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Spectral line shape models can successfully reproduce experimental Rayleigh-Brillouin spectra, but they need knowledge about the bulk viscosity ηb. Light scattering involves GHz frequencies, but since ηbis only documented at low frequencies, ηbis usually left as a free parameter, which is determined by a fit of the model to an experimental spectrum. The question is whether models work so well because of this freedom. Moreover, for light scattering in air, spectral models view “air” as an effective molecule. We critically evaluate the use of ηbas a fit parameter by comparing ηbobtained from fits of the Tenti S6 model to the result of Direct Simulation Monte Carlo (DSMC) for a mixture of Nitrogen and Oxygen. These simulations are used to compute light scattering spectra, which are then compared to experiments. The DSMC simulation parameters are cross-checked with a molecular dynamics simulation based on intermolecular potentials. At large values of the uniformity parameter y, y ≈ 4, where the Brillouin contribution to spectra is large, fitted ηbare 20% larger than the ones from DSMC, while the quality of the simulated spectra is comparable to that of the Tenti S6 line shape model. At smaller y, the difference between fitted and simulated ηbcan be as large as 100%. We hypothesize the breakdown of the bulk viscosity concept to be the cause of this fallacy.

We study the dispersion of tiny molecular clouds in turbulence by writing patterns in turbulent air and following their deformation in time. The writing is done by fusing O_{2} and N_{2} molecules into NO in the focus of a strong ultraviolet laser beam. By crossing several of these laser beams, patterns that have both small and large scales can be painted. The patterns are visualized a while later by inducing fluorescence of the NO molecules with a second UV laser and registering the image. The width of the lines that make the pattern is approximately 50 μm, a few times the Kolmogorov length η, the smallest length scale in turbulence, while the overall size of the patterns (≈4 mm) is inside the inertial range of the used turbulent jet flow. At small scales molecular clouds disperse under the joint action of molecular diffusion and turbulence. The experiments reveal for the first time this subtle, yet very important interaction. At macroscales (≈200 η) we verify the Batchelor dispersion of objects whose size is inside the inertial range; however, the expected influence of molecular diffusion is smaller than the accuracy of the experiments.

We use Faraday waves to measure interfacial tension σ between two immiscible fluids, with an interest in (ultra)low values of σ. The waves are excited by vertically oscillating the container in which the fluids reside. Using linear stability theory, we map out the accessible range of interfacial tensions. The smallest value (σmin ≈ 5 × 10-4 N/m) is limited by the joint influence of gravity and viscous dissipation. A further limitation is posed by the greatest accelerations that can be realized in a laboratory. We perform experiments on a water-dodecane interface with an increasing concentration of a surfactant in the water layer that decreases the interfacial tension into the ultralow domain [σ = [Formula: see text](10-6 N/m)]. Surprisingly, the smallest measured wavelength is larger by a factor of 2 than that predicted for vanishing σ. We hypothesize the effect of transport of the surfactant in the fluid flow associated with the waves.

Rayleigh-Brillouin light scattering spectra of CO2 at ultraviolet wavelengths are computed from molecular dynamics which depends on intermolecular potentials only. We find excellent agreement with state of the art experimental data. This agreement was reached in a minimal computational box with sides one scattering wavelength long and integrating the classical trajectories over 20 ns. We also find complete consistency with models based on kinetic theory, which take known values of the transport coefficients as input.

We study the relation between large-scale structures in the concentration field with those in the velocity field in a dye-seeded turbulent jet. The scalar concentration in a plane is measured using laser-induced fluorescence. Uniform concentration zones of an advected scalar are indentified using cluster analysis. We simultaneously measure the two-dimensional velocity field using particle image velocimetry. The structures in the velocity field are characterized by finite-time Lyapunov exponents. The measurement of the scalar- and velocity fields moves with the mean flow. In this moving frame, turbulent structures remain in focus long enough to observe well-defined ridges of the finite-time Lyapunov field. This field gauges the rate of point separation along Lagrangian trajectories; it was measured both for future and past times since the instant of observation. The edges of uniform concentration zones are correlated with the ridges of the past-time Lyapunov field, but not with those of the future-time Lyapunov field. We quantify this relation using both conditional averages and the ordinary correlation function.

Abstract Our quest is for the thumb and finger positions that maximize drag in front crawl swimming and thus maximize propulsion efficiency. We focus on drag in a stationary flow. Swimming is in water, but using Reynolds similarity the drag experiments are done in a wind tunnel. We measure the forces on real-life models of a forearm with hands, flexing the thumb and fingers in various positions. We study the influence on drag of cupping the hand and flexing the thumb. We find that cupping the hand is detrimental for drag. Swimming is most efficient with a flat hand. Flexing the thumb has a small effect on the drag, such that the drag is largest for the opened (abducted) thumb. Flow structures around the hand are visualized using robotic volumetric particle image velocimetry. From the time-averaged velocity fields we reconstruct the pressure distribution on the hand. These pressures are compared to the result of a direct measurement. The reached accuracy of $$\approx$$ ≈ 10% does not yet suffice to reproduce the small drag differences between the hand postures. Graphical Abstract

A scalar emanating from a point source in a turbulent boundary layer does not mix homogeneously, but is organized in large regions with little variation of the concentration: uniform concentration zones. We measure scalar concentration using laser-induced fluorescence and, simultaneously, the three-dimensional velocity field using tomographic particle image velocimetry in a water tunnel boundary layer. We identify uniform concentration zones using both a simple histogram technique, and more advanced cluster analysis. From the complete information on the turbulent velocity field, we compute two candidate velocity structures that may form the boundaries between two uniform concentration zones. One of these structures is related to the rate of point separation along Lagrangian trajectories and the other one involves the magnitude of strong shear in snapshots of the velocity field. Therefore, the first method allows for the history of the flow field to be monitored, while the second method only looks at a snapshot. The separation of fluid parcels in time was measured in two ways: the exponential growth of the separation as time progresses (related to finite-time Lyapunov exponents and unstable manifolds in the theory of dynamical systems), and the exponential growth as time moves backward (stable manifolds). Of these two, a correlation with the edges of uniform concentration zones was found for the past Lyapunov field but not with the time-forward future field. The magnitude of the correlation is comparable to that of the regions of strong shear in the instantaneous velocity field.

We present a new technique to study preferential concentration of droplets in a turbulent air flow. Preferential concentration is the tendency of droplets to cluster in regions of strain, while avoiding regions of rotation. We study the properties of the droplet concentration field in zero mean flow turbulence that was created using an array of synthetic jets. The droplets are made of a phosphorescent solution of Europium chelate. They are excited by a laser sheet from a pulsed UV laser, after which the glowing droplets are followed using a high-speed intensified camera. We quantify preferential concentration through measurement of moments of the coarse-grained local droplet density. At the Stokes numbers studied (St≈2) the fractal dimension, a scaling property of this coarse-grained density field, points to clustering. Clustering is a consequence of the compressibility of the droplet velocity field. We also quantify the dynamical behavior of clustering by moving with this velocity field. We find a preference for clustering in the Lagrangian frame during the time interval set by the decay of the phosphorescence.

A non-harmful system to visualize the flow around an entire swimmer in a regular swimming pool is developed. Small air bubble tracers are injected through the bottom of the swimming pool in a prescribed measurement area. The motion of these bubbles, which will be largely induced by the swimmer’s motion, is captured by a camera array. The two-dimensional velocity field of the water at arbitrary planes of interest can be resolved using a refocussing method in combination with an optical visualisation method, based on particle image velocimetry, which is commonly used in fluid dynamics research. Using this technique, it is possible to visualize coherent flow structures produced during swimming; it is demonstrated here for the dolphin kick.

Rayleigh-Brillouin scattering spectra of CO

Rayleigh-Brillouin scattering spectra of CO$_2$ were measured at pressures ranging from 0.5 to 4~bar, and temperatures from 257 to 355~K using green laser light (wavelength 532~nm, scattering angle of 55.7$^\circ$). These spectra were compared to two lineshape models, which take the bulk viscosity as a parameter. One model applies to the kinetic regime, i.e. low pressures, while the second model uses the continuum, hydrodynamic approach and takes the rotational relaxation time as a parameter, which translates into the bulk viscosity. We do not find a significant dependence of the bulk viscosity with pressure or temperature. At pressures where both models apply we find a consistent value of the ratio of bulk viscosity over shear viscosity $\eta_b/\eta_s = 0.41 \pm 0.10$. This value is four orders of magnitude smaller than the common value that is based on the damping of ultrasound, and signifies that in light scattering only relaxation of rotational modes matters, while vibrational modes remain 'frozen'., Comment: 10 pages, 6 figures

We study spectra and high-order structure functions in anisotropic wind tunnel turbulence, which is generated using an active grid. In the first experiment, we impose homogeneous shear turbulence with a constant gradient of the mean flow and (approximately) homogeneous turbulent fluctuations. We measure mixed structure functions of order 2, 3, 4, 6, and 10 using an array of two-component hotwires. These structure functions, which vanish for isotropic turbulence, display scaling with scaling exponents that highlight intermittency: the return to isotropy at small scales of large fluctuations is much slower than expected on the basis of a simple Kolmogorov-like scaling argument [J. L. Lumley, “Similarity and the turbulent energy spectrum,” Phys. Fluids 10, 855 (1967)]. In the second experiment, we impose anisotropy in otherwise homogeneous turbulence through the time modulation of the active grid. This is done by driving the grid using signals from a turbulence (shell) model, which acts as a convenient turbulent random signal generator. In this way, different statistical properties of different velocity components could be imposed. Similar to the first experiment, our interest is in the return to isotropy of the small-scale turbulent fluctuations, which is quantified using second-order quantities such as spectra and correlation functions. Also, in this case, the strongly anisotropic correlations induced by the forcing at large scales tend to return to isotropy at small, inertial-range scales, but with the imprint of large-scale anisotropy retained.

The strong shear induced by the injection of liquid sprays at high velocities induces turbulence in the surrounding medium. This, in turn, influences the motion of droplets as well as the mixing of air and vapor. Using fluorescence-based tracer particle image velocimetry, the velocity field surrounding 125–135 m/s sprays exiting a 200- $$\upmu$$ m nozzle is analyzed. For the first time, the small- and large-scale turbulence characteristics of the gas phase surrounding a spray has been measured simultaneously, using a large eddy model to determine the sub-grid scales. This further allows the calculation of the Stokes numbers of droplets, which indicates the influence of turbulence on their motion. The measurements lead to an estimate of the dissipation rate $$\epsilon \approx 35$$ m $$^{2}$$ s $$^{-3}$$ , a microscale Reynolds number Re $$_{\lambda } \approx$$ 170, and a Kolmogorov length scale of $$\eta \approx 10^{-4}$$ m. Using these dissipation rates to convert a droplet size distribution to a distribution of Stokes numbers, we show that only the large scale motion of turbulence disperses the droplet in the current case, but the small scales will grow in importance with increasing levels of atomization and ambient pressures.

The effect of finger spread on overall drag on a swimmer's hand is relatively small, but could be relevant for elite swimmers. There are many sensitivities in measuring this effect. A comparison between numerical simulations, experiments and theory is urgently required to observe whether the effect is significant. In this study, the beneficial effect of a small finger spread in swimming is confirmed using three different but complementary methods. For the first time numerical simulations and laboratory experiments are conducted on the exact same 3D model of the hand with attached forearm. The virtual version of the hand with forearm was implemented in a numerical code by means of an immersed boundary method and the 3D printed physical version was studied in a wind tunnel experiment. An enhancement of the drag coefficient of 2% and 5% compared to the case with closed fingers was found for the numerical simulation and experiment, respectively. A 5% and 8% favorable effect on the (dimensionless) force moment at an optimal finger spreading of 10° was found, which indicates that the difference is more outspoken in the force moment. Moreover, an analytical model is proposed, using scaling arguments similar to the Betz actuator disk model, to explain the drag coefficient as a function of finger spacing.

We study the shape relaxation of spherical giant unilamellar vesicles which have been deformed far from equilibrium into ellipsoids using optical tweezers. The relaxation back to a sphere is determined by elastic constants of the vesicles, and their excess area, parameters that are obtained for each stretched vesicle from shape fluctuations in thermal equilibrium, as well as low Reynolds number fluid flow. The relaxation time could be compared favorably to a simple formula which encompasses the joint effect of membrane rigidity and fluid flow. The time constant of the stretched vesicle is slower than that of its thermal fluctuations, which agrees with a recent theory; however, it is one order of magnitude faster than predicted.

Atmospheric lidar techniques for the measurement of wind, temperature, and optical properties of aerosols rely on the exact knowledge of the spectral line shape of the scattered laser light on molecules. We report on spontaneous Rayleigh–Brillouin scattering measurements in the ultraviolet at a scattering angle of 90 °o n N 2 and on dry and moist air. The measured line shapes are compared to the Tenti S6 model, which is shown to describe the scattering line shapes in air at atmospheric pressures with small but significant deviations. We demonstrate that the line profiles of N2 and air under equal pressure and temperature conditions differ significantly, and that this difference can be described by the S6 model. Moreover, we show that even a high water vapor content in air up to a volume fraction of 3:6 vol:% has no influence on the line shape of the scattered light. The results are of relevance for the future spaceborne lidars on ADM-Aeolus (Atmospheric Dynamics Mission) and EarthCARE (Earth Clouds, Aerosols, and Radiation Explorer). © 2010 Optical Society of America OCIS codes: 280.3640, 280.1310, 290.5830, 300.6390.

We study disordered capillary waves on the surface of a vertically oscillated fluid layer and try to establish their relation with weak wave turbulence. We measure the surface gradient in space and time and argue that gradient spectra are better suited for comparison to the predictions of weak wave turbulence theory than spectra of the surface elevation. Because the gradient is a vector quantity, we must distinguish longitudinal and transverse spectra. However, they prove to be related trivially through isotropy. From the measured wavenumber-frequency spectrum it appears that the dispersion relation is only satisfied approximately. In the wavenumber direction the spectral features are strongly broadened due to spatial disorder. This disagrees with weak wave turbulence theory where exact satisfaction of the dispersion relation is pivotal. We find approximate algebraic frequency and wavenumber spectra but with exponents that are different from those predicted by weak wave turbulence theory. However, other findings, such as the broadening of harmonics proportional to their frequency and the emergence of Gaussian statistics at selected wavenumber bands, point to weak wave turbulence.

We measure the absolute dispersion of clouds of monodisperse, phosphorescent droplets in turbulent air by means of high-speed image-intensified video recordings. Laser excitation allows the initial preparation of well-defined, pencil-shaped luminous droplet clouds in a completely nonintrusive way. We find that the dispersion of the clouds is faster than the dispersion of fluid elements. We speculate that preferential concentration of inertial droplet clouds is responsible for the enhanced dispersion.

Interferometric particle imaging provides a simple way to measure the probability density function (PDF) of droplet sizes from out-focus images. The optical setup is straightforward, but the interpretation of the data is a problem when particle images overlap. We propose a new way to analyze the images. The emphasis is not on a precise identification of droplets, but on obtaining a good estimate of the PDF of droplet sizes in the case of overlapping particle images. The algorithm is tested using synthetic and experimental data. We next use these methods to measure the PDF of droplet sizes produced by spinning disk aerosol generators. The mean primary droplet diameter agrees with predictions from the literature, but we find a broad distribution of satellite droplet sizes.

We study the free surface above a turbulent channel flow. We describe a laser scanning technique that can be used to measure the space–time turbulent surface gradient field along a line. A harmonically swiveling laser beam is focused on the surface and its angle of refraction is measured using a position sensing device. The registered signals can be converted easily to the desired gradient field, and spectra and correlations can be measured. Examples of measured spectra and correlation functions of the surface above a turbulent channel flow (Reynolds number R λ ≈ 250) demonstrate the viability of the technique. We further assess the validity of Taylor’s frozen turbulence hypothesis that implies that time-dependent signals measured along a line that is oriented perpendicularly to the mean channel velocity can be interpreted as 2D measurements of the surface slope. While Taylor’s hypothesis works for a turbulent velocity field, it does not work for its free surface.

Faraday waves are standing waves which arise through a parametric instability on the surface of a vertically oscillated fluid layer. They can emerge with various symmetries, simply square to N-fold rotationally symmetric, which for N > 3 are quasi-crystalline. In an experiment with a very large aspect ratio we determine the boundaries of the stability regions of waves with different rotational symmetries in the driving frequency-amplitude parameter plane. We find a remarkable agreement with a recent theory by Chen & Vinals (1999) who predict the stability boundaries at the onset amplitude. We argue why such agreement can only be observed in a very large experiment. The main nonlinear damping mechanism of the waves is a three-wave resonance. We devise a simple model that captures this mechanism and that can explain quantitatively the change of the symmetry of the waves with fluid depth. Detailed information about the surface is obtained by scanning the wave field and measuring the phase of subharmonic and harmonic components. Also the results of these measurements compare very favourably to the theoretical predictions.

We study the behavior of sources and sinks in an experiment where left and right traveling waves are excited on the free surface of a fluid that is heated by a wire stretched under the surface. To study phenomena very close to threshold the experiment is made very long (2 m), while a precise linear map of the free surface is provided by a scanning device. The observed dynamical behavior of the sources is in agreement with a recent prediction based on the coupled complex Ginzburg–Landau equation [Physica D 134 (1999) 1]. However, the behavior of the sinks disagrees with it. When sources turn unstable they eject holes which are believed to be of homoclinic type.

The result of a particle image velocimetry (PIV) measurement is a velocity field averaged over interrogation windows. This severely affects the measurement of small-scale turbulence quantities when the interrogation window size is much larger than the smallest length-scale in turbulence, the Kolmogorov length. In particular, a direct measurement of the dissipation rate demands the measurement of gradients of the velocity field, which are now underestimated because the small-scale motion is not resolved. A popular procedure is to relate the statistical properties of the measured, but underresolved gradients to those of the true ones, invoking a large-eddy argument (Sheng et al. in Chem Eng Sci 55(20):4423–4434, 2000). We argue that the used proportionality constant, the Smagorinsky constant, should depend on the window overlap, on the used elements of the strain tensor, and on the way in which derivatives are approximated. Using an analytic description, PIV measurements of velocity fields from a kinematic simulation and experiments in a synthetic jet-driven turbulent flow with zero mean velocity, we propose new values for this constant.

Impacting systems are found in a great variety of mechanical constructions and they are intrinsically nonlinear. In this paper it is shown how near-grazing systems, i.e. systems in which the impacts take place at low speed, can be described by discrete mappings. The derivation of this mapping for a harmonic oscillator with a stop is dealt with in detail. It is found that the resulting mapping for rigid obstacles is somewhat different from those presented earlier in the literature. The derivations are extended to systems with a compliant obstacle. We find that the map for impacts with a compliant obstacle is very similar to the one describing collisions with a rigid obstacle. A notable difference is a change of scale of the bifurcation parameter. We illustrate our findings in the limit of large damping, where the mechanism of period adding can be analysed exactly. The relevance of our results to experiments on practical impact systems is indicated.

International audience; An atomic force microscope which is operated in the oscillating mode is an example of an impact oscillator. The description of such dynamical systems can be reduced to a mathematical mapping, which displays a square-root singularity. A direct consequence of this property is the emergence of an infinite series of period-adding bifurcations. This extremely characteristic phenomenon should be observed in atomic force microscopes. We consider an atomic force microscope in which the tip–substrate forces are modelled by a liquid-bridge interaction. By integrating the dynamical equations we show that the atomic force microscopy (AFM) dynamical behaviour has the same characteristic bifurcation scenario as the square-root map. We point to the remarkable role of the energy that is dissipated upon impact. We finally suggest ways to improve the operation of AFM.

An impact oscillator is a periodically driven system that hits a wall when its amplitude exceeds a critical value. We study impact oscillations where collisions with the wall are with near-zero velocity (grazing impacts). A characteristic feature of grazing impact dynamics is a geometrically converging series of transitions from a nonimpacting period-1 orbit to period-M orbits that impact once per period with M=1,2,ellipsis. In an experiment we explore the dynamics in the vicinity of these period-adding transitions. The experiment is a mechanical impact oscillator with a precisely controlled driving strength. Although the excitation of many high-order harmonics in the experiment appeared unavoidable, we characterize it with only three parameters. Despite the simplicity of this description, good agreement with numerical simulations of an impacting harmonic oscillator was found. Grazing impact dynamics can be described by mappings that have a square-root singularity. We evaluate several mappings, both for instantaneous impacts and for impacts that involve soft collisions with a yielding wall. As the square-root singularity appears persistent in the reduction of the dynamics to mappings, and because impact dynamics appears insensitive to experimental nonidealities, the characteristic bifurcation scenario should be observed in a wide class of experimental systems.

The dynamical behavior of charge-stabilized colloidal crystals that consist of polystyrene spheres in highly deionized water is determined by solvent flow mediated interactions and by ionic effects. The expression of these effects strongly depends on the polarization of crystal waves. Using dynamic light scattering we trace all but the fastest known modes of motion and evaluate the influence of ion friction. We find a new mode that we ascribe to ion retardation. Our experiments point to the importance of electrophoresis for microscopic colloid dynamics.

The spectral lineshape of spontaneous Rayleigh-Brillouin scattering in CO2 is studied in a range of pressures. The spectrum is influenced by the bulk viscosity, which is a relaxation phenomenon involving the internal degrees of freedom of the molecule. The associated relaxation rates can be compared to the frequency shift of the scattered light, which demands precise measurements of the spectral lineshape. We find the value of the bulk viscosity around 5.7 X 10^{-6} kg/(ms) for the range of pressures p= 2-4 bar and for conditions of room temperature.

Using realtime signal processing techniques it is possible to obtain precise values for the scaling exponents ζ(p) of high-order structure functions. The value of these exponents differs from the Kolmogorov 1941 prediction, that they are anomalous. This anomalous behavior has been firmly confirmed in our experiments where it has been seen in structure functions which show convincing scaling behavior and that have a high statistical accuracy. The advantage of performing experiments in laboratory windtunnel turbulent flows is that development of detector technology is relatively easy. As a result, we have been able to measure transverse structure functions using a line of velocity probes. Such a configuration obviates usage of Taylor's hypothesis. Also the scaling of the transverse structure functions is anomalous. However, the transverse exponent ζT(p) is significantly different from the standard longitudinal exponent ζL(p): scaling anomaly is non-isotropic. We speculate about the meaning of this result.

Using photon correlation spectroscopy we study the various modes of motion of a colloidal crystal and the properties of charged colloidal systems in general. We have designed a dynamic light scattering experiment that is suited to study fast relaxation times. In order to obtain unambiguous results it is always operated in the heterodyne scattering mode. We provide experimental evidence for a longitudinal mode that is due to the relaxation of Debye clouds that surround moving crystal particles. Measuring the structure of our colloidal system leads to a value of Z = 360 ± 20e for the effective charge of the spheres.

Rayleigh-Brillouin (RB) scattering profiles for air have been recorded for the temperature range from 255 to 340 K and the pressure range from 640 to 3300 mbar, covering the conditions relevant for the Earth's atmosphere and for planned atmospheric light detection and ranging (LIDAR) missions. The measurements performed at a wavelength of λ = 366.8 nm detect spontaneous RB scattering at a 90° scattering angle from a sensitive intracavity setup, delivering scattering profiles at a 1% rms noise level or better. The experimental results have been compared to a kinetic line-shape model, the acclaimed Tenti S6 model, considered to be most appropriate for such conditions, under the assumption that air can be treated as an effective single-component gas with temperature-scaled values for the relevant macroscopic transport coefficients. The elusive transport coefficient, the bulk viscosity b, is effectively derived by a comparing the measurements to the model, yielding an increased trend from 1.0 to 2.5 × 10-5 kg ·m -1 · s-1 for the temperature interval. The calculated (Tenti S6) line shapes are consistent with experimental data at the level of 2%, meeting the requirements for the future RB-scattering LIDAR missions in the Earth's atmosphere. However, the systematic 2% deviation may imply that the model has a limit to describe the finest details of RB scattering in air. Finally, it is demonstrated that the RB scattering data in combination with the Tenti S6 model can be used to retrieve the actual gas temperatures. © 2013 Optical Society of America.

Disordered waves at the surface of a vertically oscillated fluid layer have a nontrivial time average. Using an image-reduction scheme we study the surface dynamics that leads to this average state. We show that the average state arises because wave maxima move erratically but are attracted to the nodes of a lattice. This lattice does not correspond to a simpler linear eigenmode of the surface. Both the surface dynamics and the appearance of the average state strongly depend on the boundary condition.

Spatiotemporal chaos in parametrically excited surface waves is compared to fully developed turbulence. Measured correlation functions decay in both space and time. In contrast to turbulence, the inertial range is absent in the Faraday experiment and intermittency is concentrated at a few preferred wavelengths.

We periodically modulate a turbulent wind-tunnel flow with an active grid. We find a resonant enhancement of the mean turbulent dissipation rate at a modulation frequency which equals the large-eddy turnover rate. Thus, we find the best frequency to inject energy into a turbulent flow. The resonant response is characterized by the emergence of vortical structures in the flow and depends on the spatial mode of the stirring grid.

Using an active grid in a wind tunnel, we generate homogeneous shear turbulence and initiate turbulent boundary layers with adjustable properties. Homogeneous shear turbulence is characterized by a constant gradient of the mean velocity and a constant turbulence intensity. It is the simplest anisotropic turbulent flow thinkable, and it is generated traditionally by equipping a wind tunnel with screens which have a varying transparency and flow straighteners. This is not done easily, and the reachable turbulence levels are modest. We describe a new technique for generating homogeneous shear turbulence using an active grid only. Our active grid consists of a grid of rods with attached vanes which can be rotated by servo motors. We control the grid by prescribing the time-dependent angle of each axis. We tune the vertical transparency profile of the grid by setting appropriate angles of each rod such as to generate a uniform velocity gradient, and set the rods in flapping motion around these angles to tailor the turbulence intensity. The Taylor Reynolds number reached was R ¿ = 870, the shear rate S = ¿U/¿y = 9.2 s-1, the nondimensional shear parameter S *= Sq 2/e = 12 and u = 1.4 ms-1. As a further application of this idea we demonstrate the generation of a simulated atmospheric boundary layer in a wind tunnel which has tunable properties. This method offers a great advantage over the traditional one, in which vortex-generating structures need to be placed in the wind tunnel to initiate a fat boundary layer.

We study the free surface of a turbulent flow, in particular the relation between the statistical properties of the wrinkled surface and those of the velocity field beneath it. Channel flow turbulence is generated using an active grid. Through a judicial choice of the stirring protocol the anisotropy of the subsurface turbulence can be controlled. The largest Taylor Reynolds number obtained is Reλ = 258. We characterize the homogeneity and isotropy of the flow and discuss Taylor's frozen turbulence hypothesis, which applies to the subsurface turbulence but not to the surface. The surface gradient field is measured using a novel laser-scanning device. Simultaneously, the velocity field in planes just below the surface is measured using particle image velocimetry (PIV). Several intuitively appealing relations between the surface gradient field and functionals of the subsurface velocity field are tested. For an irregular flow shed off a vertical cylinder, we find that surface indentations are strongly correlated with both vortical and strain events in the velocity field. For fully developed turbulence this correlation is dramatically reduced. This is because the large eddies of the subsurface turbulent flow excite random capillary–gravity waves that travel in all directions across the surface. Therefore, the turbulent surface has dynamics of its own. Nonetheless, it does inherit both the integral scale, which determines the predominant wavelength of the capillary–gravity surface waves, and the (an)isotropy from the subsurface turbulence. The kinematical aspects of the surface–turbulence connection are illustrated by a simple model in which the surface is described in terms of waves originating from Gaussian wave sources that are randomly sprinkled on the moving surface.

We study the free surface of a turbulent channel flow, in particular, the relation between the statistical properties of the wrinkled surface and those of the velocity field beneath it. For an irregular flow shed off a vertical cylinder, surface indentations are strongly correlated with vortices in the subsurface flow. For fully developed turbulence this correlation is dramatically reduced. This is because the large eddies excite random capillary-gravity waves that travel in all directions across the surface. Both their predominant wavelength and their anisotropy are determined by the subsurface turbulence.

We describe a scheme of molecular tagging velocimetry in air in which nitric oxide (NO) molecules are created out of O2 and N2 molecules in the focus of a strong laser beam. The NO molecules are visualized a while later by laser-induced fluorescence. The precision of the molecular tagging velocimetry of gas flows is affected by the gradual blurring of the written patterns through molecular diffusion. In the case of turbulent flows, molecular diffusion poses a fundamental limit on the resolution of the smallest scales in the flow. We study the diffusion of written patterns in detail for our tagging scheme which, at short (micros) delay times is slightly anomalous due to local heating by absorption of laser radiation. We show that our experiments agree with a simple convection-diffusion model that allows us to estimate the temperature rise upon writing. Molecular tagging can be a highly nonlinear process, which affects the art of writing. We find that our tagging scheme is (only) quadratic in the intensity of the writing laser.

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_{0}$ $^{3}$S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_{0}$=25\char21{}32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_{0}$ $^{3}$S\ensuremath{\rightarrow}${\mathit{n}}_{0}$ $^{3}$L, Lg2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

Brownian motion in simple shear flow is studied using the technique of dynamical light scattering. In a conventional scattering experiment the effect of Brownian motion is obscured by that of (deterministic) particle convection. We describe an experimental setup in which both effects are separated.

We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.

While the ordinary structure function in turbulence is concerned with the statistical moments of the velocity increment $\ensuremath{\Delta}u$ measured over a distance $r$, the inverse structure function is related to the distance $r$ where the turbulent velocity exits the interval $\ensuremath{\Delta}u$. We study inverse structure functions of wind-tunnel turbulence which covers a range of Reynolds numbers ${\mathrm{Re}}_{\ensuremath{\lambda}}=400--1100$. We test a recently proposed relation between the scaling exponents of the ordinary structure functions and those of the inverse structure functions [S. Roux and M. H. Jensen, Phys. Rev. E 69, 16309 (2004)]. The relatively large range of Reynolds numbers in our experiment also enables us to address the scaling with Reynolds number that is expected to highlight the intermediate dissipative range. While we firmly establish the (relative) scaling of inverse structure functions, our experimental results fail both predictions. Therefore, the question of the significance of inverse structure functions remains open.

Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their self-similar behavior to the scaling of the fractal objects.

We study dynamical behavior of local structures, such as sources and holes, in traveling-wave patterns in a very long (2 m) heated wire convection experiment. The sources undergo a transition from stable coherent behavior to erratic behavior when the driving parameter epsilon is decreased. This transition, as well as the scaling of the average source width in the erratic regime are both qualitatively and quantitatively in accord with earlier theoretical predictions. We also present results for the holes sent out by the erratic sources.

Impacting systems are intrinsically nonlinear. They are found in a great variety of mechanical constructions. The control of the impact phenomena requires a thorough understanding of the dynamics involved. It is discussed that near-grazing systems, i.e. systems in which the impacts take place at low speed, can be described by discrete mappings. The form of this mapping for a harmonic oscillator with a stop is dealt with in detail. It is pointed out how these mappings can be derived and the results are compared to results earlier published. It is indicated how the present results could be checked experimentally.

The scaling behaviour of high-order structure functions Gp(r) =〈(u(x+r)−u(x))p〉 is studied in a variety of laboratory turbulent flows. The statistical accuracy of the structure function benefits from novel instrumentation for its real-time measurement. The nature of statistical errors is discussed extensively. It is argued that integration times must increase for decreasing separations r. Based on the statistical properties of probability density functions we derive a simple estimate of the required integration time for moments of a given order. We further give a way for improving this accuracy through careful extrapolation of probability density functions of velocity differences.Structure functions are studied in two different kinematical situations. The (standard) longitudinal structure functions are measured using Taylor's hypothesis. In the transverse case an array of probes is used and no recourse to Taylor's hypothesis is needed. The measured scaling exponents deviate from Kolmogorov's (1941) prediction, more strongly so for the transverse exponents.The experimental results are discussed in the light of the multifractal model that explains intermittency in a geometrical framework. We discuss a prediction of this model for the form of the structure function at scales where viscosity becomes of importance.

We describe a new dynamic light scattering technique for measuring diffusion in sheared suspensions. It involves a scattering geometry with two crossing laser beams. A detailed analysis of the correlation function of scattered light is given. The viability of our method is demonstrated in an experiment where the effect of Taylor diffusion on the scattered light correlation function is measured.

The driven harmonic oscillator in free space is a standard example of linear theory; its solution is explicitly known as a function of the initial values and the system parameters. This drastically changes if the oscillator may have impact with an obstacle. The impact introduces a nonlinearity into the system which gives rise to intricate bifurcations. Impact oscillators are found in mechanical systems such as fittings, railway bogies, motion of ships in a harbour and of suspension bridges. For a list of references, see Ref.(6). Recently, impacting systems are used in atomic force microscopy, with which the shape of surfaces can be measured very accurately from impacting on it on a microscopic level; see Ref.(8).

We give experimental evidence for a new bifurcation structure that arises when smooth dynamical systems cross a boundary. Our experiment concerns a driven impacting leaf-spring oscillator with a very precise control of the driving amplitude. The results are in surprisingly good agreement with the predictions of a simple nonlinear mapping that is valid near grazing impact (i.e. impact with zero velocity). The agreement is surprising because a multitude of vibration modes of the spring is excited upon impact whereas the mapping is two-dimensional. Additionally, we consider the case where the impact is not instantaneous due to collisions with a nonrigid stop. This case can be captured by a mapping and we find strong support for the universality of impact phenomena, even in systems that have nonidealities.