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

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

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

Viscous effects in aircraft trailing vortices

The mechanism of merging of like-signed aircraft vortices leading to a rapid redistribution of trailed vorticity in a wake through both convective and turbulent processes was investigated. Research was done experimentally in a small wind tunnel and analytically through the use of a code which computes turbulent transport using a second-order closure turbulent model. Computations are reported which demonstrate the merging phenomenon, and comparisons are made with experimental results. The usefulness of point vortex computations in predicting merging was explored. Limited computations showed that jet exhaust does not appreciably alter the merging phenomenon. The effect of ambient atmospheric turbulence on the aging of an aircraft wake was investigated at a constant turbulent dissipation rate. It was shown that under stable atmospheric conditions, when atmospheric macroscales are less than or equal to the vortex spacing, misleading results may be obtained

Anisotropic spin freezing in the S=1/2 zigzag ladder compound SrCuO2

Using magnetic neutron scattering we characterize an unusual low temperature phase in orthorhombic SrCuO2. The material contains zigzag spin ladders formed by pairs of S=1/2 chains (J=180 meV) coupled through a weak frustrated interaction |J'|<0.1J. At T<Tc1=5.0(4)K an elastic peak develops in a gapless magnetic excitation spectrum indicating spin freezing on a time scale larger than 200 picoseconds. While the frozen state has long range commensurate antiferromagnetic order along the chains with the correlation length exceeding 200 lattice periods along the c-axis and a substantial correlation length of 60(25) spacings along the a-axis perpendicular to the zigzag plane, only 2 lattice units are correlated along the b-axis which is the direction of the frustrated interactions. The frozen magnetic moment of each Cu ion is very small, 0.033(7) Bohr magneton even at T=0.35K, and has unusual temperature dependence with a cusp at Tc2=1.5K reminiscent of a phase transition. We argue that slow dynamics of stripe-like cooperative magnetic defects in tetragonal a-c planes yield this anisotropic frozen state.Comment: 4 pages, LaTeX, submitted to PR

MagAO Imaging of Long-period Objects (MILO). I. A Benchmark M Dwarf Companion Exciting a Massive Planet around the Sun-like Star HD 7449

We present high-contrast Magellan adaptive optics (MagAO) images of HD 7449, a Sun-like star with one planet and a long-term radial velocity (RV) trend. We unambiguously detect the source of the long-term trend from 0.6-2.15 \microns ~at a separation of \about 0\fasec 54. We use the object's colors and spectral energy distribution to show that it is most likely an M4-M5 dwarf (mass \about 0.1-0.2 \msun) at the same distance as the primary and is therefore likely bound. We also present new RVs measured with the Magellan/MIKE and PFS spectrometers and compile these with archival data from CORALIE and HARPS. We use a new Markov chain Monte Carlo procedure to constrain both the mass ($> 0.17$ \msun ~at 99$\%$ confidence) and semimajor axis (\about 18 AU) of the M dwarf companion (HD 7449B). We also refine the parameters of the known massive planet (HD 7449Ab), finding that its minimum mass is $1.09^{+0.52}_{-0.19}$ \mj, its semimajor axis is $2.33^{+0.01}_{-0.02}$ AU, and its eccentricity is $0.8^{+0.08}_{-0.06}$. We use N-body simulations to constrain the eccentricity of HD 7449B to $\lesssim$ 0.5. The M dwarf may be inducing Kozai oscillations on the planet, explaining its high eccentricity. If this is the case and its orbit was initially circular, the mass of the planet would need to be $\lesssim$ 1.5 \mj. This demonstrates that strong constraints on known planets can be made using direct observations of otherwise undetectable long-period companions.Comment: Corrected planet mass error (7.8 Mj --> 1.09 Mj, in agreement with previous studies