Experimental and theoretical models are used to explore the break of a moraine dam by catastrophic erosional incision initiated by an overtopping wave. The experiments are conducted in a rectangular tank with an erodible barrier made from sand and grit. Theory combines shallow-water hydrodynamics with an empirical model of erosion. The models confirm that dams can be broken by a catastrophic incision. However, the displacement wave does not break the dam in its first passage but excites a long-lived seiche that repeatedly washes over the dam. The cumulative erosion of the downstream face by the overtopping seiches eventually allows an incipient channel to form, and catastrophic incision follows. Estimates are presented of the strength of the initial disturbance required to break the dam, the maximum discharge and the duration of the runaway incision.

We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid.

A study of the Faraday instability of diffuse interfaces between pairs of miscible liquids of different densities, by means of experiments and by a nonlinear numerical model, is presented. The experimental set-up consisted of a rectangular cell in which the lighter liquid was placed above the denser one. The cell in this initially stable configuration was then subjected to vertical vibrations. The subsequent behaviour of the ‘interface’ between the two liquids was observed with a high-speed camera. This study shows that above a certain acceleration threshold an instability developed at the interface. The amplitude of the instability grew during the experiments which then led to the mixing of the liquids. The instability finally disappeared once the two liquids were fully mixed over a volume, considerably larger than the initial diffuse region. The results of a companion two-dimensional nonlinear numerical model that employs a finite volume method show very good agreement with the experiments. A physical explanation of the instability and the observations are advanced.

Three-dimensional linear BiGlobal instability of two-dimensional states over a periodic array of T-106/300 low-pressure turbine (LPT) blades is investigated for Reynolds numbers below 5000. The analyses are based on a high-order spectral/hp element discretization using a hybrid mesh. Steady basic states are investigated by solution of the partial-derivative eigenvalue problem, while Floquet theory is used to analyse time-periodic flow set-up past the first bifurcation. The leading mode is associated with the wake and long-wavelength perturbations, while a second short-wavelength mode can be associated with the separation bubble at the trailing edge. The leading eigenvalues and Floquet multipliers of the LPT flow have been obtained in a range of spanwise wavenumbers. For the most general configuration all secondary modes were observed to be stable in the Reynolds number regime considered. When a single LPT blade with top to bottom periodicity is considered as a base flow, the imposed periodicity forces the wakes of adjacent blades to be synchronized. This enforced synchronization can produce a linear instability due to long-wavelength disturbances. However, relaxing the periodic restrictions is shown to remove this instability. A pseudo-spectrum analysis shows that the eigenvalues can become unstable due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulations confirm all perturbations identified herein. An optimum growth analysis based on singular-value decomposition identifies perturbations with energy growths O(105).

Laboratory measurements of the post-breaking velocity field due to unsteady deep-water breaking are presented. Digital particle image velocimetry (DPIV) is used to measure the entire post-breaking turbulent cloud with high-resolution imagery permitting the measurement of scales from O(1m) down to O(1mm). Ensemble-averaged quantities including mean velocity, turbulent kinetic energy (TKE) density and Reynolds stress are presented and compare favourably with the results of Melville, Veron & White (J. Fluid Mech., vol. 454, 2002, pp. 203–233; MVW). However, due to limited resolution, MVW's measurements were not spatially coherent across the turbulent cloud, and this restricted their ability to compute turbulent wavenumber spectra. Statistical spatial quantities including the integral length scale L11, Taylor microscale λf and the Taylor microscale Reynolds number Reλ are presented. Estimation of an eddy viscosity for the breaking event is also given based on analysis of the image data. Turbulent wavenumber spectra are computed and within 12 wave periods after breaking exhibit what have been termed ‘spectral bumps’ in the turbulence literature. These local maxima in the spectra are thought to be caused by an imbalance between the transport of energy from large scales and the dissipation at small scales. Estimates of the dissipation rate per unit mass are computed using both direct and indirect methods. Horizontally averaged terms in the TKE budget are also presented up to 27 wave periods after breaking and are discussed with regard to the dynamics of the post-breaking flow. Comparisons of the TKE density in the streamwise and cross-stream planes with the three-dimensional full TKE density are given in an appendix.

In this paper we study two-dimensional flow around regular polygons with an arbitrary but even number of edges N and one apex pointing to the free stream, with comparison to circular-cylinder flow. Both inviscid flow and low-Reynolds-number viscous flow are addressed. For inviscid flow, we obtained the exact solution for pure potential flow through Schwarz–Christoffel transformation, with the emphasis on the role of edge number, N, on the flow details. We also studied the behaviour, stationary lines and stability of vortex pair and found new stationary lines compared to circular cylinder. For viscous flow we derived the equation of stream function in the mapped (circle) domain, based on which approximate expressions for the critical Reynolds numbers and Strouhal number, as functions of the edge number, are obtained. The Reynolds number is based on the diameter of the circumscribed circle. For the steady flow, the first critical Reynolds number is a monotonically decreasing function of N, while N → ∞ corresponds to that for circular cylinder. The bifurcation point is ahead of the bifurcation point for circular cylinder. For unsteady flow, the critical Reynolds number for vortex shedding and the Strouhal number are both monotonically decreasing functions of N.

As a stepping stone towards understanding acoustic resonances in axial flow compressors, acoustic resonances are computed numerically in fixed single and tandem plate cascades in an infinitely long annular duct. Applying perfectly matched layer absorbing boundary conditions in the form of the complex scaling method of atomic and molecular physics to approximate the radiation condition the resonance problem is transformed into an eigenvalue problem. Of particular interest are resonances with zero radiation damping (trapped modes) or very small radiation damping (nearly trapped modes). Such resonances can be excited by wakes from compressor cascades or struts. If the shedding frequency is sufficiently close to an acoustic resonant frequency, the latter may control the vortex shedding causing high-intensity tonal noise or occasionally even blade failure. All resonances are computed for zero mean flow approximating low-Mach-number flows. The influence of various cascade parameters on the resonant frequencies is studied and, whenever possible, our numerical results are compared with published experimental findings.

A theoretical foundation for two widely used statistical representations of multiphase flows, namely the Eulerian–Eulerian (EE) and Lagrangian–Eulerian (LE) representations, is established in the framework of the probability density function (p.d.f.) formalism. Consistency relationships between fundamental statistical quantities in the EE and LE representations are rigorously established. It is shown that fundamental quantities in the two statistical representations bear an exact relationship to each other only under conditions of spatial homogeneity. Transport equations for the probability densities in each statistical representation are derived. Exact governing equations for the mean mass, mean momentum and second moment of velocity corresponding to the two statistical representations are derived from these transport equations. In particular, for the EE representation, the p.d.f. formalism is shown to naturally lead to the widely used ensemble-averaged equations for two-phase flows. Galilean-invariant combinations of unclosed terms in the governing equations that need to be modelled are clearly identified. The correspondence between unclosed terms in each statistical representation is established. Hybrid EE–LE computations can benefit from this correspondence, which serves in consistently transferring information from one representation to the other. Advantages and limitations of each statistical representation are identified. The results of this work can also serve as a guiding framework for direct numerical simulations of two-phase flows, which can now be exploited to precisely quantify unclosed terms in the governing equations in the two statistical representations.

The moving layer at the surface of a granular bed sheared by a viscous flow has been investigated experimentally. The fluid and particle velocities have been measured using particle imaging velocimetry (PIV) and particle tracking, respectively, with a technique of matched index of refraction. The mean velocity profiles are found to be parabolic. The models of Bagnold (Phil. Trans. R. Soc. Lond. A, vol. 249, 1956, pp. 235–297) and Leighton & Acrivos (Chem. Engng Sci., vol. 41, 1986, pp. 1377–1384) fail to account for the observations. A simplified model assuming uniform particle concentration provides good agreement close to the threshold.

The relationship between the fluctuating velocity vector and the temperature fluctuation has been examined using direct numerical simulation databases of a turbulent channel flow with passive scalar transport using a constant time-averaged heat flux at each wall for h+ = 180, 395, 640 and 1020 (where h is the channel half-width with the superscript denoting normalization by wall variables) at Prandtl number Pr=0.71. The analogy between spectra corresponding to the kinetic energy and scalar variance is reasonable in both inner and outer regions irrespective of whether the spectra are plotted in terms of kx or kz, the wavenumbers in the streamwise and spanwise directions respectively. Whereas all three velocity fluctuations contribute to the energy spectrum when kx is used, the longitudinal velocity fluctuation is the major contributor when kz is used. The quality of the analogy in the spectral domain is confirmed by visualizations in physical space and reflects differences between spatial organizations in the velocity and scalar fields. The similarity between the spectra corresponding to the enstrophy and scalar dissipation rate is not as good as that between the kinetic energy and scalar variance, emphasizing the prominence of the scalar sheets as the centre of the channel is approached. The ratio R between the characteristic time scales of the velocity and scalar fluctuations is approximately constant over a major part of the channel and independent of h+, when the latter is sufficiently large. This constancy, which is not observed in quantities such as the turbulent Prandtl number, follows from the spectral similarities discussed in this paper and has implications for turbulent heat transport models.

Rotating convection in cylindrical containers is a canonical problem in fluid dynamics, in which a variety of simplifying assumptions have been used in order to allow for low-dimensional models or linear stability analysis from trivial basic states. An aspect of the problem that has received only limited attention is the influence of the centrifugal force, because it makes it difficult or even impossible to implement the aforementioned approaches. In this study, the mutual interplay between the three forces of the problem, Coriolis, gravitational and centrifugal buoyancy, is examined via direct numerical simulation of the Navier–Stokes equations in a parameter regime where the three forces are of comparable strengths in a cylindrical container with the radius equal to the depth so that wall effects are also of order one. Two steady axisymmetric basic states exist in this regime, and the nonlinear dynamics of the solutions bifurcating from them is explored in detail. A variety of bifurcated solutions and several codimension-two bifurcation points acting as organizing centres for the dynamics have been found. A main result is that the flow has simple dynamics for either weak heating or large centrifugal buoyancy. Reducing the strength of centrifugal buoyancy leads to subcritical bifurcations, and as a result linear stability is of limited utility, and direct numerical simulations or laboratory experiments are the only way to establish the connections between the different solutions and their organizing centres, which result from the competition between the three forces. Centrifugal effects primarily lead to the axisymmetrization of the flow and a reduction in the heat flux.

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non-ideal equation of state.

In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

Homogeneous, approximately isotropic turbulence at two Taylor-scale Reynolds numbers, Rλ=50, 190, with a mean transverse temperature gradient is passed through an axisymmetric contraction. The effects of the straining on the velocity field, and on the passive scalar field, are investigated within the contraction as are the effects of releasing the strain in the post-contraction region. Components of the fluctuating velocity and scalar gradient covariance are measured in order to understand their relation to the large-scale anisotropy of the flow. The scale-dependent spectral evolution of the scalar is also determined. A tensor model is constructed to predict the evolution of the fluctuating scalar gradient covariance. The model constants are determined in the post-contraction relaxation region, where the flow geometry does not vary. The model is shown to perform well throughout the flow, even in the contraction in which the geometry varies. Rapid distortion theory is applied to the scalar field in the contraction, and its solutions are compared to the experimental results.

Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynolds-averaged Navier–Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch – the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at near-critical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.

This paper describes an experiment in which a uniformly sheared turbulence was subjected to simultaneous streamwise flow curvature and rotation about the streamwise axis. The distortion of the turbulence is complex but well defined and may serve as a test case for turbulence model development. The uniformly sheared turbulence was developed in a straight wind tunnel and then passed into a curved tunnel section. At the start of the curved section the plane of the mean shear was normal to the plane of curvature so as to create a three-dimensional or ‘out of plane’ curvature configuration. On entering the curved tunnel, the flow developed a streamwise mean vorticity that rotated the mean shear about the tunnel centreline through approximately 70°, so that the shear was nearly in the plane of curvature and oriented so as to have a stabilizing effect on the turbulence. Hot wire measurements of the mean velocity, mean vorticity, mean rate of strain and Reynolds stress anisotropy development along the wind tunnel centreline are reported. The observed effect of the mean shear rotation on the turbulence was to diminish the shear stress in the plane normal to the plane of curvature while generating non-zero values of the shear stress in the plane of curvature. A rotating frame was identified for which the measured mean velocity field took the form of a simple shear flow. The turbulence anisotropy was transformed to this frame to estimate the effects of frame rotation on the structure of sheared turbulence.

Multiple alternating zonal jets observed in the ocean are studied with an idealized quasigeostrophic model of flow in a zonal channel. The jets are maintained by the eddies generated by the imposed, supercritical background flow. The formation, nonlinear dynamics and equilibration of the jets are explained in terms of linear stability arguments and nonlinear self-interactions of the linear eigenmodes. In the proposed mechanism, energy of the background flow is released to the primary instability mode with long meridional and short zonal length scales. This mode undergoes secondary, transverse instability that sets the meridional scale of the emerging multiple zonal jets. This instability channels energy into several weakly damped zonal eigenmodes that amplify the jets. The emerging jets feed back on the instabilities through the partial meridional localization of the most unstable eigenmodes.

Assuming that the sediment flux in the Exner equation can be linearly related to the local bed slope, we establish a one-dimensional model for the bed-load transport of sediment in a coastal-plain depositional system, such as a delta and a continental margin. The domain of this model is defined by two moving boundaries: the shoreline and the alluvial–bedrock transition. These boundaries represent fundamental transitions in surface morphology and sediment transport regime, and their trajectories in time and space define the evolution of the shape of the sedimentary prism. Under the assumptions of fixed bedrock slope and sea level the model admits a closed-form similarity solution for the movements of these boundaries. A mapping of the solution space, relevant to field scales, shows two domains controlled by the relative slopes of the bedrock and fluvial surface: one in which changes in environmental parameters are mainly recorded in the upstream boundary and another in which these changes are mainly recorded in the shoreline. We also find good agreement between the analytical solution and laboratory flume experiments for the movements of the alluvial–bedrock transition and the shoreline.