Complex eigenvalues for the stability of Couette flow

The eigenvalue problem for the linear stability of Couette flow between rotating concentric cylinders to axisymmetric disturbances is considered. It is shown by numerical calculations and by formal perturbation methods that when the outer cylinder is at rest there exist complex eigenvalues corresponding to oscillatory damped disturbances. The structure of the first few eigenvalues in the spectrum is discussed. The results do not contradict the principle of exchange of stabilities, namely, for a fixed axial wavenumber the first mode to become unstable as the speed of the inner cylinder is increased is nonoscillatory as the stability boundary is crossed

Spiral vortices traveling between two rotating defects in the Taylor-Couette system

Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio $\eta=0.5$ and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. Existence and spatio temporal properties of rotating defects, of modulated Ekman vortices, and of the spiral vortex structures in the bulk are elucidated in quantitative detail.Comment: 9 pages, 9 figure

Influence of boundaries on pattern selection in through-flow

The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally imposed flow is determined for six different inlet/outlet boundary conditions. Results are obtained by numerical simulations of the Navier-Stokes equations and by comparison with the corresponding Ginzburg-Landau amplitude equation. A unique selection process is observed being a function of the control parameters and the boundary conditions but independent of the history and the system length. The problem can be formulated in terms of a nonlinear eigen/boundary value problem where the frequency of the propagating pattern is the eigenvalue. PACS: 47.54.+r, 47.20.Bp, 47.27.Te, 47.20.KyComment: 8 pages, 5 Postscript figures, Physica D 97, 253-263 (1996

Evaluating the Causes of Land Subsidence on the U.S. Mid-Atlantic Coast Measured with InSAR

Land subsidence is a frequently overlooked geologic hazard that is caused by natural processes and anthropogenic stressors. The goal of this study is to quantify vertical land motion (VLM) on Long Island, New York and Virginia’s Eastern Shore and evaluate the potential causes of subsidence. The causes considered in this work are glacial isostatic adjustment, groundwater extraction, infrastructure loading, and land cover. This study utilizes interferometric synthetic aperture radar (InSAR) satellite data from Sentinel-1 to calculate linear VLM trends from 2017 to 2023. Datasets for each hypothesis were qualitatively compared to VLM data. Subsidence rates in both regions were found to be anthropogenic and associated with golf courses, cemeteries, farms, and landfills. Long Island and the Eastern Shore have maximum subsidence rates of 19.3 cm/yr and 8.78 cm/yr, respectively, that each occur in landfills. In addition to landfills, subsidence can be caused by soil compaction due to stressors like foot and vehicle traffic, farming processes, and moisture changes in surficial materials. For golf courses, the aeration process is thought to play a role. A relation between wetland, cropland, and urban land cover types and subsidence was found. Additionally, results suggest that groundwater extraction may facilitate subsidence, especially in wetlands on Long Island. Both regions exhibit apparent uplift, which is considered to be an error to some degree due to the use of C-band wavelength, which cannot penetrate dense vegetation. Comparison of results to GPS data and a published VLM dataset suggests that further refinement of InSAR data is necessary to improve confidence in this study’s findings

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in- and outlet. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system's length. They do, however, depend on the axial boundary conditions, the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that one of linear front propagation. PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript

Applying Laser Doppler Anemometry inside a Taylor-Couette geometry - Using a ray-tracer to correct for curvature effects

In the present work it will be shown how the curvature of the outer cylinder affects Laser Doppler anemometry measurements inside a Taylor-Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor-Couette flow for the case of outer cylinder rotation

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Manufacturing program for predicting equipment requirements (MAPPER)

A computerized Manufacturing Program for Predicting Equipment Requirements (MAPPER) has been developed. MAPPER can be used to interpret component production requirements from shipping schedules, calculate equipment loading versus equipment capacity, display six months prior equipment utilization and display process yield data. MAPPER is written in BASIC computer language and can be executed using GE Mark II time-sharing equipment. A typical example of the use of MAPPER is presented

Selective and scalable oxygenation of heteroatoms using the elements of nature: air, water, and light

Sustainable oxidation protocols aim to provide an environmentally friendly and cost-effective method for the production of various chemicals and materials. The development of such protocols can lead to reduced energy consumption, fewer harmful byproducts, and increased efficiency in industrial processes. As such, this field of research is of great importance and interest to both academia and industry. This work showcases a sustainable and catalyst-free oxidation method for heteroatoms (e.g., S, P, and Se) using only air, water and light. An additional reaction pathway is proposed in which the incorporated oxygen on the heteroatoms originates from water. Furthermore, the addition of certain additives enhances productivity by affecting kinetics. The industrial potential is demonstrated by conveniently transferring the batch protocol to continuous flow using the HANU flow reactor, indicating scalability and improving safety.</p

Long-Term Functional Effects of Medulloblastoma Treatments

All studies relate directly to components of the evidence-based practice question and were used to understand the possible long-term effects of treatment for clients diagnosed with medulloblastoma cancer. This Critically Appraised Topic (CAT) contains 6 research articles from both national and international journals. Study designs include two cohort studies with a control group, 1 cross sectional study with a control group, 1 retrospective cohort study without a control group, 1 descriptive report on a Randomized Control Trial (RCT), and 1 descriptive study. Through these studies, we found that radiation treatment is associated with impaired IQ and academic achievement and that generalized or separation anxiety is common among medulloblastoma patients after treatment. We also found that better outcomes in functioning were associated with age, dosage, time of diagnosis, and medulloblastoma type. Our recommendations for OT practice include assessing processing speed, working memory, verbal skills, executive function, and attention and monitoring cognitive effects of occupational therapy interventions using a Goal Attainment Scale (GAS)