Numerical studies of the deposition of material released from fixed and rotary wing aircraft

The computer code AGDISP (AGricultural DISPersal) has been developed to predict the deposition of material released from fixed and rotary wing aircraft in a single-pass, computationally efficient manner. The formulation of the code is novel in that the mean particle trajectory and the variance about the mean resulting from turbulent fluid fluctuations are simultaneously predicted. The code presently includes the capability of assessing the influence of neutral atmospheric conditions, inviscid wake vortices, particle evaporation, plant canopy and terrain on the deposition pattern. In this report, the equations governing the motion of aerially released particles are developed, including a description of the evaporation model used. A series of case studies, using AGDISP, are included

Computing aerodynamic sound using advanced statistical turbulence theories

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability

Model predictions of wind and turbulence profiles associated with an ensemble of aircraft accidents

The feasibility of predicting conditions under which wind/turbulence environments hazardous to aviation operations exist is studied by examining a number of different accidents in detail. A model of turbulent flow in the atmospheric boundary layer is used to reconstruct wind and turbulence profiles which may have existed at low altitudes at the time of the accidents. The predictions are consistent with available flight recorder data, but neither the input boundary conditions nor the flight recorder observations are sufficiently precise for these studies to be interpreted as verification tests of the model predictions

Atmospheric-wake vortex interactions

The interactions of a vortex wake with a turbulent stratified atmosphere are investigated with the computer code WAKE. It is shown that atmospheric shear, turbulence, and stratification can provide the dominant mechanisms by which vortex wakes decay. Computations included the interaction of a vortex wake with a viscous ground plane. The observed phenomenon of vortex bounce is explained in terms of secondary vorticity produced on the ground. This vorticity is swept off the ground and advected about the vortex pair, thereby altering the classic hyperbolic trajectory. The phenomenon of the solitary vortex is explained as an interaction of a vortex with crosswind shear. Here, the vortex having the sign opposite that of the sign of the vorticity in the shear is dispersed by a convective instability. This instability results in the rapid production of turbulence which in turn disperses the smoke marking the vortex

Computer program for prediction of the deposition of material released from fixed and rotary wing aircraft

This is a user manual for the computer code ""AGDISP'' (AGricultural DISPersal) which has been developed to predict the deposition of material released from fixed and rotary wing aircraft in a single-pass, computationally efficient manner. The formulation of the code is novel in that the mean particle trajectory and the variance about the mean resulting from turbulent fluid fluctuations are simultaneously predicted. The code presently includes the capability of assessing the influence of neutral atmospheric conditions, inviscid wake vortices, particle evaporation, plant canopy and terrain on the deposition pattern

Vortex interactions and decay in aircraft wakes

The dynamic interaction of aircraft wake vortices was investigated using both inviscid and viscous models. For the viscous model, a computer code was developed using a second-order closure model of turbulent transport. The phenomenon of vortex merging which results in the rapid aging of a vortex wake was examined in detail. It was shown that the redistribution of vorticity during merging results from both convective and diffusive mechanisms

Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Is the Wild Coast in eastern South Africa a distinct marine bioregion?

Abstract: The South African coastline can be divided into at least four temperature-defined marine bioregions, including the tropical north-east coast, the subtropical east coast, the warm-temperate south coast, and the cool-temperate west coast. There are also two biogeographical transition zones, the south-west coast and the south-east coast (or Wild Coast). The former is sometimes considered a distinct marine bioregion, but no such status has yet been suggested for the Wild Coast. Previous data on the distribution of a recently described but very common coastal crab, Hymenosoma longicrure, indicated that this species could be a Wild Coast endemic. If confirmed, this would be a first indication that this region harbours unique fauna, and that additional research is required to determine whether the Wild Coast constitutes a distinct bioregion that needs to be managed separately from other coastal regions. In the present study, we generated novel genetic data for H. longicrure and compared the species’ range with that of its southern African congeners. We found that H. longicrure occurs north of the Wild Coast, where its range overlaps with that of H. projectum. This finding rejects the idea that the Wild Coast harbours endemic fauna and suggests that the ranges of the two species may be linked to the subtropical and tropical bioregions, respectively, with some southward dispersal facilitated by the southward-flowing Agulhas Current. We conclude that there is as yet no compelling evidence that the Wild Coast is a distinct marine bioregion, and concur with previous biogeographical studies which have suggested that the Wild Coast is an area in which species from the subtropical and warm-temperate bioregions have overlapping ranges. Nonetheless, that fact that no biological information is available for the majority of the region’s estuaries highlights the necessity of comprehensively documenting the biodiversity of this understudied region to fully resolve this issue

XO-2b: a hot Jupiter with a variable host star that potentially affects its measured transit depth

The transiting hot Jupiter XO-2b is an ideal target for multi-object photometry and spectroscopy as it has a relatively bright ($V$-mag = 11.25) K0V host star (XO-2N) and a large planet-to-star contrast ratio (R$_{p}$/R$_{s}\approx0.015$). It also has a nearby (31.21") binary stellar companion (XO-2S) of nearly the same brightness ($V$-mag = 11.20) and spectral type (G9V), allowing for the characterization and removal of shared systematic errors (e.g., airmass brightness variations). We have therefore conducted a multiyear (2012--2015) study of XO-2b with the University of Arizona's 61" (1.55~m) Kuiper Telescope and Mont4k CCD in the Bessel U and Harris B photometric passbands to measure its Rayleigh scattering slope to place upper limits on the pressure-dependent radius at, e.g., 10~bar. Such measurements are needed to constrain its derived molecular abundances from primary transit observations. We have also been monitoring XO-2N since the 2013--2014 winter season with Tennessee State University's Celestron-14 (0.36~m) automated imaging telescope to investigate stellar variability, which could affect XO-2b's transit depth. Our observations indicate that XO-2N is variable, potentially due to {cool star} spots, {with a peak-to-peak amplitude of $0.0049 \pm 0.0007$~R-mag and a period of $29.89 \pm 0.16$~days for the 2013--2014 observing season and a peak-to-peak amplitude of $0.0035 \pm 0.0007$~R-mag and $27.34 \pm 0.21$~day period for the 2014--2015 observing season. Because of} the likely influence of XO-2N's variability on the derivation of XO-2b's transit depth, we cannot bin multiple nights of data to decrease our uncertainties, preventing us from constraining its gas abundances. This study demonstrates that long-term monitoring programs of exoplanet host stars are crucial for understanding host star variability.Comment: published in ApJ, 9 pages, 11 figures, 3 tables; updated figures with more ground-based monitoring, added more citations to previous work