Instability in Lagrangian stochastic trajectory models,and a method for its cure

A number of authors have reported the problem of unrealistic velocities (“rogue trajectories”) when computing the paths of particles in a turbulent flow using modern Lagrangian stochastic (LS) models, and have resorted to ad hoc interventions. We suggest that this problem stems from two causes: (1) unstable modes that are intrinsic to the dynamical system constituted by the generalized Langevin equations, and whose actual triggering (expression) is conditional on the fields of the mean velocity and Reynolds stress tensor and is liable to occur in complex, disturbed flows (which, if computational, will also be imperfect and discontinuous); and, (2) the “stiffness” of the generalized Langevin equations, which implies that the simple stochastic generalization of the Euler scheme usually used to integrate these equations is not sufficient to keep round-off errors under control. These two causes are connected, with the first cause (dynamical instability) exacerbating the second (numerical instability); removing the first cause does not necessarily correct the second, and vice versa. To overcome this problem, we introduce a fractional-step integration scheme that splits the velocity increment into contributions that are linear (U _i ) and nonlinear (U _i U _j ) in the Lagrangian velocity fluctuation vector U, the nonlinear contribution being further split into its diagonal and off-diagonal parts. The linear contribution and the diagonal part of the nonlinear contribution to the solution are computed exactly (analytically) over a finite timestep Δt, allowing any dynamical instabilities in the system to be diagnosed and removed, and circumventing the numerical instability that can potentially result in integrating stiff equations using the commonly applied explicit Euler scheme. We contrast results using this and the primitive Euler integration scheme for computed trajectories in a drastically inhomogeneous urban canopy flow.     

Biodegradation of Petroleum Hydrocarbons in Fractured, Unsaturated Dolomite at a Field Site

Gasoline constituents were detected in unsaturated soil and rock during abandonment of a leaky underground storage tank (UST). The unsaturated sequence beneath the former UST consists of 90 feet of silty till, fractured dolomite, and friable sand-stone. Pore gas probes were installed in each of the unsaturated units, both in the source area and in a background on-site location. Pore gas samples were collected to evaluate the nature, extent, and fate of residual hydrocarbons in the vadose zone. Pore gas from the till and dolomite in the source area was enriched in petroleum hydrocarbons and carbon dioxide, and was depleted in oxygen, relative to pore gas from the background area. During two years of ground water monitoring at the site, methyl tertiary butyl ether was periodically detected in the ground water beneath the source area as pulses of recharge passed through the unsaturated zone, but no other gasoline constituents were detected. Apparently, the most degradable fraction of the gasoline (aromatic hydrocarbons) is being attenuated in the vadose zone before the water table is reached.     

Recurrence statistics of concentration fluctuations in plumes within a near-neutral atmospheric surface layer

This study examines the statistical properties of the concentration derivative, , for a dispersing plume in a near-neutrally stratified atmospheric surface layer. Towards this goal, the probability density function (pdf) of , and the conditional pdf of given a fixed concentration level, , have been measured. These pdfs are found to be modeled well by a generalizedq-Gaussian (gqG) distribution with intermittency exponent,q, equal to 0.3 and 3/4, respectively. These results highlight the strong intermittency effect (patchiness) of the small-scale concentration eddy structures in the plume. The distribution of time intervals between successive high peaks in the squared derivative process, x², is found to be well approximated by a power-law distribution, implying that occurrences of these high peaks are much more clustered than would be predicted by a Poisson or shot-noise process. The results are used to improve models for the joint pdf of and , and for the expected number of upcrossings per unit time interval of a fixed concentration level that have been proposed by Kristensenet al. (1989). The predictions of the improved models are in accord with observations, and suggest that the intercorrelation between and must be explicitly incorporated if good estimates of the upcrossing intensity are to be obtained.     

Toxicity comparison of biosurfactants and synthetic surfactants used in oil spill remediation to two estuarine species

The relative environmental toxicities of synthetic and biogenic surfactants used in oil spill remediation efforts are not well understood. Acute and chronic toxicities of three synthetic surfactants and three microbiologically produced surfactants were determined and compared in this study for the estuarine epibenthic invertebrate, Mysidopsis bahia and the inland silverside, Menidia beryllina. The toxicities of the surfactant were determined in standard laboratory static and static-renewal tests of 4-7 d duration. Results were specific to the surfactant, response parameter and test species. The LC50 values (nominal concentrations) for M. bahia ranged from 3.3 mg/l (Triton X-100) to >1000 mg/l (PES-61) and 2.5 mg/l (Triton X-100) to 413.6 mg/l (PES-61) for M. beryllina. Chronic first-effect concentrations (mg/l) for the six surfactants ranged from 2.3 to 465.0 (M. beryllina) and 1.0 to >1000.0 (M. bahia) based on reductions in growth and fecundity. Few generalizations could be made concerning the results due to their variability but M. bahia was generally the more sensitive species and the toxicities of the biosurfactants were intermediate to those of the synthetic surfactants.     

Use of archaeology to date liquefaction features and seismic events in the New Madrid seismic zone,Central United States

Prehistoric earthquake-induced liquefaction features occur in association with Native American occupation horizons in the New Madrid seismic zone. Age control of these liquefaction features, including sand-blow deposits, sand-blow craters, and sand dikes, can be accomplished by extensive sampling and flotation processing of datable materials as well as archaeobotanical analysis of associated archaeological horizons and pits. This approach increases both the amount of carbon for radiocarbon dating and the precision dating of artifact assemblages. Using this approach, we dated liquefaction features at four sites northwest of Blytheville, Arkansas, and found that at least one significant earthquake occurred in the New Madrid seismic zone between A.D. 1180 and 1400, probably about A.D. 1300 ± 100 yr. In addition, we found three buried sand blows that formed between 3340 B.C. and A.D. 780. In this region where very large to great earthquakes appear to be closely timed, archaeology is helping to develop a paleoearthquake chronology for the New Madrid seismic zone. © 1996 John Wiley & Sons, Inc.