Geoffrey Spedding

Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid

Late wakes ( Nt > 20) of towed spheres in a stably stratified fluid were analysed in a plane using a reliable, customized DPIV technique that provides sufficient spatial and temporal resolution to cover all important scales of motion in this freely decaying geophysical flow. Systematic experiments were conducted with independent variation of Re ∈ [10 3 , 10 4 ] and F ∈ [1, 10] (F ≡ 2 U/ND is an internal Froude number based on the buoyancy frequency, N , and the sphere radius, D /2), and for selected { Re, F } pairs above this range. The normalized wake width grows at approximately the same rate as in a three-dimensional unstratified wake, but it becomes narrower, not wider, with decreasing F (i.e. as stratification effects become more important). The centreline defect velocity, on the other hand, reaches values an order of magnitude above those measured for three-dimensional unstratified wakes at equivalent downstream locations. Both observations are argued to be consequences of the very high degree of order and coherence that emerge in the late-wake vortex structures. Streamwise-averaged turbulence quantities, such as the velocity fluctuation magnitude, and mean-square enstrophy, show similar power law behaviour for all Re ≤ 5 × 10 3 , with exponents equal to those expected in three-dimensional axisym-metric turbulent wakes. There is no obvious physical reason why three-dimensional arguments are so successful in such a flow, and at such long evolution times. The scaling collapses none of the cases for Re below 4 – 5 × 10 3 , appearing to establish a minimum Re for a class of self-similar stratified wake flows that evolve from fully turbulent initial conditions. Individual vortex cross-sections appear to be well approximated by Gaussian distributions at all Re , F and Nt studied here. The scaling behaviour of individual vortices mimics that of the statistical, wake-averaged quantities, and differs measurably from a simple two-dimensional viscous diffusion model. The importance of formulating a realistic three-dimensional model is discussed, and some limited steps in this direction point to future useful experiments and modelling efforts.

Performance analysis and application of grid interpolation techniques for fluid flows

Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid. Both techniques are global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global functional proportional to the Laplacian of the velocity field. In this way, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow.Performance curves are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise the interpolation errors, given various external constraints. Some illustrative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also pointed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the development of surface spline techniques for problems involving large numbers of data points.

The evolution of initially turbulent bluff-body wakes at high internal Froude number

Coherent vortex structures are formed in the late wakes of towed spheres for all values of the internal Froude number, F≡2U/ND∈ [10, 240] (U is the body speed, D its diameter, and N is the buoyancy frequency). The eventual emergence of the long-lived and stable pattern of alternating-signed patches of vertical vorticity is characteristic of all towed-sphere wakes, from those dominated by internal lee waves at F=1, to initially fully turbulent early wakes at F[ges ]4. At late times, the local Froude number is always low, and a characteristic stratified wake structure and dynamics result. These wakes have high mean wake defect velocities compared with non-stratified wakes, but the decay rates of energy and enstrophy are similar. Experimental evidence is presented for the existence of an intermediate non-equilibrium (NEQ) regime with very low decay rates of kinetic energy, that precedes the late wake. The NEQ regime is the period when the initial turbulence reorganizes under the increasingly (relative to the decaying turbulent kinetic energy) powerful influence of the background density gradient, accompanied by conversion of potential to kinetic energy as the wake turbulence collapses. The stable long-lived late-wake structure that eventually emerges has a high degree of order and coherence that reflects the initial wake instability. A universal curve for the energy decay of all stratified drag wakes at high Froude and Reynolds numbers is proposed.

Quantitative studies of the wakes of freely flying birds in a low-turbulence wind tunnel

A novel application of DPIV methods is presented for measuring velocity and vorticity distributions in vertical cross sections through the wake of a freely flying bird (thrush nightingale) in a wind tunnel. A dual-camera system is used, and successive cross-correlation operations remove lens/camera distortions, and then the undisturbed background flow, so that the final operation simply examines the disturbance effect of the bird alone. The concentration and tuning of processing methods to the disturbance quantities allows full exploitation of the correlation calculation and estimation algorithms. Since the ultimate objective is to deduce forces and power requirements on the bird itself from the wake structure, the analytical procedure is followed through an example on a fixed airfoil, before sample results from extensive bird flight tests are described. The wake structure of the thrush nightingale in slow (5-m/s) flight is qualitatively quite similar to those previously described in the literature, but certain quantitative details are different in important respects.

Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes

The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers, Re = UD/ν ∈ [5 × 10 3 , 10 5 ] and internal Froude numbers, Fr = 2 U /( ND ) ∈ [4, 64] ( U , D are characteristic velocity and length scales, and N is the buoyancy frequency) is examined. The maximum value of Re and the range of Fr values considered allow extrapolation of the results to geophysical and naval applications. At higher Re , the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lower Re . At Re = 5 × 10 3 , vertical fluid motions are rapidly suppressed, but at Re = 10 5 , secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up to Nt ≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy. These results agree with existing scaling of buoyancy-driven shear on Re / Fr 2 and suggest that, in the field, the NEQ regime may last up to Nt ≈ 1000. At a given high Re value, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent of Fr . This first systematic numerical investigation of stratified turbulence (as defined by Lilly, J. Atmos. Sci. vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.

Stratified propelled wakes

This paper presents experimental results on the wake of a propelled bluff body towed at a constant horizontal speed in a linearly stratified fluid. Three regimes of the wake have been found, depending on the angle of attack and on the ratio of drag force to propeller thrust. Most of the experiments were obtained in a first regime where a strong momentum flux is created in the wake, which can be oriented backward or frontward depending on the ratio of drag force to thrust of the propeller. The velocity amplitude, wake width and Strouhal number of the wake can be predicted by defining a momentum thickness based on the drag coefficient of the bluff body and the thrust of the propeller. A second regime is obtained on a narrow band of towing velocities, with a relative width of 4%, in which the momentum flux is found to vanish. The wake is characterised by the velocity fluctuations; the scaling exponents of the velocity, vorticity and width of the wake are measured. A third regime is obtained for wakes with a small angle of attack, with a null momentum flux. The mean profile of the wake is found to be asymmetric and its amplitude and wake width are measured. Finally, the relevance of these results to the case of a real self-propelled bluff body is discussed. The presence of weak internal waves or of weak fluctuations of background velocity would lead to a wake in the regime with momentum flux, and would allow prediction of the amplitude, width and Strouhal number of the wake.

Lunate-tail swimming propulsion. Part 2. Performance analysis

The theory of an oscillating, high-aspect-ratio, lifting surface with a curved centreline (Cheng & Murillo 1984) is applied to a performance analysis of lunate-tail swimming propulsion. Thrust, power and propulsive efficiency are calculated for model lunate tails with various combinations of mode shapes and morphological features to ascertain the viability of the proportional-feathering concept, and to determine the influence of sweep and centreline curvature. One of the principal conclusions concerns the interchangeability of the heaving amplitude of the peduncle (identified with the major pitching axis) with the centreline sweep, and its effect on the propulsive efficiency, while maintaining the same thrust. Hydrodynamic reasons are also offered for the apparent preference for the crescent-moon fin shape over the V-shape at moderate sweep angles, and for the large sweep angles often found in V-shaped fins.

Anisotropy in turbulence profiles of stratified wakes

At sufficiently high values of the Reynolds number (Re⩾4.5×103) and internal Froude number (F⩾4), initially turbulent bluff body wakes evolve in the presence of a stable background density gradient with wake-averaged mean and turbulence length and velocity scales that are independent of Re and F for at least two orders of magnitude extension in both parameters. The way in which the initially three-dimensional motions transition to the characteristic (and Re- and F-independent) late wakes (where vertical velocities, w≪u,v) is both of great practical interest, and complex, hence somewhat unclear. Here, digital particle imaging velocimetry type measurements on towed-sphere wakes are described, so that the development of anisotropy can be measured by the time development of turbulence profiles in horizontal and vertical centerplanes. The observed anisotropies can be associated with energy transfer to internal wave modes, and suppression of other vertical displacements, that contrasts with sphere wakes at simi...

Self-preservation in stratified momentum wakes

A general model is described for drag wakes in a linearly stratified fluid, based on the self-preservation of the flow. It is assumed that the buoyancy-controlled self-similar wake expands in the horizontal direction due to turbulent diffusion and in the vertical direction due to viscous diffusion. The mean characteristics of the wake (height, width and velocity defect) are analytically derived and show good agreement with existing data from experimental and numerical results. Moreover, the three regimes previously found in the literature that characterize different dynamical phases of the wake evolution are recovered, and two new regimes are found. The model allows for prediction of characteristic length and velocity scales at the high Reynolds numbers of large-scale applications of geophysical and naval origin.

Beyond robins: aerodynamic analyses of animal flight

Recent progress in studies of animal flight mechanics is reviewed. A range of birds, and now bats, has been studied in wind tunnel facilities, revealing an array of wake patterns caused by the beating wings and also by the drag on the body. Nevertheless, the quantitative analysis of these complex wake structures shows a degree of similarity among all the different wake patterns and a close agreement with standard quasi-steady aerodynamic models and predictions. At the same time, new data on the flow over a bat wing in mid-downstroke show that, at least in this case, such simplifications cannot be useful in describing in detail either the wing properties or control prospects. The reasons for these apparently divergent results are discussed and prospects for future advances are considered.