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-

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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

This is the second of a two-part paper. This part reports the results of a systematic experimental study of the near acoustic field of a high-speed jet. The aim is to shed light on the noise source characteristics of the jet. A microphone array consisting of twenty-one semicircular rings of microphones is built for the experiment. The microphone array extends from one diameter from the nozzle exit to a distance of thirty-one diameters downstream. The microphones lie on a conical surface of ten degrees half-apex angle surrounding the jet. Two-point space-time pressure correlations are measured. There are two principal objectives in this study. The first objective is to validate the near field to far field continuation method, developed in the Part I paper, with experimental data. For this purpose, two series of validation tests are performed. First is a comparison of far field noise spectra between those continued from near field measurements on the conical surface and those measured directly in the far field. Another test series consists of comparisons of far field directivities at selected Strouhal numbers, again, between those continued from the near field measurements to the far field and those measured directly in the far field. Favorable agreements are found. These tests not only validate the continuation method developed in the Part I paper but also support the recognition that the two-point space-time pressure correlation function on the conical surface is the equivalent source of jet noise. This realization offers a way to investigate the characteristics of jet noise sources by analyzing those of the equivalent noise sources. The second objective of this experimental study is to investigate the noise source location, strength, size, convection speed, degree of randomness and other characteristics along the length of the jet. The noise source can also be decomposed into azimuthal modes. It will be shown that the axisymmetric noise source mode is the most dominant. Contributions to the radiated noise from modes higher than the second mode are negligible. Other modal characteristics such as propagation speed, location of maximum intensity and others will be reported. Finally, strong evidence will be presented to show the wave-like nature of the source of high-speed jet noise.

Continuation of Near-Acoustic Fields of Jets to the Far Field: Part II Experimental Validation and Noise Source Characteristics

Broadband shock-cell noise from dual stream jets is investigated. The present work is confined to the cases of supersonic secondary jet and subsonic primary jet. Previous studies on single stream supersonic jets reveal that broadband shock-cell noise from these jets is generated by the interaction of the large turbulence structures and the shock cells in the jet plume as the former propagate downstream through the latter. A prominent characteristic of the radiated noise is that it is most intense in the upstream direction and drops off with an increase in inlet angle. An important result of the present investigation is the discovery that there are two sets of broadband shock-cell noise. One set is the classical shock-cell noise, similar to that of single stream jets. The second set radiates sound primarily in the downstream direction. Its intensity is low at 90°, but the intensity increases with inlet angle until a critical angle is reached beyond which it starts to decrease rapidly. It is believed that the first sound field is generated by the interaction of the large turbulence structures and the shock cells in the outer shear layer of the dual stream jet. The second sound field is generated in a similar manner involving the large turbulence structures and the shock cells in the inner shear layer of the jet. The inner shear layer separates the secondary and the primary jet. A simplified mathematical model capable of elucidating the generation, transmission and radiation of broadband shock-cell noise from dual stream jets is developed. The model provides formulas relating the direction of radiation and the frequencies of broadband shock-cell noise at the peaks of the noise spectra for both sets of sound fields. Good agreement is found between the predictions from these formulas and experimental measurements, thereby providing support for the validity of the model.

Broadband Shock-Cell Noise from Dual Stream Jets

On the failure of the acoustic analogy theory to identify the correct noise sources

This is a review of the two-source model of jet noise. The model was developed phenomenologically a number of years ago. One of the principal results associated with this model was the identification of two similarity jet noise spectra. This was accomplished through extensive comparisons with a large set of NASA spectrum data. It was found that these two noise spectra when combined appropriately would fit measured noise spectra of jets in any direction regardless of jet temperature and Mach number. Other experimental data in support of the two-source model have since been found. They are discussed in this paper. One of the purposes of this paper is to elaborate on the flow physics of turbulence, noise generation mechanisms and directivity that are the underpinnings of the model. More recent works show the similarity spectra are applicable, well beyond their original database, to noise of military jets, rockets and even volcanoes. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0078

A phenomenological approach to jet noise: the two-source model.

Direct numerical simulations of noise generation and radiation from aircraft flap side edges are performed in the presented paper. The objective of this work is to identify the generating mechanism of flap side edge noise. A CFD/CAA approach is taken in which the mean flow field around a three element high-lift system is provided by RANSICFD calculations and the unsteady flow field involving shear layer instability waves and acoustic waves is calculated by a linearized Euler/CAA method. The high accuracy DRP finite difference scheme with PML boundary conditions is used to guarantee the accuracy of the unsteady calculations. A multi-domain, multiple time step technique is used to enhance the efficiency of the calculations. The computed results indicate that the feedback/interaction among side-edge shear layer instability waves is the dominant noise generating mechanism.

Christopher K. W. Tam

Papers

Continuation of Near-Acoustic Fields of Jets to the Far Field: Part II Experimental Validation and Noise Source Characteristics

Broadband Shock-Cell Noise from Dual Stream Jets

On the failure of the acoustic analogy theory to identify the correct noise sources

A phenomenological approach to jet noise: the two-source model.

Direct numerical simulations of flap side edge noise