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This article shows how George Batchelor, in close collaboration with Dietrich Küchemann, succeeded in founding Euromech, the European Mechanics Committee, in the sixties during the rise of the ‘Cold War’. It is argued that the initial success of Euromech was due to the organisation of Euromech Colloquia, i.e. meetings of at most 50 scientists, focussing on a sufficiently specialised topic and leaving ample time for informal discussions. The maturation of Euromech into the European Mechanics Society in the nineties is then analysed. This transition was in part made necessary by the creation of five series of large European Conferences in Fluid and Solid Mechanics, Turbulence, Nonlinear Oscillations and Mechanics of Materials. The collective action of George Batchelor and a few outstanding European scientists is brought to light.

A global stability analysis of the boundary layer in the leading edge of a swept wing is performed in the incompressible flow regime. It is demonstrated that the global eigenfunctions display the features characterizing the local instability of the attachment line, as in swept Hiemenz flow, and those of local cross-flow instabilities further downstream along the wing. A continuous connection along the chordwise direction is established between the two local eigenfunctions. An adjoint-based receptivity analysis reveals that the global eigenfunction is most responsive to forcing applied in the immediate vicinity of the attachment line. Furthermore, a sensitivity analysis identifies the wavemaker at a location that is also very close to the attachment line where the corresponding local instability analysis holds: the local cross-flow instability further along the wing is merely fed by its attachment-line counterpart. As a consequence, global mode calculations for the entire leading-edge region only need to include attachment-line structures. The result additionally implies that effective open-loop control strategies should focus on base-flow modifications in the region where the local attachment-line instability prevails.

The spiral form of vortex breakdown observed in the numerical simulations of Ruith et al. (J. Fluid Mech., vol. 486, 2003, p. 331) is interpreted as a nonlinear global mode originating at the convective/absolute instability transition point in the lee of the vortex breakdown bubble. The local absolute frequency at the transition station is shown to yield a satisfactory prediction of the precession frequency measured in the three-dimensional direct numerical simulations.

Since the experiments of Monkewitz et al. (J. Fluid Mech. vol. 213, 1990, p. 611), sufficiently hot circular jets have been known to give rise to self-sustained synchronized oscillations induced by a locally absolutely unstable region. In the present investigation, numerical simulations are carried out in order to determine if such synchronized states correspond to a nonlinear global mode of the underlying base flow, as predicted in the framework of Ginzburg–Landau model equations. Two configurations of slowly developing base flows are considered. In the presence of a pocket of absolute instability embedded within a convectively unstable jet, global oscillations are shown to be generated by a steep nonlinear front located at the upstream station of marginal absolute instability. The global frequency is given, within 10% accuracy, by the absolute frequency at the front location and, as expected on theoretical grounds, the front displays the same slope as a $k^-$-wave. For jet flows displaying absolutely unstable inlet conditions, global instability is observed to arise if the streamwise extent of the absolutely unstable region is sufficiently large: while local absolute instability sets in for ambient-to-jet temperature ratios $S \\le 0.453$, global modes only appear for $S \\le 0.3125$. In agreement with theoretical predictions, the selected frequency near the onset of global instability coincides with the absolute frequency at the inlet. For lower $S$, it gradually departs from this value.

The linear amplification of axisymmetric external forcing in incompressible jet flows is investigated within a fully non-parallel framework. Experimental and numerical studies have shown that isothermal jets preferably amplify external perturbations for Strouhal numbers in the range $0. 25\\leq {\\mathit{St}}_{D} \\leq 0. 5$ , depending on the operating conditions. In the present study, the optimal forcing of an incompressible jet is computed as a function of the excitation frequency. This analysis characterizes the preferred amplification as a pseudo-resonance with a dominant Strouhal number of around $0. 45$ . The flow response at this frequency takes the form of a vortical wavepacket that peaks inside the potential core. Its global structure is characterized by the cooperation of local shear-layer and jet-column modes.

The objective of the study is first to examine the optimal transient growth of Görtler–Hämmerlin perturbations in swept Hiemenz flow. This configuration constitutes a model of the flow in the attachment-line boundary layer at the leading-edge of swept wings. The optimal blowing and suction at the wall which minimizes the energy of the optimal perturbations is then determined. An adjoint-based optimization procedure applicable to both problems is devised, which relies on the maximization or minimization of a suitable objective functional. The variational analysis is carried out in the framework of the set of linear partial differential equations governing the chordwise and wall-normal velocity fluctuations. Energy amplifications of up to three orders of magnitude are achieved at low spanwise wavenumbers ($k\\,{\\sim}\\,0.1$) and large sweep Reynolds number ($\\hbox{\\textit{Re}}\\,{\\sim}\\,2000$). Optimal perturbations consist of spanwise travelling chordwise vortices, with a vorticity distribution which is inclined against the sweep. Transient growth arises from the tilting of the vorticity distribution by the spanwise shear via a two-dimensional Orr mechanism acting in the basic flow dividing plane. Two distinct regimes have been identified: for $k\\,{\\lesssim}\\,0.25$, vortex dipoles are formed which induce large spanwise perturbation velocities; for $k\\,{\\gtrsim}\\,0.25$, dipoles are not observed and only the Orr mechanism remains active. The optimal wall blowing control yields for instance an 80% decrease of the maximum perturbation kinetic energy reached by optimal disturbances at $\\hbox{\\textit{Re}}\\,{=}\\,550$ and $k\\,{=}\\,0.25$. The optimal wall blowing pattern consists of spanwise travelling waves which follow the naturally occurring vortices and qualitatively act in the same manner as a more simple constant gain feedback control strategy.

The objective of the study is to determine the absolute/convective nature of the secondary instability experienced by finite-amplitude streaks in the flat-plate boundary layer. A family of parallel streaky base flows is defined by extracting velocity profiles from direct numerical simulations of nonlinearly saturated optimal streaks. The computed impulse response of the streaky base flows is then determined as a function of streak amplitude and streamwise station. Both the temporal and spatio-temporal instability properties are directly retrieved from the impulse response wave packet, without solving the dispersion relation or applying the pinching point criterion in the complex wavenumber plane. The instability of optimal streaks is found to be unambiguously convective for all streak amplitudes and streamwise stations. It is more convective than the Blasius boundary layer in the absence of streaks; the trailing edge-velocity of a Tollmien–Schlichting wave packet in the Blasius boundary layer is around 35% of the free-stream velocity, while that of the wave packet riding on the streaky base flow is around 70%. This is because the streak instability is primarily induced by the spanwise shear and the associated Reynolds stress production term is located further away from the wall, in a larger velocity region, than for the Tollmien–Schlichting instability. The streak impulse response consists of the sinuous mode of instability triggered by the spanwise wake-like profile, as confirmed by comparing the numerical results with the absolute/convective instability properties of the family of two-dimensional wakes introduced by Monkewitz (1988). The convective nature of the secondary streak instability implies that the type of bypass transition studied here involves streaks that behave as amplifiers of external noise.

The initial perturbation with the largest transient energy growth is computed in the context of the swept leading-edge boundary layer. The highest energy amplification is found for perturbations which are homogeneous in the spanwise z-direction, although on shorter time scales the most amplified disturbances have a finite spanwise wavenumber. In both cases the production term associated with the shear of the spanwise velocity is responsible for the energy amplification in the perturbation energy equation. A connection is made with the amplification mechanism exhibited by optimal perturbations in streaky boundary layers (Hoepffner et al. J. Fluid Mech. vol. 537, 2005, p.91) and the results are compared to the optimal Görtler–Hämmerlin disturbances computed by Guégan et al. (J. Fluid Mech. vol. 566, 2006, p. 11).

A realistic, efficient and robust technique for the control of amplifier flows has been investigated. Since this type of fluid system is extremely sensitive to upstream environmental noise, an accurate model capturing the influence of these perturbations is needed. A subspace identification algorithm is not only a convenient and effective way of constructing this model, it is also realistic in the sense that it is based on input and output data measurements only and does not require other information from the detailed dynamics of the fluid system. This data-based control design has been tested on an amplifier model derived from the Ginzburg–Landau equation, and no significant loss of efficiency has been observed when using the identified instead of the exact model. Even though system identification leads to a realistic control design, other issues such as state estimation, have to be addressed to achieve full control efficiency. In particular, placing a sensor too far downstream is detrimental, since it does not provide an estimate of incoming perturbations. This has been made clear and quantitative by considering the relative estimation error and, more appropriately, the concept of a visibility length, a measure of how far upstream a sensor is able to accurately estimate the flow state. It has been demonstrated that a strongly convective system is characterized by a correspondingly small visibility length. In fact, in the latter case the optimal sensor placement has been found upstream of the actuators, and only this configuration was found to yield an efficient control performance. This upstream sensor placement suggests the use of a feed-forward approach for fluid systems with strong convection. Furthermore, treating upstream sensors as inputs in the identification procedure results in a very efficient and robust control. When validated on the Ginzburg–Landau model this technique is effective, and it is comparable to the optimal upper bound, given by full-state control, when the amplifier behaviour becomes convection-dominated. These concepts and findings have been extended and verified for flow over a backward-facing step at a Reynolds number $\\mathit{Re}= 350$ . Environmental noise has been introduced by three independent, localized sources. A very satisfactory control of the Kelvin–Helmholtz instability has been obtained with a one-order-of-magnitude reduction in the averaged perturbation norm. The above observations have been further confirmed by examining a low-order model problem that mimics a convection-dominated flow but allows the explicit computation of control-relevant measures such as observability. This study casts doubts on the usefulness of the asymptotic notion of observability for convection-dominated flows, since such flows are governed by transient effects. Finally, it is shown that the feed-forward approach is equivalent to an optimal linear–quadratic–Gaussian control for spy sensors placed sufficiently far upstream or for sufficiently convective flows. The control design procedure presented in this paper, consisting of data-based subspace identification and feed-forward control, was found to be effective and robust. Its implementation in a real physical experiment may confidently be carried out.

A possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatial–temporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating ‘mean-flow distortion’. It is demonstrated that this ‘mean field’ radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a non-compact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterizing the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growth–attenuation–decay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterized by a single-lobed directivity pattern beamed at an angle about 45°–60° to the jet axis and a broadband spectrum centred at a Strouhal number St ≈ 0.07–0.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations.