The interaction of a sharp density interface with oscillating-grid-induced shear-free turbulence was experimentally investigated. A linear photodiode array was used in conjunction with laser-induced fluorescence to measure the concentration of dye that was initially only in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical velocity in and above the density interface at a point where the dye concentration was also measured. Potential refractive-index-fluctuation problems were avoided using solutes that provided a homogeneous optical environment across the density interface. Internal wave spectra, amplitudes and velocities, as well as the vertical mass flux were measured. The results indicate that mixing occurs in intermittent bursts and that the gradient (local) Richardson number remains constant for a certain range of the overall Richardson number Rj, defined in terms of an integral lengthscale, buoyancy jump and turbulence intensity. The spectra of the internal waves decay as f−3 at frequencies below the maximum Brunt-Väisälä frequency. These findings give support to a model for oceanic mixing proposed by Phillips (1977) in which the internal waves are limited in their spectral density by sporadic local instabilities and breakdown to turbulence. The results also indicate that, for a certain Rj range, the thickness of the interfacial layer (normalized by the integral lengthscale of the turbulence) is a decreasing function of Rj. At sufficiently high Rj the interfacial thickness becomes limited by diffusive effects. Finally, we discuss a simple model for entrainment at a density interface in the presence of shear-free turbulence.

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgrid-scale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off.

Recent controlled experiments by Kachanov & Levchenko (1984) and others indicate that, during some slower kinds of transition to turbulence in boundary layers, three-dimensionality can come into play initially as a resonant-triad phenomenon, depending on the disturbance sizes present. The triad interaction, suggested theoretically in the boundary-layer context by Craik (1971) and others, is studied in the present work by means of multi-structured analysis for high characteristic Reynolds numbers. A finite-amplitude/relatively high-frequency approach leads rationally to the nonlinear triad equations, solutions for which are then obtained analytically and computationally in certain central cases of interest (temporal and spatial). The solutions have a rather chaotic spiky appearance as continual energy exchange develops between the two- and three-dimensional nonlinear modes, whose large-scale response seems governed by inviscid dynamics but subject to important, continual ‘rejuvenation’ from small- (fast-) scale viscous action in-between. The three-dimensional growth rate is thereby increased, but not the two-dimensional. Subsequently the disturbed flow enters a higher-amplitude regime similar to that studied in some related papers by the authors and co-workers. Comparisons with the experiments are very supportive of the theory (in the small and in the large), yielding both qualitative and quantitative agreement.

Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centreline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behaviour of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behaviour of the pressure spectrum is also consistent with local isotropy and compares favourably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centreline as the magnitude of the mean strain rate increases.

This paper describes the consequences of pair interactions in dilute suspensions of rigid rods of length 2l and radius a subjected to weak, steady shear flows. The combination of hydrodynamic and Brownian forces increases alignment with the flow, thereby enhancing the shear thinning and strain thickening expected from dilute theories. The theory is asymptotic in Pe [Lt ] 1 and ε = (ln 2l/a)−1 [Lt ] 1 but requires an ad hoc approximation to simplify the form of the hydrodynamic interactions and the rod-rod excluded volume. The theoretical predictions of the Huggins coefficient in simple shear flow are compared with data in the literature for Xanthan gum, a semi-rigid biopolymer. Comparison with semi-dilute theories emphasizes the fundamentally different nature of the interactions in the two regimes and indicates that the transition between the two lies in the range 1.5 [les ][η]0n [les ] 6.

Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack ($=4^{\circ }$). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness.

This paper deals with the study of the response of a cold wire used as a thermal sensor in a turbulent flow for different types of probes and for several gases (air, argon and helium). It is now well known that in the case of air flows the transfer function of the probe shows a typical step at low frequencies, as pointed out by Perry, Smits & Chong (1979).

In this plateau region the wire temperature may be influenced by the prong temperature through two different paths. The first is conduction between prong and wire, as already discussed by Maye (1970) using the ‘cold length’ lc, introduced by Betchov (1948). As suggested by Hojstrup, Rasmussen & Larsen (1975) the second is the result of the thermal boundary layer on the prong being very large at low velocities in gases of large thermal diffusivity; this region of influence (by the prong) extends over a length of the wire characterized by the thickness lb, of the thermal boundary layer on the prong.

In this paper a simple analysis of the behaviour of the transfer function of cold wires taking these two effects into account is presented by introducing the parameter η = lb/lc. An experimental investigation of these phenomena has been undertaken using a procedure which allows temperature fluctuations to be produced over a larger range of frequencies than has been usually made up to now.

Good agreement is obtained between experimental results and predictions using this analysis for several types of prong in different gaseous flows (air, argon and helium). An important step in the frequency response is found in the latter case because of the large thermal diffusivity of helium. Furthermore an example of the thermal prong–wire interaction is presented in the ease of intermittent temperature measurements.

The effect of time-periodical blowing through a spanwise slot on the near-wall turbulence characteristics is investigated. The blowing velocity changes in a cyclic manner from 0 to 5 wall units. The frequency of the oscillations is nearly equal to the median frequency of the near-wall turbulence. The measurements of the wall shear stress and the streamwise velocity are reported and discussed. The flow field near the blowing slot is partly relaminarized during the acceleration phase of the injection velocity which extends 40 wall units downstream. The imposed unsteadiness is confined to the buffer layer, and the time-mean structural parameters under unsteady blowing are found to be close to those of isotropic turbulence in this region. The relaminarized phase is unstable and gives way to a coherent spanwise structure that increases the shear from 80 to 300 wall units downstream of the slot in a predictable way. This phenomenon is strongly imposed-frequency dependent.

Miles’ (1977b) model of the Mach reflexion of a solitary wave by a vertical wall is tested by laboratory experiments. The model over-predicts the measured run-up at the wall, and no evidence of the predicted maximum was found. The measurements provide support for the predicted critical angle of incidence at which Mach reflexion is replaced by regular reflexion. It is shown that mass and energy conservation determine the length of the reflected wave in Miles’ model and that this is not consistent with momentum conservation in the neighbourhood of the end point of the reflected wave. It is suggested that the discrepancy between the measurements and the model may result from this failure of the model.

When a drop impacts a smooth, dry surface at a velocity above the so-called critical speed for drop splashing, the initial liquid volume loses its integrity, fragmenting into tiny droplets that are violently ejected radially outwards. Here, we make use of the model of Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507), together with a one-dimensional approximation describing the flow in the ejected liquid sheet and of balances of mass and momentum at the border of the sheet, to calculate mean sizes and velocities of the ejected drops. The predictions of the model are in good agreement with experiments.

A transonic interaction between a shock wave and a turbulent boundary layer is experimentally and theoretically investigated. The configuration is a transonic channel flow over a bump, where a shock wave causes the separation of the boundary layer in the form of a recirculating bubble downstream of the shock foot. Different experimental techniques allow for the identification of the main unsteadiness features. As recognised in similar shock-wave/boundary-layer interactions, the flow field exhibits two distinct characteristic frequencies, whose origins are still controversial: a low-frequency motion which primarily affects the shock wave; and medium-frequency perturbations localised in the shear layer. A Fourier analysis of a series of Schlieren snapshots is performed to precisely characterise the structure of the perturbations at low- and medium-frequencies. Then, the Reynolds-averaged Navier–Stokes (RANS) equations closed with a Spalart–Allmaras turbulence model are solved to obtain a mean flow, which favourably compares with the experimental results. A global stability analysis based on the linearization of the full RANS equations is then performed. The eigenvalues of the Jacobian operator are all damped, indicating that the interaction dynamic cannot be explained by the existence of unstable global modes. The input/output behaviour of the flow is then analysed by performing a singular-value decomposition of the Resolvent operator; pseudo-resonances of the flow may be identified and optimal forcings/responses determined as a function of frequency. It is found that the flow strongly amplifies both medium-frequency perturbations, generating fluctuations in the mixing layer, and low-frequency perturbations, affecting the shock wave. The structure of the optimal perturbations and the preferred frequencies agree with the experimental observations.

It is known that large-scale streamwise velocity-fluctuating structures ($u^{\prime }$) are frequently observed in the log region of a zero pressure gradient turbulent boundary layer, and that these motions significantly influence near-wall small-scale $u^{\prime }$-structures by modulating the amplitude (Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28; Mathis et al., J. Fluid Mech., vol. 628, 2009, pp. 311–337). In the present study, we provide evidence that the spatial organization of large-scale structures in the log region is significantly influenced by the strength of adverse pressure gradients in turbulent boundary layers based on a direct numerical simulation dataset. For a mild adverse pressure gradient boundary layer flow, groups of hairpin vortices are coherently aligned in the streamwise direction to form hairpin vortex packets, and streamwise merging events of the induced large-scale $u^{\prime }$-structures create a larger streamwise length scale of structures than that for a zero pressure gradient boundary layer flow. As the pressure gradient strength increases further, however, the formation of hairpin packets is continuously suppressed, and large-scale motions are consequently not concatenated to create a longer motion, resulting in a significant reduction of the streamwise coherence of large-scale structures in the log layer. Although energy spectrum maps for $u^{\prime }$-structures show that the large-scale energy is continuously intensified above the log layer with an increase in the pressure gradient, amplitude modulation of the near-wall small-scale motions is dominantly induced by log region large-scale structures for adverse pressure gradient flows. Conditional averaged flow fields with large-scale Q2 and Q4 events indicate that large-scale counter-rotating roll modes play an important role in organizing the flows under the pressure gradients, and the large-scale roll modes associated with Q4 events are more enhanced in the outer layer than those associated with Q2 events, reducing the streamwise coherence of the vortices in a packet.

Instantaneous and phase averaged pressure distributions in the near field of a jet, and their effects on the conditions for the onset of cavitation are studied in detail. The measurements are performed by using microscopic bubbles as pressure sensors, and holography as a means of detecting them. Experiments are performed at Red exceeding 4 × 105, with and without acoustic excitation. The results show that the highest negative pressure peaks (–0.97) and the resulting cavitation inception occur because of vortex pairing. Prior to pairing the negative peaks are between –0.8 and –0.9. Weak acoustic excitation changes the entire flow structure and the spatial distributions of bubbles, but has little effect on the onset of cavitation. Downstream of the potential core the highest pressure peaks (∼ –0.6) are considerably smaller, in agreement with the occurrence of cavitation there. It is also shown that although the r.m.s. values of pressure fluctuations do not vary with the jet speed, the probability distribution changes significantly, causing a reduction in the inception index with increasing velocity. The probability of cavitation inception is estimated from the distributions of bubbles and pressure peaks. It is shown that the actual, non-uniform bubble distribution increases the probability of inception owning to migration of the bubbles to the low pressure regions.

Linear instability analysis is applied to the slowly diverging mean profile of a turbulent axisymmetric jet and used to predict the transverse structure and axial evolution of large-scale wavelike modes with azimuthal wavenumber m = 1. Comparisons are made with measurements of filtered velocity fluctuations, and of pressure fluctuations, taken in a jet with coherent forcing at the exit plane, at Strouhal numbers St = fD/U0 around 0.5,f = ω/2π being the frequency, D the nozzle diameter and U0 the mean centreline exit velocity. The transverse structure at each axial station is well predicted by linear theory, as is the phase speed and its variation with axial distance. The downstream evolution of amplitude is much less well predicted, presumably because of cumulative nonlinear effects in the experiments, though the inclusion of mean-flow divergence itself constitutes a significant improvement over the theory for parallel flow, and in somecases permits calculation of the wave evolution well into the decay phase without any reference to viscous effects on the disturbance.

Experiments were conducted to investigate the response of a rigid two-dimensional elastically mounted smooth circular cylinder, with oscillations restricted to a plane normal to the incident flow, as influenced by the vicinity of an identical fixed body placed inside the wake. The static lift and drag coefficients, as well as the vibration amplitude and frequency of the upstream cylinder as functions of relative position of the pair of cylinders are given. Most measurements were carried out under two conditions of free-stream turbulence. Whilst turbulence decreased the magnitude of drag coefficients, it had no appreciable effect on lift coefficients. The forces on the upstream body were found to be influenced by the proximity to the downstream one in a significant way only when the streamwise spacing is less than two diameters.

In the dynamic tests, two kinds of instability, namely a vortex-resonance and galloping, were observed, with the latter only occurring when the downstream cylinder was well submerged in the near wake of the upstream one. The vortex-shedding frequency was always found to lock to oscillation frequency. Whereas the vibration characteristics remained essentially unaffected with changing turbulence intensity, the galloping amplitudes were observed to be sensitive to cylinders’ aspect ratio. A quasi-steady theory was developed to predict the galloping behaviour.

The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Péclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

Laboratory experiments were conducted on a double-diffusing fluid stabilized by the faster diffuser ($T$) and destabilized by the slower diffuser ($S$), the arrangement that leads to salt fingering. The experiments were conducted in three tanks of depths 2 m, 1 m or 0.3 m, with initial linear profiles of $S$ and $T$ between two reservoirs at fixed or known values, $S_0 + \Delta S, T_0 + \Delta T$ in the top reservoir, $S_0, T_0$ in the bottom reservoir.

In the thermohaline staircase regime consisting of an alternating stack of convecting layers and finger layers, the overall fluxes $F_S$ and $F_T$ are clearly not depth independent. The overall Nusselt number, $N_S$ varies inversely with the number $n$ of finger layers plus convecting layers occurring in the experimental fluid. The largest Nusselt number occurs for $n = 1$. The number $n$ increases with increasing mean vertical gradient, up to a point. If the vertical gradients are large, $n$ is always equal to 1.

Internal measurements show that in the Rayleigh number range $|R_S|\sim 10^{15}$ and density ratio range $R_{\rho}\sim 1.1$ to 1.2, the finger flux $F^f_S\sim {(\delta S/h)}R_S^a R_{\rho}^b$ with $a = 0.18$ to 0.19 and $b = 1.8$ to 2.1. The data show dependence of $F^f_S$ on finger layer thickness $h$. In the convecting layers, $N^c_S \propto R^{0.21}$ for large enough aspect ratio.

In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.

The paper presents a linear analytical model to predict the frequency characteristics of the discrete oscillations of the jet-edge feedback cycle. The jet is idealized as having top-hat profile with vortex-sheet shear layers, and the nozzle from which it issues is represented by a parallel plate duct. At a stand-off distance h, a flat plate is inserted along the centreline of the jet, and a sinuous instability wave with real frequency w is assumed to be created in the vicinity of the nozzle and to propagate towards the splitter plate. Its interaction with the splitter plate produces an irrotational feedback field which, near the nozzle exit, is a periodic transverse flow producing singularities at the nozzle lips. Vortex shedding is assumed to occur, alleviating the singularities and allowing a trailing-edge Kutta condition to be satisfied; this Kutta condition is claimed to be the phase-locking criterion. The shed vorticity develops into a sinuous spatial instability, and the cycle of events is repeated periodically.

Problems corresponding to the various physical processes described are analysed, for in viscid flow with vortex-sheet shear layers and aligned flat-plate boundaries, and solved in an appropriate asymptotic sense by Wiener-Hopf methods. Calculation of the phase changes occurring in the constituents of the cycle gives an equation for the frequency w in the Nth ‘stage’ as a function of jet width 2b, jet velocity U0, standoff distance h, and stage label N: \[ \omega b/U_0 = (b/h)^{\frac{3}{2}}[4\pi(N-{\textstyle\frac{3}{8}})]^{\frac{3}{2}}. \] The variations with b, U0, h and N are in excellent agreement with edge-tone experiments; the principal disagreement lies in the overall numerical factor $(4\pi)^{\frac{3}{2}}$ and explanations are given for this. Possible effects associated with the inclusion of displacement thickness fluctuations in the splitter-plate boundary layers, and the enforcement of a leading-edge Kutta condition, are also considered and shown not to affect the frequencies of the operating stages.

The linear stability analysis predicts that the Mack second mode propagating in the boundary layer on a sufficiently cold plate can radiate acoustic waves into the outer inviscid flow. This effect, which is called as a spontaneous radiation (or emission) of sound, is associated with synchronization of the second mode with slow acoustic waves of the continuous spectrum. The theoretical predictions are confirmed by direct numerical simulations of wave trains and wave packets propagating in the boundary layer on a flat plate at free-stream Mach number 6 and wall-to-edge temperature ratio $T_{w}/T_{e}=0.5$. A non-uniform distribution of the wave packet components and the interference between the radiated acoustic waves result in an intricate pattern of the outer acoustic field. The spontaneous radiation of sound, in turn, strongly affects the wave packet in the boundary layer causing its elongation and modulation. This phenomenon may alter the downstream development of instability and delay the transition onset.