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).

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

Control of Flow Over a Bluff Body

By L I Sedov London: Cleaver-Hume Press Ltd Pp xvi + 363 Price 105s This is really two separate books within the same pair of covers First of all Chapters 1-3, some 145 pages, are devoted to the discussion of similarity and dimensional, methods and their application to a variety of problems in mechanics and fluid mechanics

http://iopscience.iop.org/article/10.1088/0031-9112/11/6/008/pdf

Similarity and Dimensional Methods in Mechanics

A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations (LES) of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs (such as when the filter scale approaches the limits of the inertial range), the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the...

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A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows

The analysis of the importance of the forces that act over an ensemble of particles in a turbulent field has been carried out by using direct numerical simulation for a wide range of density ratios (2.65<ρ<2650). It has been observed that, compared to the Stokes drag, the added mass is always negligible, the pressure drag is relevant for density ratios O(1), and the Basset force is appreciable for the whole range investigated. However, the effect of these forces on the particle dispersion is about 1% for ρ∼1 as well as for large density ratios.

The importance of the forces acting on particles in turbulent flows

In this study, the effects of small-scale velocity fluctuations on the motion of tracer particles is investigated by releasing particles in a turbulent channel flow at Reτ=175, and following their motion in time. Two types of numerical experiments were carried out: first, the Eulerian velocity field was evaluated by the direct numerical simulation (DNS) and the particles were advanced in time using the resolved and several filtered velocity fields to study the effect of the subgrid-scale velocity fluctuations on particle motion without the influence of modeling errors. In the second stage, the particle-motion study was performed using independent DNS and large-eddy simulations (LES), thus including the effect of interpolation and subgrid-scale stress modeling errors on the dispersion statistics. At this Reynolds number the small scales were found to have a limited effect on the statistics examined (one-particle dispersion, one-particle velocity autocorrelation, Lagrangian integral time scale, turbulent di...

Effect of the subgrid scales on particle motion

Boundary-forced stratified turbulence is studied in the prototypical case of turbulent channel flow subject to stable stratification. The large-eddy simulation approach is used with a mixed subgrid model that involves a dynamic eddy viscosity component and a scale-similarity component. After an initial transient, the flow reaches a new balanced state corresponding to active wall-bounded turbulence with reduced vertical transport which, for the cases in our study with moderate-to-large levels of stratification, coexists with internal wave activity in the core of the channel. A systematic reduction of turbulence levels, density fluctuations and associated vertical transport with increasing stratification is observed. Countergradient buoyancy flux is observed in the outer region for sufficiently high stratification. Mixing of the density field in stratified channel flow results from turbulent events generated near the boundaries that couple with the outer, more stable flow. The vertical density structure is thus of interest for analogous boundary-forced mixing situations in geophysical flows. It is found that, with increasing stratification, the mean density profile becomes sharper in the central region between the two turbulent layers at the upper and lower walls, similar to observations in field measurements as well as laboratory experiments with analogous density-mixing situations. Channel flow is strongly inhomogeneous with alternative choices for the Richardson number. In spite of these complications, the gradient Richardson number, Ri g , appears to be the important local determinant of buoyancy effects. All simulated cases show that correlation coefficients associated with vertical transport collapse from their nominal unstratified values over a narrow range, 0.15 Ri g < 0.25. The vertical turbulent Froude number, Fr w , has an O (1) value across most of the channel. It is remarkable that stratified channel flow, with such a large variation of overall density difference (factor of 26) between cases, shows a relatively universal behaviour of correlation coefficients and vertical Froude number when plotted as a function of Ri g . The visualizations show wavy motion in the core region where the gradient Richardson number, Ri g , is large and low-speed streaks in the near-wall region, typical of unstratified channel flow, where Ri g is small. It appears from the visualizations that, with increasing stratification, the region with wavy motion progressively encroaches into the zone with active turbulence; the location of Ri g ≃ 0.2 roughly corresponds to the boundary between the two zones.

An investigation of stably stratified turbulent channel flow using large-eddy simulation

Wall roughness produces a downward shift of the mean streamwise velocity profile in the log region, known as the roughness function. The dependence of the roughness function on the height and arrangement of roughness elements has been confirmed in several studies where regular rough walls were analysed; less attention has been paid to non-regular rough walls. Here, a numerical analysis of turbulent flows over irregularly shaped rough walls is performed, clearly identifying the importance of a parameter, called the effective slope (ES) of the wall corrugations, in characterizing the geometry of non-smooth irregular walls. The effective slope proves to be one of the fundamental geometric parameters for scaling the roughness function. Specifically, for a moderate range of roughness heights, both in the transitionally and in the fully rough regime, ES appears to scale the roughness function for a wide range of irregular rough geometric configurations. The effective slope determines the relative importance of friction drag and pressure drag. For ES ~ 0.15 we find that the friction contribution to the total wall stress is nearly in balance with the pressure-drag contribution. This value separates the region where the roughness function ΔU+ = f(ES) is linear from that where a smooth nonlinear behaviour is observed. In the cases investigated, value ES ~ 0.15 also separates the transitionally rough regime from the fully rough regime.

Vincenzo Armenio

Papers

The importance of the forces acting on particles in turbulent flows

Effect of the subgrid scales on particle motion

An investigation of stably stratified turbulent channel flow using large-eddy simulation

The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows

On the analysis of sloshing of water in rectangular containers: numerical study and experimental validation