed as expected from the linear formulation, but that an asymmetry between the response for an eastward and westward flow results from the nonlineawr curvature (centrifugal) terms. In general, the amplitude of an eastward flowing wind will be less after adjustment than a westward wind. For instance, if the initial wind velocity is 300 m/s, the linearized theory predicts a final wind speed of 240 m/s, regardless of the flow direction. However, the nonlinear curvature terms modify the response and produce a final wind speed of only 200 m/s for an initial eastward wind and a final wind speed of almost 300 m/s for an initial westward flow direction. Also, less gravity wave energy is produced by the adjustment of the westward flow than by the adjustment of the eastward flow. The implications are that the response of the thermosphere should be significantly different on the dawn and dusk sides of the auroral oval. Larger flow velocities would be expected on the dusk side since the plasma will accelerate the flow in a westward direction in that sector.

Larsen, M. F.↗
NASA NTRS1989

Jupiter's Great Red Spot as a shallow water system

Voyager cloud-top velocity data for Jupiter's Great Red Spot (GRS) is used to derive the bottom topography up to a constant that depends on the unknown radius of deformation. The bottom topography is inferred from the Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity values derived from the velocity data. The results are used to calculate potential vorticity versus latitude far from the vortex. It is found that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical experiments are conducted to study the time-dependent behavior of the shallow water analog of Jupiter's analog.

Dowling, Timothy E.↗
NASA NTRS1985

A Kalman filter for a two-dimensional shallow-water model

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Parrish, D. F.↗
NASA NTRS1972

Evaluation of factors affecting resolution of shallow water bottom features

To ensure good aerial photography, the effects that factors such as submergence depth, sun angle, film and filter type, exposure, aircraft altitude, and polarization have on the photographic resolution of an underwater object must be determined. Various subjects were photographed, such as the deck of a small submersible, colored and gray scale panels, and natural bottom features. No underwater resolution target was used.

Mason, C. C.↗
NASA NTRS1981

An analysis of intermittent updating for the shallow water equations

The method of intermittent updating for a model system is analyzed. How updating one variable of the system affects the other variables, what the factors are which influence the rate of convergence of this procedure, and how measurement error affects the procedure are considered.

Bube, K. P.↗
NASA NTRS1984

A Lagrangian method for a two layer shallow water model

One of the biggest drawbacks of Eulerian methods is the presence of the nonlinear convective terms which leads to inaccurate representations of advection and fronts. An alternative and conceptually simpler approach is the Lagrangian approach in which the fluid particles themselves are tracked and equations are derived based on local spatial interaction. In this formulation the nonlinear convective terms do not appear. The main drawback with the Lagrangian formulation, however, is that the local spatial interactions are time dependent. That is, at each time level, one must know the current neighbors of a given particle to accurately compute the forces acting on the particle. The Voroni Mesh which is continuously deforming and always linking nearest neighbors is needed. The effectiveness of a simple Lagrangian method for simulating the onset of a Kelvin-Helmholtz instability in a 2 layer fluid is demonstrated.

Augenbaum, J. M.↗
NASA NTRS1992

Annual sea level variations in the southern tropical Indian Ocean from Geosat and shallow-water simulations

Sea level variations in the Indian Ocean north of 20 deg S are analyzed from Geosat satellite altimeter data in 1987-1988. These observed variations are compared with numerical simulations from a reduced-gravity model forced by observed winds over the same period. The first complex empirical orthogonal function of observed and simulated variations is an annual signal. For this signal, observations and simulations are highly correlated in both time and space. Off-equatorial sea level variations propagate westward and poleward as Rossby waves. The strongest annual variations occur in the southeastern tropical Indian Ocean. The maximum amplitude (about 12 cm) is located at about 90 deg E, 12 deg S, although the wind stress curl is weak there and east of it. The signal propagates from the eastern boundary to the southwest across almost all the basin.

Perigaud, Claire↗
NASA NTRS1993

Solution of the linear shallow water equations by the fourth-order leapfrog scheme

Numerical schemes of the first and second order of approximation introduce numerical distortion when the wave propagation over a long distance is investigated. To alleviate this problem, the fourth-order leapfrog scheme is constructed. The standard leapfrog method is based on the truncated Taylor series expansion which depicts an error proportional to the second-order terms. In the proposed method the numerical solution is corrected for these terms. The space and time corrections work well in diminishing numerical dispersion and dissipation.

Kowalik, Z.↗