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.

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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

It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.

Jet mixing noise from fine scale turbulence

Indirect Combustion Noise of Auxiliary Power Units

It is known that the use of high-order central difference schemes on a Cartesian grid is preferable for the computation of acoustic wave propagation problems. Those schemes tend to be less dispersive and dissipative. They are also more capable of providing an accurate wave speed. In this paper, a Cartesian boundary treatment for problems involving the scattering of acoustic waves by solid objects with curved boundary surfaces, designed to be used in conjunction with such high-order central difference schemes, is proposed. The development of this method is motivated by the observation that a solid wall actually exerts a pressure force on the fluid to keep it from flowing across the wall surface. In this method, ghost values of pressure are introduced at mesh points adjacent to the solid boundary inside the object. The ghost values are them chosen so that the solid wall boundary condition is satisfied. The method is also applicable to objects with sharp corners. Numerical examples are provided.

Cartesian boundary treatment of curved walls for high-order, computational aeroacoustics finite difference schemes

Experimental measurements indicate that the noise radiated from a jet depends not just on the jet-exit velocity alone, but is significantly affected by the jet temperature. Now, there is evidence to support the proposition that jet mixing noise consists of two principal components. These are the noise from the large turbulence structures of the jet flow and the fine-scale turbulence. The prediction of fine-scale turbulence noise from hot jets is considered. Earlier Tam and Auriault developed a semi-empirical theory capable of predicting the fine-scale turbulence noise from cold to moderate temperature jets. In this work, their semi-empirical theory is extended to high-temperature jets, up to a temperature ratio above that of present day commercial engines. The density gradient present in hot jets promotes the growth of Kelvin-Helmholtz instability in the jet mixing layer. This causes a higher level of turbulent mixing and stronger turbulence fluctuations. In addition, recent experiments reveal that the two-point space-time correlation function of turbulent mixing for hot jets is substantially different from that for cold jets. The eddy decay time is shorter, and the eddy size is slightly reduced. These changes have an appreciable impact on the noise radiated. In the present extended fine-scale turbulence theory, both effects are taken into account

Christopher K. W. Tam

Papers

Jet mixing noise from fine scale turbulence

Indirect Combustion Noise of Auxiliary Power Units

Cartesian boundary treatment of curved walls for high-order, computational aeroacoustics finite difference schemes

Fine Scale Turbulence Noise from Hot Jets

On finite amplitude spinning acoustic modes and subsonic choking