To investigate turbulent properties of the tidally induced bottom boundary layer (TBBL) in a rotating frame, we performed three-dimensional numerical experiments under unstratified conditions, varying the temporal Rossby number Rot = |σ*/f*|, where σ* and f* are the tidal frequency and the Coriolis parameter, respectively. The vertical profiles of the time-averaged currents and stresses showed good similarity and coincided well with the turbulent Ekman layer, when they were normalized by the modified ‘outer’ scales, the frictional velocity u*τ, T* = 1/|f* + σ*| and δ* = u*τ/|f* + σ*| for the velocity, time and length scales (σ* is positive when the tidal ellipse rotates anticlockwise). This means that the similarity in turbulent statistics is universally applicable to the TBBL in the world's ocean except near the equator. Although strong inertial waves contaminated the perturbation field when Rot ~ 1 and masked the similarity, the apparent diffusivity κ*ap estimated by tracer experiments again showed similarity, since the inertial waves did not affect the mixing process in the present experiments. Thus, κ*ap can be represented in terms of the three external parameters: the latitude (f*), the tidal frequency (σ*) and the tidal amplitude (u*τ). The obtained scaling of u*τ δ* = u*τ2/|f*+σ*| for κ*ap suggests that effective mixing may occur when Rot ~ 1, i.e. near the critical latitude.

The lattice Boltzmann method was applied to simulate the free rise of monodisperse non-coalescing spherical bubbles in slightly inclined channels bound by solid walls. The Reynolds number based on the relative velocity between the bubbles and the fluid ranged from 4 to 16, the volume fraction from 5% to 10% and the inclination angle from 2° to 6°. The simulations revealed that the weak buoyancy component normal to the walls led to a layer of bubbles near the upper wall and a depleted layer near the bottom wall. These thin layers drove a nearly viscometric shear flow within the bulk of the channel that allowed an unambiguous determination of the lift force in a sheared homogeneous and freely evolving bubble suspension. The lift force coefficients calculated from our simulations were always higher than those for isolated spherical bubbles, suggesting that the lift force is enhanced by hydrodynamic interactions among the bubbles. Experimental measurements of the velocity gradient in 10% volume fraction bubble suspensions in glycerine–water–electrolyte mixtures in slightly inclined channels yielded lift coefficients in excess of those predicted for isolated bubbles and confirmed the qualitative predictions of the simulations.

Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flow's near-field regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity–pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthill's analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D=75. Retarded time topologies of the predicted field at 90° and 30° are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m=0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows.

Periodic linear waves in a vertically sheared flow are considered in a continuously stratified layer of rotating fluid between homogeneous layers along a sloping bottom. This generalized Phillips' configuration has cyclonic horizontal shear and supports the Rossby modes related to the thickness variations of the homogeneous layers and inertia–gravity waves (IGW). While long Rossby modes with streamwise wavenumber κ < f/V (f is the Coriolis parameter, V is the maximum velocity) can be approximated by a neutral balanced solution, short waves with κ > f/V are found to have an inertial critical level and unbalanced gravity-wave-like structure beyond this level. Such ageostrophic unstable normal modes are shown explicitly to couple short Rossby waves with Doppler-shifted gravity waves. They exist even for small Froude number, although the growth rate of ageostrophic unstable modes is exponentially small in Froude number as in the Eady model. This lack of balance in continuously stratified flows agrees with the ultraviolet problem for Ripa's sufficient conditions of stability in a multi-layer model when the number of layers tends to infinity.

The main objective of this study is to examine the robustness of the inner-layer scaling similarity of near-wall turbulence. The turbulent boundary layer of interest is over a very rough surface with a very high Reynolds number and significant outer-layer disturbances. This is not consistent with the canonical turbulent flows studied in laboratories, but it is common in urban areas. The investigation was conducted using the comprehensive outdoor scale model (COSMO) facility. COSMO is composed of a regular array of 1.5 m concrete cubes on a 50×100 m2 flat concrete base. This unique facility allows us to obtain the turbulent dataset within the vertical constant stress region under near-neutral stratification at high Reynolds numbers. The turbulent spectra and the standard deviation of velocity fluctuations from COSMO were compared with the values obtained over rural and urban surfaces, and in wind-tunnel experiments.

The results confirmed that the inner-layer scaling similarity was robust for the wall-normal fluctuations and the Reynolds stress, independent of the roughness types and the outer-layer conditions. The inner-layer scaling similarity failed for the horizontal velocity fluctuations owing to the influence of the outer-layer disturbance. The relative importance of outer-layer turbulence to inner-layer-scale eddies in the horizontal velocity fluctuations was successfully quantified in terms of the roughness scale normalized by the outer-layer scale.

Two-point hot-wire measurements of streamwise velocity were performed in the logarithmic and wake regions of turbulent pipe flow for Reynolds numbers, based on pipe diameter, ranging from 7.6 × 104 to 8.3 × 106 at four wall-normal positions with azimuthal probe separation. The azimuthal correlations were found to be consistent with the presence of very large-scale coherent regions of low-wavenumber, low-momentum fluid observed in previous studies of wall-bounded flows and were found to be independent of changing Reynolds number and surface roughness effects. At the edge of the logarithmic layer the azimuthal scale determined from the correlations was found to be similar to that observed for channel flows but larger than that observed for boundary layers, inconsistent with the concept of a universal logarithmic region. As the wall-normal position increased outside the logarithmic layer, there was a decrease in azimuthal scale relative to that of channel flow. Using cross-spectral analysis, high-wavenumber motion was found to grow azimuthally with wall-normal distance at a faster rate than the low-wavenumber motions.

Analysis of combustion instabilities relies in most cases on linear analysis but most observations of these processes are carried out in the nonlinear regime where the system oscillates at a limit cycle. The objective of this paper is to deal with these two manifestations of combustion instabilities in a unified framework. The flame is recognized as the main nonlinear element in the system and its response to perturbations is characterized in terms of generalized transfer functions which assume that the gain and phase depend on the amplitude level of the input. This ‘describing function’ framework implies that the fundamental frequency is predominant and that the higher harmonics generated in the nonlinear element are weak because the higher frequencies are filtered out by the other components of the system. Based on this idea, a methodology is proposed to investigate the nonlinear stability of burners by associating the flame describing function with a frequency-domain analysis of the burner acoustics. These elements yield a nonlinear dispersion relation which can be solved, yielding growth rates and eigenfrequencies, which depend on the amplitude level of perturbations impinging on the flame. This method is used to investigate the regimes of oscillation of a well-controlled experiment. The system includes a resonant upstream manifold formed by a duct having a continuously adjustable length and a combustion region comprising a large number of flames stabilized on a multipoint injection system. The growth rates and eigenfrequencies are determined for a wide range of duct lengths. For certain values of this parameter we find a positive growth rate for vanishingly small amplitude levels, indicating that the system is linearly unstable. The growth rate then changes as the amplitude is increased and eventually vanishes for a finite amplitude, indicating the existence of a limit cycle. For other values of the length, the growth rate is initially negative, becomes positive for a finite amplitude and drops to zero for a higher value. This indicates that the system is linearly stable but nonlinearly unstable. Using calculated growth rates it is possible to predict amplitudes of oscillation when the system operates on a limit cycle. Mode switching and instability triggering may also be anticipated by comparing the growth rate curves. Theoretical results are found to be in excellent agreement with measurements, indicating that the flame describing function (FDF) methodology constitutes a suitable framework for nonlinear instability analysis.

The theory of two-layer hydraulics is extended to topography with co-varying width and height. When these variations of the non-dimensional width and total depth have a power law relationship, the solutions can still be presented in the Froude-number plane for both unidirectional and exchange flows. These differ from previous solutions, which were limited to treating width and height variations separately.

The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier–Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation.

The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values.

For a representative current height of O(10–100m), the linear stability analysis provides the most amplified wavelength in the range of 250–2500m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break.

To understand the fluid dynamics of a biologically inspired unsteady low-aspect-ratio propulsor, unsteady pressure distributions were measured and compared with time-averaged thrust performance and wake visualizations. The experiments were performed on rigid rectangular panels with different aspect ratios, pitching in a uniform flow. Panel aspect ratio and pitching amplitude were shown to affect the magnitude and time dependence of the pressure distribution on the panel surface, the vorticity generation on the panel, and thrust production. A new scaling is proposed that includes these parameters and collapses the oscillating pressure magnitude and the thrust coefficient.

A general theoretical formalism is developed to assess how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. It also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. This formalism is based on a sensitivity analysis of any global eigenvalue to base-flow modifications. The base-flow modifications investigated are either arbitrary or specific ones induced by a steady force. This leads to a definition of the so-called sensitivity to base-flow modifications and sensitivity to a steady force. These sensitivity analyses are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range 47≤Re≤80. First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. Upon modelling the presence of a control device by a steady force acting on the base flow, these predictions are then extensively compared with the experimental results of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, p. 71). A physical interpretation of the suppression of vortex shedding by use of a control cylinder is proposed in the light of the sensitivity analysis.

The primary objective of this investigation is to determine experimentally the sources of jet mixing noise. In the present study, four different approaches are used. It is reasonable to assume that the characteristics of the noise sources are imprinted on their radiation fields. Under this assumption, it becomes possible to analyse the characteristics of the far-field sound and then infer back to the characteristics of the sources. The first approach is to make use of the spectral and directional information measured by a single microphone in the far field. A detailed analysis of a large collection of far-field noise data has been carried out. The purpose is to identify special characteristics that can be linked directly to those of the sources. The second approach is to measure the coherence of the sound field using two microphones. The autocorrelations and cross-correlations of these measurements offer not only valuable information on the spatial structure of the noise field in the radial and polar angle directions, but also on the sources inside the jet. The third approach involves measuring the correlation between turbulence fluctuations inside a jet and the radiated noise in the far field. This is the most direct and unambiguous way of identifying the sources of jet noise. In the fourth approach, a mirror microphone is used to measure the noise source distribution along the lengths of high-speed jets. Features and trends observed in noise source strength distributions are expected to shed light on the source mechanisms. It will be shown that all four types of data indicate clearly the existence of two distinct noise sources in jets. One source of noise is the fine-scale turbulence and the other source is the large turbulence structures of the jet flow. Some of the salient features of the sound field associated with the two noise sources are reported in this paper.

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier–Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νμ (<νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at νm) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a universal criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower ‘dynamic’ friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids.

A variety of microfluidic technologies utilise electrokinetic transport over rigid surfaces possessing rapid variations in charge. Here, as a paradigmatic model system for such situations, we consider electro-osmosis past a flat plate possessing a discontinuous jump in surface charge. Although the problem is relatively simple to pose, our analysis highlights a number of interesting and somewhat surprising features. Notably, the standard assumption that the electric field outside the diffuse screening layer is equal to the uniform applied field leads to a violation of ion conservation, since the applied field drives an ionic surface current along the diffuse layer downstream of the jump, whereas there is zero surface current upstream. Instead, at the surface charge discontinuity, field lines are drawn into the diffuse layer to supply ions from the bulk electrolyte, thereby ensuring ion conservation. A simple charge conservation argument reveals that the length-scale over which this process occurs is of the order of the ratio of surface-to-bulk electrolyte conductivities, LH=σs/σb. For a highly charged surface, LH can be several orders of magnitude greater than the Debye screening length λD, which is typically nanometres in size. Remarkably, therefore, nano-scale surface conduction may cause micrometre-scale gradients in the bulk electric field. After a distance O(LH) downstream, the bulk field ‘heals’ and is once again equal to the applied field. Scaling all distances with the ‘healing length’ LH yields a universal set of equations for the bulk field and fluid flow, which are solved numerically. Finally, we discuss the role of surface conduction in driving a non-uniform ion distribution, or concentration polarization, in the bulk electrolyte.

When surface wetting drives liquids to invade porous media or microstructured materials with uniform channels, the penetration distance is known to increase as the square root of time. We demonstrate, experimentally and theoretically, that shape variations of the channel, in the flow direction, modify this ‘diffusive’ response. At short times, the shape variations are not significant and the imbibition is still diffusive. However, at long times, different power-law responses occur, and their exponents are uniquely connected to the details of the geometry. Experiments performed with conical tubes clearly show the two theoretical limits. Several extensions of these ideas are described.

The interaction between two localized disturbances is analysed in a subcritical channel flow through direct numerical simulations. The initial perturbations are in the form of two pairs of counter-rotating vortices. One of them interacts with the wall-normal vorticity layers set up near the wall, by locally compressing or stretching part of them through the straining motion it induces. The breakdown of spanwise symmetry leads to the rapid development of a new wall-normal vorticity patch that is tilted by the shear and rolls up into a new small-scale streamwise vortex. The process results in a localized turbulent spot at later stages of development. A detailed analysis is carried out to determine the role of different parameters entering the physics of the mechanism. Several critical thresholds that trigger the interactive bypass transition process are found and analysed. The similarity parameters resulting from the parametric investigation coincide well with those governing the self-sustaining Reynolds-shear-stress-producing eddies in the buffer layer of a fully developed turbulent wall flow. It is suggested that the mechanism we propose may play a role in the regeneration cycle of the near-wall turbulence-generating structures by bypassing the three-dimensional streak instability mechanism.

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

A swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity and referred to as a squirmer. The centre of mass of the sphere may be displaced from the geometric centre, and the effects of inertia and Brownian motion are neglected. The well-known Stokesian dynamics method is modified in order to simulate squirmer motions in a concentrated suspension. The movement of 216 identical squirmers in a concentrated suspension without any imposed flow is simulated in a cubic domain with periodic boundary conditions, and the coherent structures within the suspension are investigated. The results show that (a) a weak aggregation of cells appears as a result of the hydrodynamic interaction between cells; (b) the cells generate collective motions by the hydrodynamic interaction between themselves; and (c) the range and duration of the collective motions depend on the volume fraction and the squirmers' stresslet strengths. These tendencies show good qualitative agreement with previous experiments.

The boundary layer generated by the propagation of a solitary wave is investigated by means of direct numerical simulations of continuity and Navier–Stokes equations. The obtained results show that, for small wave amplitudes, the flow regime is laminar. Turbulence appears when the wave amplitude becomes larger than a critical value which depends on the ratio between the boundary-layer thickness and the water depth. Moreover, turbulence is generated only during the decelerating phase, or conversely, turbulence is present only behind the wave crest. Even though the horizontal velocity component far from the bed always moves in the direction of wave propagation, the fluid particle velocity near the bottom reverses direction as the irrotational velocity decelerates. The strength and length of time of flow reversal are affected by turbulence appearance. Also the bed shear stress feels the effects of turbulence presence.

Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp=(ν/ρU3τ)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws.