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All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1993

Interannual Sea Level Variations in the Tropical Indian Ocean from Geosat and Shallow Water Simulations

Sea level variations of the Indian Ocean north of 20 deg S are analyzed from Geosat satellite altimeter data over April 1985-September 1989. These variations are compared and interpreted with numerical simulations derived from a reduced gravity model forced by FSU observed winds over the same period. After decomposition into complex empirical orthogonal functions, the low-frequency anomalies are described by the first two modes for observations as well as for simulations. The sums of the two modes contain 34% and 40% of the observed and simulated variances, respectively. Averaged over the basin, the observed and simulated sea level changes are correlated by 0.92 over 1985-1988. The strongest change happens during the El Ninio 1986-1987: between winter 1986 and summer 1987 the basin-averaged sea level rises by approx. 1 cm. These low-frequency variations can partly be explained by changes in the Sverdrup circulation. The southern tropical Indian Ocean between 1O deg and 20 deg S is the domain where those changes are strongest: the averaged sea level rises by approx. 4.5 cm between winter 1986 and winter 1987. There, the signal propagates southwestward across the basin at a speed similar to free Rossby waves. Sensitivity of observed anomalies is examined over 1987-1988, with different orbit ephemeris, tropospheric corrections, and error reduction processes. The uncertainty of the basin-averaged sea level estimates is mostly due to the way the orbit error is reduced and reaches approx. 1 cm. Nonetheless, spatial correlation is good between the various observations and better than between observations and simulations. Sensitivity of simulated anomalies to the wind uncertainty, examined with Former Soviet Union (FSU) and European Center for Medium-Range Weather Forecasting (ECMWF) forcings over 1985-1988, shows that the variance of the simulations driven by ECMWF is 52% smaller, as FSU winds are stronger than ECMWF. Results show that the wind strength also affects the dynamic response of the ocean: anomalies propagate westward across the basin more than twice as fast with FSU than with ECMWF. It is found that the discrepancy is larger between ECMWF and FSU simulations than between observations and FSU simulations.

Perigaud, Claire↗
NASA NTRS1996

Assimilation of Geosat Altimetric Data in a Nonlinear Shallow-Water Model of the Indian Ocean by Adjoint Approach. Part II: Some Validation and Interpretation of the Assimilated Results: Some Validation and Interpretation of the Assimilated Results - Part 2

This paper examines the results of assimilating Geosat sea level variations relative to the November 1986-November 1988 mean reference, in a nonlinear reduced-gravity model of the Indian Ocean, Data have been assimilated during one year starting in November 1986 with the objective of optimizing the initial conditions and the yearly averaged reference surface. The thermocline slope simulated by the model with or without assimilation is validated by comparison with the signal, which can be derived from expandable bathythermograph measurements performed in the Indian Ocean at that time. The topography simulated with assimilation on November 1986 is in very good agreement with the hydrographic data. The slopes corresponding to the South Equatorial Current and to the South Equatorial Countercurrent are better reproduced with assimilation than without during the first nine months. The whole circulation of the cyclonic gyre south of the equator is then strongly intensified by assimilation. Another assimilation experiment is run over the following year starting in November 1987. The difference between the two yearly mean surfaces simulated with assimilation is in excellent agreement with Geosat. In the southeastern Indian Ocean, the correction to the yearly mean dynamic topography due to assimilation over the second year is negatively correlated to the one the year before. This correction is also in agreement with hydrographic data. It is likely that the signal corrected by assimilation is not only due to wind error, because simulations driven by various wind forcings present the same features over the two years. Model simulations run with a prescribed throughflow transport anomaly indicate that assimilation is rather correcting in the interior of the model domain for inadequate boundary conditions with the Pacific.

Greiner, Eric↗
NASA NTRS2003

Vertical Distribution of Shallow Water in the Distinguishable Regions at Low and High Latitudes of Mars: Neutron Data Deconvolution of HEND

High Energy Neutron Detector (HEND) is the part of Gamma-Ray Spectrometer suite onboard NASA Mars Odyssey orbiter [1-4]. During 16 months of mapping stage of Odyssey mission HEND has accumulated the set of maps of neutron emission of Mars at more than seven decades of energies range from the Cadmium threshold of 0.4 eV up to 15 MeV. These maps present very large variations of neutrons at different regions of Mars and they also show quite strong changes along Martian seasons.

I G Mitrofanov↗
NASA NTRS2003

Global Distribution of Shallow Water on Mars: Neutron Mapping of Summer-Time Surface by HEND/Odyssey

Orbital mapping of induced neutrons and gamma-rays by Odyssey has recently successfully proven the applicability of nuclear methods for studying of the elementary composition of Martian upper-most subsurface. In particular, the suite of Gamma-Ray Spectrometer (GRS) has discovered the presence of large water-ice rich regions southward and northward on Mars. The data of neutron mapping of summer-time surface are presented below from the Russian High Energy Neutron Spectrometer (HEND), which is a part of GRS suite. These maps represent the content of water in the soil for summer season at Southern and Northern hemispheres, when the winter deposit of CO2 is absent on the surface. The seasonal evolution of CO2 coverage on Mars is the subject of the complementary paper.

Mitrofanov, I. G.↗
NASA NTRS2009

Shallow-Water Nitrox Diving, the NASA Experience

NASA s Neutral Buoyancy Laboratory (NBL) contains a 6.2 million gallon, 12-meter deep pool where astronauts prepare for space missions involving space walks (extravehicular activity EVA). Training is conducted in a space suit (extravehicular mobility unit EMU) pressurized to 4.0 - 4.3 PSI for up to 6.5 hours while breathing a 46% NITROX mix. Since the facility opened in 1997, over 30,000 hours of suited training has been completed with no occurrence of decompression sickness (DCS) or oxygen toxicity. This study examines the last 5 years of astronaut suited training runs. All suited runs are computer monitored and data is recorded in the Environmental Control System (ECS) database. Astronaut training runs from 2004 - 2008 were reviewed and specific data including total run time, maximum depth and average depth were analyzed. One hundred twenty seven astronauts and cosmonauts completed 2,231 training runs totaling 12,880 exposure hours. Data was available for 96% of the runs. It was revealed that the suit configuration produces a maximum equivalent air depth of 7 meters, essentially eliminating the risk of DCS. Based on average run depth and time, approximately 17% of the training runs exceeded the NOAA oxygen maximum single exposure limits, with no resulting oxygen toxicity. The NBL suited training protocols are safe and time tested. Consideration should be given to reevaluate the NOAA oxygen exposure limits for PO2 levels at or below 1 ATA.

Fitzpatrick, Daniel T.↗
NASA NTRS2009

The Principle of Energetic Consistency: Application to the Shallow-Water Equations

If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.

Cohn, Stephen E.↗
NASA NTRS2010

Shallow Water Diving - The NASA Experience

This slide presentation reviews some of the problems and solutions that personnel have experienced during sessions in the Neutral Bu0yancy Lab (NBL). It reviews the standard dive that occurs at the NBL, Boyles and Henry's laws as they relate to the effects of diving. It then reviews in depth some of the major adverse physiologic events that happen during a diving session: Ear and Sinus Barotrauma, Decompression Sickness, (DCS), Pulmonary Barotrauma (i.e., Arterial Gas Embolism (AGE). Mediastinal Emphysema, Subcutaneous Emphysema, and Pneumothorax) Oxygen Toxicity and Hypothermia. It includes information about the pulmonary function in NBL divers. Also included is recommendations about flying after diving.

Fitzpatrick, Daniel↗