to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

/pdf/local-and-global-instabilities-in-spatially-developing-flows-ja4x14nrk6.pdf

Local and global instabilities in spatially developing flows

Perturbed Free Shear Layers

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

/pdf/direct-numerical-simulation-a-tool-in-turbulence-research-2a650vh1lf.pdf

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

ACOUSTIC liners are widely used in industry for noise reduction. They are indispensable noise-suppression devices for jet engines. Acoustic liners are effective over a wide band of frequencies. To account for such characteristics, broadband impedance models are used for time-domain computation. The acoustic impedance of a surface, Z ! , is originally defined in the frequency domain. Problems involving noise propagation over impedance surfaces may be solved in the time domain. Time-domain methods have obvious advantages over frequency-domain methods for broadband and nonlinear problems. However, because an impedance boundary condition is set up for use in the frequency domain, an equivalent time-domain impedance boundary condition is needed. Mathematically, the time-domain equivalent may be derived by taking its inverse Fourier transform. For the equivalent time-domain impedance condition to be physical, the impedance function must be causal, real, and passive [1]. In general, the inverse Fourier transform of a frequency-domain impedance boundary condition would lead to a convolution integral. Computation of the convolution integral is time consuming. However, if the impedance can be represented by a sum of certain special functions, the evaluation of the convolution may be carried out in a simple systematic manner. Tam and Auriault [2] introduced a three-parameter time-domain impedancemodel. Thismodel can provide accurate representation of liner impedance for single discrete frequency problems. But the three-parameter model cannot offer a general representation of liner impedance over awide band of frequencies. Rienstra [1] proposed an extended Helmholtz resonator model. The free parameters of the model are the geometrical dimensions of the resonator. The impedance of the model is derived by the response of the Helmholtz resonator to periodic acoustic input. A comparison study by Richter et al. [3] indicated that a numerical instability could occur in some cases. A filtering technique has to be applied for avoiding this problem. Recently, Reymen et al. [4] developed a new and efficient time-domain impedance boundary condition based on the use of recursive convolution. The key to their method is the representation of the impedance by a series of simple poles in the complex plane. For the method to work efficiently, the value of the function in the convolution integral within a time step must be approximated by a linear or quadratic function. This impedance model has been proven to be physical, causal, and real. The primary objective of this paper is to develop an improved multipole broadband time-domain impedance boundary condition. A secondary objective is to derive an analytical solution for problems involving damping of broadband acoustic input by liners with broadband impedance characteristics. These solutions may serve for benchmarking numerical computations involving broadband sound. This paper is organized as follows. Section II discusses the improved multipole broadband impedance model. The implementation of the time-domain impedance boundary condition is presented in Sec. III. Section IV presents analytical solutions of twodimensional problems with broadband incident acoustic waves. These solutions are then used to validate numerical results with a liner having broadband impedance properties. Section IV concludes this work.

Improved Multipole Broadband Time-Domain Impedance Boundary Condition

Recent experiments conducted at NASA Langley show that twin supersonic jets separating by a distance of approximately two nozzle diameters (center to center) exhibit resonant oscillations under a wide range of operating conditions. In this paper the mechanism responsible for the synchronized resonant oscillations is investigated. A vortex sheet jet model is used in the analysis. The model shows that kinematically two modes of twin jet resonance can occur. One mode involves flapping motion of both jets symmetric with respect to the mid-plane separating the two jets. The other mode involves antisymmetric flapping motion. The symmetric mode is consistent with experimental observations. The vortex sheet jet model is, however, unable to provide quantitative estimates of the shift in screech frequency (as compared to a single jet) due to the resonance phenomenon. The reason for this is discussed. Possible improvement of the model and directions for future work are indicated.

Analysis of twin supersonic plume resonance

Nowadays, commercial aircrafts, invariably, use high-bypass-ratio dual-stream jets for propulsion. As yet, there is still an urgent need for an accurate physics-based noise prediction theory for jets of this configuration. Thus, an investigation is made to determine whether the Tam and Auriault theory, originally developed for predicting the fine-scale turbulence noise of single-stream jets, is capable of predicting accurately the fine-scale turbulence noise of dual-stream jets from separate flow nozzles operating at various bypass ratios. The configuration of a separate flow nozzle is fairly complex. Hence, the jet flow and turbulence in the nozzle region and in the region immediately downstream are also fairly complex. However, these are also the most important noise source regions of the jet. To enable an accurate computation of the mean flow and turbulence level in these regions, a computational aeroacoustics marching algorithm for calculating the parabolized Reynolds averaged Navier-Stokes equations supplemented by the k-e turbulence model is provided

Fine-Scale Turbulence Noise from Dual-Stream Jets

A Modified k-e Turbulence Model for Calculating the Mean Flow and Noise of Hot Jets

Shadowgraphic observations of the flow structure of a wall jet downstream of the trailing edge of a flat plate were carried out. Shadowgraphs obtained at jet exit Mach number 0.3 to 0.8 consistently showed an orderly large oscillatory flow structure. It is believed that these large scale disturbances are the result of flow instabilities. It is also believed that these orderly disturbances are responsible for generating the dominant part of trailing edge noise either directly or indirectly. The interaction of sound generated by these coherent oscillatory flow disturbances and the plate was investigated theoretically. It is found that the farfield noise directivity is strongly influenced by diffraction of sound at the leading edge of the plate.

Christopher K. W. Tam

Papers

Improved Multipole Broadband Time-Domain Impedance Boundary Condition

Analysis of twin supersonic plume resonance

Fine-Scale Turbulence Noise from Dual-Stream Jets

A Modified k-e Turbulence Model for Calculating the Mean Flow and Noise of Hot Jets

Trailing edge noise