The macroeconomic underpinnings of adjustment lending

Drawing on conditionality and implementation information for 184 World Bank adjustment loans to 62 countries during the 1980s, the authors examine the macroeconomic underpinnings of Bank supported adjustment programs. After looking at recent experience with macroeconomic conditionality they conclude that macroeconomic policy reform and improved macroeconomic performance are critical to successful implementation and sustainability of structural reform. Further, they conclude that macroeconomic policy and sequencing issues increasingly have been addressed explicitly in the design of recent adjustment loans, but there is still scope for : 1) strengthening the analytical framework and macroeconomic policy conditionality in adjustment loans; and 2) greater realism about the time and external resources needed to achieve adjustment and growth objectives.Economic Stabilization,Environmental Economics&Policies,Economic Theory&Research,Macroeconomic Management,Country Strategy&Performance

The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas

Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit $J_t \to 0$, collapse time equals sedimentation time. As $J_t$ increases, the collapse time decreases roughly linearly with $J_t$ until $J_t \gtrsim 0.4$ when it becomes approximately equal to the dynamical time

A universal time scale for vortex ring formation

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers

Dynamical systems analysis of fluid transport in time-periodic vortex ring flows

It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization experiments of turbulent vortex rings suggests that a similar process might be at play. However, what precise modes of unsteadiness are responsible for stirring in a turbulent vortex ring is left as an open question. The second situation is that of two leapfrogging rings. The unstable manifold shows striking agreement with even the fine features of smoke visualization photographs, suggesting that fluid elements in the vicinity of the manifold are drawn out along it and begin to reveal its structure. We suggest that interpretations of these photographs that argue for complex vorticity dynamics ought to be reconsidered. Recently, theoretical and computational tools have been developed to locate structures analogous to stable and unstable manifolds in aperiodic, or finite-time systems. The usefulness of these analogs is demonstrated, using vortex ring flows as an example, in the paper by Shadden, Dabiri, and Marsden [Phys. Fluids 18, 047105 (2006)]

Detached-Eddy Simulation Based on the v2-f Model

Detached eddy simulation (DES) based on the v2-f RANS model is proposed. This RANS model incorporates the anisotropy of near-wall turbulence which is absent in other RANS models commonly used in the DES community. In LES mode, the proposed DES formulation reduces to a transport equation for the subgrid-scale kinetic energy. The constant, CDES, required by this model was calibrated by simulating isotropic turbulence. In the final paper, DES simulations of canonical separated flows will be presented

Two-dimensional mesh embedding for Galerkin B-spline methods

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain

Detached Eddy Simulation of Flap Side-Edge Flow

Detached Eddy Simulation (DES) of flap side-edge flow was performed with a wing and half-span flap configuration used in previous experimental and numerical studies. The focus of the study is the unsteady flow features responsible for the production of far-field noise. The simulation was performed at a Reynolds number (based on the main wing chord) of 3.7 million. Reynolds Averaged Navier-Stokes (RANS) simulations were performed as a precursor to the DES. The results of these precursor simulations match previous experimental and RANS results closely. Although the present DES simulations have not reached statistical stationary yet, some unsteady features of the developing flap side-edge flowfield are presented. In the final paper it is expected that statistically stationary results will be presented including comparisons of surface pressure spectra with experimental data

Making Aircraft Vortices Visible to Radar by Spraying Water into the Wake

Aircraft trailing vortices pose a danger to following aircraft during take-off and landing. This necessitates spacing rules, based on aircraft type, to be enforced during approach in IFR (Instrument Flight Regulations) conditions; this can limit airport capacity. To help choose aircraft spacing based on the actual location and strength of the wake, it is proposed that wake vortices can be detected using conventional precipitation and cloud radars. This is enabled by spraying a small quantity water into the wake from near the wing. The vortex strength is revealed by the doppler velocity of the droplets. In the present work, droplet size distributions produced by nozzles used for aerial spraying are considered. Droplet trajectory and evaporation in the flow-field is numerically calculated for a heavy aircraft, followed by an evaluation of radar reflectivity at 6 nautical miles behind the aircraft. Small droplets evaporate away while larger droplets fall out of the wake. In the humid conditions that typically prevail during IFR, a sufficient number of droplets remain in the wake and give good signal-to-noise ratios (SNR). For conditions of average humidity, higher frequency radars combined with spectral processing gives good SNR