Non-polynomial Lagrangian theories
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Salam, A.↗
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Numerical modeling of pollutant transport using a Lagrangian marker particle technique
A derivation and code were developed for the three-dimensional mass transport equation, using a particle-in-cell solution technique, to solve coastal zone waste discharge problems where particles are a major component of the waste. Improvements in the particle movement techniques are suggested and typical examples illustrated. Preliminary model comparisons with analytic solutions for an instantaneous point release in a uniform flow show good results in resolving the waste motion. The findings to date indicate that this computational model will provide a useful technique to study the motion of sediment, dredged spoils, and other particulate waste commonly deposited in coastal waters.
Spaulding, M.↗
CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 2: Program user's manual
The CELFE computer program and user's manual, together with the execution of the CELFE/NASTRAN system, are described. The execution procedure and the transfer of data between the CELFE and NASTRAN programs are controlled through the use of DATA files in the Univac 1100 system. Five data files are used to control the runstream and data transfer, and three files are used to hold the programs. These files are contained on a single tape. Changes in NASTRAN routines required by the present analysis are also discussed in this report. All the program listings, except the last two files (where the absolute and relocatable elements are stored), are included in the appendixes.
Lee, C. H.↗
A Lagrangian method for the numerical solution of the Euler equations for transonic flows
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Klopfer, G. H.↗
Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies
The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.
Broucke, R.↗
Some Eulerian and Lagrangian diagnostics for a model stratospheric warming
The Eliassen-Palm (EP) cross sections for the model are discussed. EP cross sections conveniently display the principal eddy fluxes of heat, momentum, and quasi-geostrophic potential vorticity on one diagram. The EP diagnostics are used to follow the evolution of the mean flow through into the second stage of the model warming, which includes the reversal of the polar westerlies and which appears to have more in common with observed warmings. The transformed Eulerian-mean equations presented by Andrews and McIntyre (1976, 1978) provide the basis for an investigation in which an especially clear picture of the warming dynamics is obtained. In the second stage of the model warming, the decelerating torque per unit mass is large throughout a deep layer in the middle atmosphere, spanning several scale heights.
Dunkerton, T.↗
Lagrangian circulation study near Cape Henry, Virginia
A study of the circulation near Cape Henry, Virginia, was made using surface and seabed drifters and radar tracked surface buoys coupled to subsurface drag plates. Drifter releases were conducted on a line normal to the beach just south of Cape Henry. Surface drifter recoveries were few; wind effects were strongly noted. Seabed drifter recoveries all exhibited onshore motion into Chesapeake Bay. Strong winds also affected seabed recoveries, tending to move them farther before recovery. Buoy trajectories in the vicinity of Cape Henry appeared to be of an irrotational nature, showing a clockwise rotary tide motion. Nearest the cape, the buoy motion elongated to almost parallel depth contours around the cape. Buoy motion under the action of strong winds showed that currents to at least the depth of the drag plates substantially are altered from those of low wind conditions near the Bay mouth. Only partial evidence could be found to support the presence of a clockwise nontidal eddy at Virginia Beach, south of Cape Henry.
Johnson, R. E.↗
Lagrangian least-squares prediction of solar activity
Statistical prediction methods for short-term (months) and long-term (years) forecasting of solar activity were studied. The comparisons indicate that better predictions, in a chi square sense, are possible by lining up the maximum (or minimums, or both) by cycle number. Evidence is also presented to support the existence of an aperiodic variation in the periods as well as the amplitudes.
Holland, R. L.↗
Orbits of the Tethys Lagrangian bodies
Preliminary libration parameters are derived for the objects found in 1980 at the triangular libration points of Tethys. The parameters are obtained from an orbit analysis of ground-based and Voyager I data obtained in 1980 for the separation from Saturn along the ring major axis, the projected separations from the Tethys L4 and L5 points and the separations from Tethys in orbital longitude. The best fitting libration parameters indicate a small (approximately 2 deg) libration amplitude for the L4 body. Data for the object at the L5 point may be fit either by orbits with libration amplitudes greater than 50 deg, or with small libration amplitudes, which are in agreement with recent Voyager II observations.
Reitsema, H. J.↗
Numerical Simulation for Droplet Combustion Using Lagrangian Hydrodynamics
A predictive model of spray combustion must incorporate models for the wide variety of physical environments in a practical combustor. In regions where droplets are closely spaced, combustion resembles a diffusion flame; where they are well separated, an envelope or wake flame results. The relative velocity field between the fuel droplets and oxidizer in influences boundary layer development about the droplet, recirculating flow patterns, and droplet shape and stability. A model must encompass these interacting temporal and spatial effects as well as complicated combustor boundaries. The objective of the current work is to develop the triangular gridding method for describing the individual and collective properties of vaporizing and burning fuel droplets.
Fritts, M. J.↗
A simple Lagrangian forecast system with aviation forecast potential
A trajectory forecast procedure is developed which uses geopotential tendency fields obtained from a simple, multiple layer, potential vorticity conservative isentropic model. This model can objectively account for short-term advective changes in the mass field when combined with fine-scale initial analyses. This procedure for producing short-term, upper-tropospheric trajectory forecasts employs a combination of a detailed objective analysis technique, an efficient mass advection model, and a diagnostically proven trajectory algorithm, none of which require extensive computer resources. Results of initial tests are presented, which indicate an exceptionally good agreement for trajectory paths entering the jet stream and passing through an intensifying trough. It is concluded that this technique not only has potential for aiding in route determination, fuel use estimation, and clear air turbulence detection, but also provides an example of the types of short range forecasting procedures which can be applied at local forecast centers using simple algorithms and a minimum of computer resources.
Petersen, R. A.↗
Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization
A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.
Navon, I. M.↗
Lagrangian observations of surface circulation at the Emperor Seamount chain
In a Kuroshio tracking experiment initiated in February 1977, two satellite-reporting buoys, drogued to 100-m depth, were released southeast of Kuyshu Island, Japan. These drifters crossed the Shatskiy Rise in the Kuroshio extension during May and October and then traversed the Emperor Seamount Chain. Although they reached the chain 117 days apart, their movements near the seamounts display remarkably similar patterns, demonstrating upstream meanders in the surface flow; cyclonic eddy activity immediately west of the chain; passage through the same gap associated with the Jingu and Nintoku seamounts; and a wavelike pattern present over the Hess Rise east of the chain. One drifter exhibited cyclonic eddy motion east of the chain in the lee of the Kinmei Seamount.
Vastano, A. C.↗
Constituent transport in the winter stratosphere from a Lagrangian-mean viewpoint
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Rood, R. B.↗
Three-dimensional algorithms for grid restructuring in Free-Lagrangian calculations
Grid restructuring algorithms which lower the price of three-dimensional Free-Lagrange calculations are presented. The algorithms are first given for the case of planar triangulated surfaces embedded in and spanning a three-dimensional region. The tetrahedra generated by this technique form a Delaunay mesh if the interplane spacing is comparable to the resolution within the planes. The algorithm can therefore be used for efficient determinations of Voronoi connections for initial grids. Modifications of the algorithm for the case of closely spaced surfaces are demonstrated in the context of restructuring algorithms which can accommodate colliding surfaces. Then, the restriction to planar surfaces is removed and regular surfaces are examined. The basic algorithm is the same, with an additional operation to project the vertices of one surface onto another. Finally, vertices on the surface are allowed to migrate anywhere in space.
Fritts, M.↗
Quasi-Lagrangian measurements of density surface fluctuations and power spectra in the stratosphere
Pressure and temperature data from eight superpressure balloon flights at 26 km in the southern hemisphere stratosphere are analyzed. The balloons, which float on a constant density surface, travel steadily westward during summer and eastward during winter, as expected from local climatology. Two types of fluctuations are observed: neutral buoyancy oscillations (NBO) of around 4 min, and 0.1- to 1-hour oscillations that are characterized as small-amplitude density surface fluctuations. Lapse rates and densities are calculated and found to agree well with the expected values. Examples of wave damping and simultaneous fluctuation at two nearby balloons are presented. Spectral analysis is performed clearly showing the NBO and that the majority of the power is in the mesoscale range. Spectral slopes of power versus frequency are measured to be on the average -2.18 + or - 0.24 for pressure and -1.72 + or - 0.24 for temperature. These slopes are compared to the predictions of turbulence theories and the theory of a universal gravity wave spectrum.
Quinn, Elizabeth P.↗
Fluid particle motion and Lagrangian velocities for pulsatile flow through a femoral artery branch model
A flow visualization study using selective dye injection and frame by frame analysis of a movie provided qualitative and quantitative data on the motion of marked fluid particles in a 60 degree artery branch model for simulation of physiological femoral artery flow. Physical flow features observed included jetting of the branch flow into the main lumen during the brief reverse flow period, flow separation along the main lumen wall during the near zero flow phase of diastole when the core flow was in the downstream direction, and inference of flow separation conditions along the wall opposite the branch later in systole at higher branch flow ratios. There were many similarities between dye particle motions in pulsatile flow and the comparative steady flow observations.
Cho, Y. I.↗
Temporal variations of particle fluxes in the deep subtropical and tropical North Atlantic - Eulerian versus Lagrangian effects
The flux of particles measured by sediment traps in the deep water of the Sargasso Sea and western tropical North Atlantic undergoes pronounced temporal variation. In the Sargasso Sea the variability is largely due to seasonal changes in mixed-layer depth and attendant changes in primary productivity affecting a wide region. By contrast, the variability in the western tropical Atlantic appears to be caused by patches of elevated nutrient and pigment concentrations which have their origin in the plumes of the Amazon and Orinoco rivers. Coastal zone color scanner scenes demonstrate the great seasonal and interannual differences in the direction and dispersal patterns of the plumes. The river plumes break up into irregular patches which may pass through the catchment area of a sediment trap at varying rates, thereby creating the impression of almost random temporal flux variability at a fixed trap site.
Deuser, W. G.↗