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

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

Feasibility of an onboard wake vortex avoidance system

It was determined that an onboard vortex wake detection system using existing, proven instrumentation is technically feasible. This system might be incorporated into existing onboard systems such as a wind shear detection system, and might provide the pilot with the location of a vortex wake, as well as an evasive maneuver so that the landing separations may be reduced. It is suggested that this system might be introduced into our nation's commuter aircraft fleet and major air carrier fleet and permit a reduction of current landing separation standards, thereby reducing takeoff and departure delays

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

Examining Natural Selection by Sketching and Making Models of the Finches of the Galapagos Islands

This practical lesson describes how students in six eighth grade science classes participated in a lesson combining the National Core Arts Standards with the Next Generation Science Standards. The goal of the lesson was to provide visual representations of finch beak form and function so students could better understand genetic variation and how environmental pressures influence natural selection. Students sketched a finch with a large, medium, or small beak, corresponding to an experiment they had conducted with picking up different sizes of seeds with different sizes of binder clips. Using modeling with a variety of media, students created bird beaks based on information from online and text research. Students identified how each beak was related to the bird’s diet and made comparisons with the beaks of the other birds in the environment. In addition to their increased knowledge of natural selection, students voiced their enjoyment of the inclusion of art

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

Eighth Graders Explore Form and Function of Modern and Fossil Organisms

Arts integration into science has been shown to motivate students and promote long-term retention of content. To add to the literature addressing arts integration, an experiment was conducted with middle school students studying the anatomical similarities and differences between modern and fossil marine invertebrates and different types of extant insects. Eighth grade students participated in a counterbalanced-design, quasi-experimental study to determine if the integration of art into the science curriculum would influence student retention of content, enjoyment, motivation, and perceived learning toward learning science concepts supporting the Next Generation Science Standards including engineering-related concepts. The lessons addressed Life Science standard MS-LS4-2. Results showed that the integration of an art activity had a significant effect on knowledge retention favoring the experimental condition with a medium effect size on the posttest and a large effect on the distal posttest. Student enjoyment, motivation, and perceived learning also showed significant differences overall and specifically for enjoyment and for perceived learning favoring the experimental conditions of arts integration with a small effect size