Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

A study is carried out of the linear global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. It is based on direct numerical simulations of the complete linearized Navier–Stokes equations obtained with the novel velocity–vorticity method described in Davies & Carpenter (2001). As the equations are linear, they become separable with respect to the azimuthal coordinate, $\theta$. This permits us to simulate a single azimuthal mode. Impulse-like excitation is used throughout. This creates disturbances that take the form of wavepackets, initially containing a wide range of frequencies. When the real spatially inhomogeneous flow is approximated by a spatially homogeneous flow (the so-called parallel-flow approximation) the results ofthe simulations are fully in accordance with the theory of Lingwood (1995). If the flow parameters are such that her theory indicates convective behaviour the simulations clearly exhibit the same behaviour. And behaviour fully consistent with absolute instability is always found when the flow parameters lie within the theoretical absolutely unstable region. The numerical simulations of the actual inhomogeneous flow reproduce the behaviour seen in the experimental study of Lingwood (1996). In particular, there is close agreement between simulation and experiment for the ray paths traced out by the leading and trailing edges of the wavepackets. In absolutely unstable regions the short-term behaviour of the simulated disturbances exhibits strong temporal growth and upstream propagation. This is not sustained for longer times, however. The study suggests that convective behaviour eventually dominates at all the Reynolds numbers investigated, even for strongly absolutely unstable regions. Thus the absolute instability of the rotating-disc boundary layer does not produce a linear amplified global mode as observed in many other flows. Instead the absolute instability seems to be associated with transient temporal growth, much like an algebraically growing disturbance. There is no evidence of the absolute instability giving rise to a global oscillator. The maximum growth rates found for the simulated disturbances in the spatially inhomogeneous flow are determined by the convective components and are little different in the absolutely unstable cases from the purely convectively unstable ones. In addition to the study of the global behaviour for the usual rigid-walled rotating disc, we also investigated the effect of replacing an annular region of the disc surface with a compliant wall. It was found that the compliant annulus had the effect of suppressing the transient temporal growth in the inboard (i.e. upstream) absolutely unstable region. As time progressed the upstream influence of the compliant region became more extensive

Survey and Evaluation of Supersonic Base Flow Theories

Survey and evaluation of supersonic base flow theorie

The initial development of the general non-isoenergetic compressible free shear layer

Numerical solution of partial differential equations governing intial development of general nonisoenergetic compressible free shear laye

Growth mechanisms of perturbations in boundary layers over a compliant wall

The temporal modal and nonmodal growth of three-dimensional perturbations in the boundary-layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity/wall-normal vorticity formalism, the dynamic boundary condition at the compliant wall admits a linear dependence on the eigenvalue parameter, as compared to a quadratic one in the canonical formulation of the problem. This greatly simplifies the accurate calculation of the continuous spectrum by means of a spectral method, thereby yielding a very effective filtering of the pseudospectra as well as a clear identification of instability regions. The regime of global instability is found to be matching the regime of the favorable phase of the forcing by the flow on the compliant wall so as to enhance the amplitude of the wall. An energy-budget analysis for the least-decaying hydroelastic (static-divergence, traveling-wave-flutter and near-stationary transitional) and Tollmien--Schlichting modes in the parameter space reveals the primary routes of energy flow. Moreover, the flow exhibits a slower transient growth for the maximum growth rate of a superposition of streamwise-independent modes due to a complex dependence of the wall-boundary condition with the Reynolds number. The initial and optimal perturbations are compared with the boundary-layer flow over a solid wall; differences and similarities are discussed. Unlike the solid-wall case, viscosity plays a pivotal role in the transient growth. A slowdown of the maximum growth rate with the Reynolds number is uncovered and found to originate in the transition of the fluid-solid interaction from a two-way to a one-way coupling. Finally, a term-by-term energy budget analysis is performed to identify the key contributors to the transient growth mechanism

Laser Interferometer Gravitational-Wave Observatory beam tube component and module leak testing

Laser Interferometer Gravitational-Wave Observatory (LIGO) is a joint project of the California Institute of Technology and the Massachusetts Institute of Technology funded by the National Science Foundation. The project is designed to detect gravitational waves from astrophysical sources such as supernova and black holes. The LIGO project constructed observatories at two sites in the U.S. Each site includes two beam tubes (each 4 km long) joined to form an "L" shape. The beam tube is a 1.25 m diam 304 L stainless steel, ultrahigh vacuum tube that will operate at 1×10^–9 Torr or better. The beam tube was manufactured using a custom spiral weld tube mill from material processed to reduce the outgassing rate in order to minimize pumping costs. The integrity of the beam tube was assured by helium mass spectrometer leak testing each component of the beam tube system prior to installation. Each 2 km long, isolatable beam tube module was then leak tested after completion

Effects of wall compliance on the laminar–turbulent transition of torsional Couette flow

Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar–turbulent flow transition is investigated. Data obtained from analysing flow visualizations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar–turbulent transition process of torsional Couette flow

Toward The Goal Of Teaching Excellence In Accounting: Reexamining The Role Of Neutrality And Conservatism In The Development Of Pension Accounting Standards

Pension accounting is replete with complexities that present difficulties to even the most seasoned accounting practitioners.  It thus represents one of the more problematic areas of the accounting curriculum for accounting students and instructors alike.  Traditional approaches toward the teaching of pension accounting rely heavily on memorization techniques that tend to serve students’ needs on a short-term basis.  The authors present an alternative approach to instruction in which students assume the role of accounting standard setters and seek to develop pension accounting rules that favor corporate interests.  This approach allows students to recognize the economic consequences that standard setters sometimes consider in their promulgation of accounting and financial reporting rules.  The result is that students acquire a greater depth and breadth of understanding of pension accounting rules and why those rules exist as they do.  They also acquire a keener understanding of the broader standard setting process.  This logic-based approach is likely to better serve the long-term needs of our future accounting professionals

Accounting For Defined Benefit Pension Plans: Is FASB Finally Fulfilling Its 25 Year Old Promise?

With the September 2006 release of Statement No. 158, “Employers’ Accounting for Defined Benefit Pension and Other Postretirement Plans,” the Financial Accounting Standards Board (FASB) has completed the first phase of its ongoing pension accounting project.  The new standard improves the accounting for defined benefit pensions by requiring employers to report the over(under)funded status of their plans as an asset(liability) within the main body of their balance sheet. This requirement represents a significant change from previously-existing pension accounting standards, and represents a major step forward toward the goal of increased transparency in financial reporting.  This article provides a discussion of the very lengthy and controversial history of employer pension accounting, and examines the improvements that have finally resulted from Statement No. 158. Also provided is a discussion of the potential outcome of the second and final phase of the FASB’s pension accounting projec

Expanding The Accounting Education Horizon: Sensitizing Students To The Professions Societal Obligations

This paper presents an alternative teaching pedagogy that goes beyond the learning of complex rules to provide accounting students with a better appreciation for their profession’s societal obligations.  The proposed pedagogy presents students with the evolution of accounting standards in a given topical area, and challenges them to evaluate the extent to which the different stages of evolution succeeded in meeting the profession’s obligations to society.  These obligations are defined in terms of the financial reporting objectives set forth in the Concepts Statements of the Financial Accounting Standards Board.  The proposed pedagogy is offered as a means of addressing problems with respect to the more conventional “memorize these rules” method of accounting instruction.  Our aim is to develop students who take a greater interest in the standard setting process and in fulfilling its promise of meeting the financial reporting needs of society

Propagation of Small Disturbance Waves in a Fluid Flow across the Junctions between Rigid and Compliant Panels

The problem of wave propagation in a fluid flow across the junction between the rigid and the compliantpanelsin a channelhas beenstudied.In vorticalTollmien-Schlichting-type waves, thejump conditions are obtainedby the half-Fouriertransforms definedon both the sides of thejunction along withthe adjointmethod. The methoddevelopedis fairlygenericand is applicableto similarproblems. A comparison of the results obtained in the present study with those obtained from direct numerical simulations' shows good agreement