This paper is devoted to an experimental investigation of receptivity of a laminar swept-wing boundary layer due to scattering of free-stream vortices on localized (in the streamwise direction) surface vibrations. The experiments were conducted under completely controlled disturbance conditions by means of a hot-wire anemometer on a model of a swept wing with a sweep angle of 25°. Both the free-stream vortices and the surface vibrations were generated by disturbance sources; their frequency–wavenumber spectra were measured thoroughly. The free-stream vorticity vectors were directed perpendicular to the incident-flow velocity vector and parallel to the swept-wing-model surface. The linearity of the receptivity mechanism under investigation (in a sense that the corresponding receptivity coefficients are independent of the disturbances amplitudes) has been checked carefully. The main goal of this experiment was to estimate the vibration-vortex receptivity coefficients as functions of the disturbance frequency, spanwise wavenumber and vortex offset parameter. This goal has been attained. Being defined in Fourier space, the obtained receptivity coefficients are independent of the specific surface vibration shape and can be used for verification of various receptivity theories.

A wide range of initial-value problems in fluid mechanics in particular, and in the physical sciences in general, are described by nonlinear partial differential equations. Recourse must often be made to numerical solutions, but a powerful, well-established technique is to solve the problem in terms of similarity variables. A disadvantage of the similarity solution is that it is almost always independent of any specific initial conditions, with the solution to the full differential equation approaching the similarity solution for times $t\gg t_{\ast }$, for some $t_{\ast }$. But what is $t_{\ast }$? In this paper we consider the situation of viscous gravity currents and obtain useful formulae for the time of approach, $\unicode[STIX]{x1D70F}(p)$, for a number of different initial shapes, where $p$ is the percentage disagreement between the radius of the current as determined by the full numerical solution of the governing partial differential equation and the similarity solution normalised by the similarity solution. We show that for any initial shape of volume $V,\unicode[STIX]{x1D70F}\propto 1/(\unicode[STIX]{x1D6FD}V^{1/3}\unicode[STIX]{x1D6FE}_{0}^{8/3}p)$ (as $p\downarrow 0$), where $\unicode[STIX]{x1D6FD}=g\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}/(3\unicode[STIX]{x1D707})$, with $g$ representing the acceleration due to gravity, $\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$ the density difference between the gravity current and the ambient, $\unicode[STIX]{x1D707}$ the dynamic viscosity of the fluid that makes up the gravity current and $\unicode[STIX]{x1D6FE}_{0}$ the initial aspect ratio. This framework can used in many other situations, including where it is not an initial condition (in time) that is studied but one valid for specified values at a special spatial coordinate.

Here we show that weakly nonlinear flexural-gravity wave packets, such as those propagating on the surface of ice-covered waters, admit three-dimensional fully localized solutions that travel with a constant speed without dispersion or dissipation. These solutions, that are formed at the intersection of line-soliton mean-flow tracks, have exponentially decaying tails in all directions and are called dromions in contrast to lumps that decay only algebraically. We derive, by asymptotic expansion and assuming multiple scales for spatial and temporal variations, the three-dimensional weakly nonlinear governing equations that describe the coupled motion of the wavepacket envelope and the underlying mean current. We show that in the limit of long waves and strong flexural rigidity these equations reduce to a system of nonlinear elliptic–hyperbolic partial differential equations similar to the Davey–Stewartson I (DSI) equation, but with major differences in the coefficients. Specifically, and contrary to DSI equations, the elliptic and hyperbolic operators in the flexural-gravity equations are not canonical resulting in complications in analytical considerations. Furthermore, standard computational techniques encounter difficulties in obtaining the dromion solution to these equations owing to the presence of a spatial hyperbolic operator whose solution does not decay at infinity. Here, we present a direct (iterative) numerical scheme that uses pseudo-spectral expansion and pseudo-time integration to find the dromion solution to the flexural-gravity wave equation. Details of this direct simulation technique are discussed and properties of the solution are elaborated through an illustrative case study. Dromions may play an important role in transporting energy over the ice cover in the Arctic, resulting in the ice breaking far away from the ice edge, and also posing danger to icebreaker ships. In fact we found that, contrary to DSI dromions that only exist in water depths of less than 5 mm, flexural-gravity dromions exist for a broad range of ice thicknesses and water depths including values that may be realized in polar oceans.

In the context of an Eulerian fluid description, we investigate the dynamics of a shock wave that is driven by the steady impulsively initiated motion of a two-dimensional planar piston with small corrugations superimposed on its surface. This problem was originally solved by Freeman (Proc. Royal Soc. A, vol. 228, 1955, pp. 341–362), who showed that piston-driven shocks are unconditionally stable when the fluid medium through which they propagate is an ideal gas. Here, we generalize Freeman’s mathematical framework to account for a fluid characterized by an arbitrary equation of state. We find that a sufficient condition for shock stability is , where is the D’yakov parameter and is a critical value less than unity. For values of within this range, linear perturbations imparted to the front by the piston at time attenuate asymptotically as . Outside of this range, the temporal behaviour of perturbations is more difficult to determine and further analysis is required to assess the stability of a shock front under such circumstances. As a benchmark of the main conclusions of this paper, we compare our generalized expression for the linearized shock-ripple amplitude with an independent Bessel-series solution derived by Zaidel’ (J. Appl. Math. Mech., vol. 24, 1960, pp. 316–327) and find excellent agreement.

The numerical simulation of gravity-driven flow of smooth inelastic hard disks through a channel, dubbed ‘granular’ Poiseuille flow, is conducted using event-driven techniques. We find that the variation of the mass-flow rate ($Q$) with Knudsen number ($Kn$) can be non-monotonic in the elastic limit (i.e. the restitution coefficient $e_{n}\rightarrow 1$) in channels with very smooth walls. The Knudsen-minimum effect (i.e. the minimum flow rate occurring at $Kn\sim O(1)$ for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with $e_{n}<0.99$, irrespective of the value of the wall roughness. Another rarefaction phenomenon, the bimodality of the temperature profile, with a local minimum ($T_{\mathit{min}}$) at the channel centerline and two symmetric maxima ($T_{\mathit{max}}$) away from the centerline, is also studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality (i.e. the ‘excess’ temperature, ${\rm\Delta}T=(T_{\mathit{max}}/T_{\mathit{min}}-1)\neq 0$) near the continuum limit ($Kn\sim 0$), but the rarefaction being its origin (as in the molecular gas) holds beyond $Kn\sim O(0.1)$. The dependence of the excess temperature ${\rm\Delta}T$ on the restitution coefficient is compared with the predictions of a kinetic model, with reasonable agreement in the appropriate limit. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both the mass-flow rate and the temperature bimodality on $Kn$ and $e_{n}$ in this flow. The validity of the Navier–Stokes-order hydrodynamics for granular Poiseuille flow is discussed with reference to the prediction of bimodal temperature profiles and related surrogates.

A time-stepping numerical model of uniform circular orbital flow around a cylinder provides results which are compared with the steady-state predictions of a boundary-layer solution by Riley. At small amplitudes of motion excellent agreement is found in most respects, but in the numerical model the outer recirculating flow and related components of loading do not reach a steady state after any finite time. At a Stokes parameter β of 500, the boundary-layer approach remains reasonably accurate for amplitudes of motion up to about 8 % of the cylinder diameter; for amplitudes up to twice this at the same value of β the flow remains largely attached. The strength of the outer recirculating flow is enhanced by nonlinear interactions, but the computed nonlinear loading exceeds that observed in experiments. Flow visualization shows a three-dimensional structure in the flow, and it is argued that this has an important effect on the loading that cannot yet be predicted. A computed force component at a frequency of about 30 % of that of the ambient flow is related to the retrogressive motion of vortex structures around the cylinder.

The influence of a cube-based canopy on coherent structures of the flow was investigated in a high Reynolds number boundary layer (thickness $\unicode[STIX]{x1D6FF}\sim 30\,000$ wall units). Wind tunnel experiments were conducted considering wall configurations that represent three idealised urban terrains. Stereoscopic particle image velocimetry was employed using a large field of view in a streamwise–spanwise plane ($0.55\unicode[STIX]{x1D6FF}\times 0.5\unicode[STIX]{x1D6FF}$) combined to two-point hot-wire measurements. The analysis of the flow within the inertial layer highlights the independence of its characteristics from the wall configuration. The population of coherent structures is in agreement with that of smooth-wall boundary layers, i.e. consisting of large- and very-large-scale motions, sweeps and ejections, as well as smaller-scale vortical structures. The characteristics of vortices appear to be independent of the roughness configuration while their spatial distribution is closely linked to large meandering motions of the boundary layer. The canopy geometry only significantly impacts the wall-normal exchanges within the roughness sublayer. Bi-dimensional spectral analysis demonstrates that wall-normal velocity fluctuations are constrained by the presence of the canopy for the densest investigated configurations. This threshold in plan area density above which large scales from the overlying boundary layer can penetrate the roughness sublayer is consistent with the change of the flow regime reported in the literature and constitutes a major difference with flows over vegetation canopies.

This paper contains temporally and spatially resolved flow visualization and DPIV measurements characterizing the frequency–amplitude response and three-dimensional vortex structure of a circular cylinder mounted like an inverted pendulum. Two circular cylinders were examined in this investigation. Both were 2.54 cm in diameter and ~140 cm long with low mass ratios, m* = 0.65 and 1.90, and mass–damping ratios, m*ζ = 0.038 and 0.103, respectively. Frequency–amplitude response analysis was done with the lighter cylinder while detailed wake structure visualization and measurements were done using the slightly higher-mass-ratio cylinder. Experiments were conducted over the Reynolds number range 1900≤Re≤6800 corresponding to a reduced velocity range of 3.7 ≤ U* ≤ 9.6. Detailed examination of the upper branch of the synchronization regime permitted, for the first time, the identification of short-time deviations in cylinder oscillation and vortex-shedding frequencies that give rise to beating behaviour. That is, while long-time averages of cylinder oscillation and vortex-shedding frequencies are identical, i.e. synchronized, it is shown that there is a slight mismatch between these frequencies over much shorter periods when the cylinder exhibits quasi-periodic beating. Data are also presented which show that vortex strength is also modulated from one cylinder oscillation to the next. Physical arguments are presented to explain both the origins of beating as well as why the quasi-periodicity of the beating envelopes becomes irregular; it is believed that this result may be generalized to a broader class of fluid–structure interactions. In addition, observations of strong vertical flows associated with the Kármán vortices developing 2–3 diameters downstream of the cylinder are presented. It is hypothesized that these three-dimensionalities result from both the inverted pendulum motion as well as free-surface effects.

Transonic high-Reynolds-number flows through channels which are so narrow that the classical boundary-layer approach fails locally are considered in the presence of a weak stationary normal shock. As a consequence, the properties of the inviscid core and the viscosity-dominated boundary-layer region can no longer be determined in subsequent steps but have to be calculated simultaneously in a small interaction region. Under the requirement that the core-region flow should be considered to be one-dimensional to the leading order the resulting problem of shock–boundary-layer interaction is formulated by the means of matched asymptotic expansions for laminar flows of dense gases (Bethe–Zel'dovich–Thompson, or BZT, fluids). Such fluids have the distinguishing feature that the fundamental derivative of gas dynamics can become negative or even change sign under the thermodynamic conditions to be considered. The regularizing properties of the mechanism of viscous–inviscid interactions on the different anomalous shock forms possible in the flow of dense gases with mixed nonlinearity, namely rarefaction, sonic, double-sonic and split shocks, will be discussed. To this end we show the consistency of the resulting internal-shock profiles because of strong shock–boundary-layer interaction with a generalized shock admissibility criterion formulated for the case of purely inviscid flows. Representative solutions for the internal-shock structures are presented, and the importance of such flow phenomena in technical applications in the near future are shortly discussed by considering estimates of the actual dimensions of the interaction region for a specific representative situation in which the BZT fluid PP10 (C13F22) has been selected.

Stratified cocurrent flow of air and water was studied experimentally in a 5 cm diameter horizontal pipe. The velocity in the liquid phase was measured using planar particle image velocimetry, and the instantaneous interfacial profile was recorded using a separate camera. The resulting velocity fields extended from the pipe wall to the wavy interface. The principal aims of the study were to investigate the laminar–turbulent transition of the liquid phase in stratified gas–liquid flow, and to explore the interaction between the transition process and the interfacial waves. The boundaries of transition were determined in both the smooth and the wavy region. The occurrence of waves had the effect of increasing the Reynolds numbers at the end of transition. On the other hand, the transition to turbulence caused a change from the ‘2D small-amplitude’ to the ‘3D small-amplitude’ wave pattern, which were seen to correspond to the capillary–gravity and gravity–capillary solutions of the dispersion relationship respectively. In light of this, the flowmap of the wavy region was recast into Weber number–Froude number coordinates, which provided a physical interpretation of the interaction between the developing turbulence and the changing wave patterns.

The motion of a spherical particle suspended in an incompressible Newtonian fluid flowing longitudinally between hexagonally arranged circular cylinders has been numerically analysed by a finite-element method in the Stokes flow regime. The results are applied to study the diffusive and convective transport of spherical solutes across the vascular endothelial surface glycocalyx, based on the quasi-periodic ultrastructural model. The obtained values of diffusive permeability and reflection coefficient of the solutes show a reasonable agreement with experimental observations, and conform to the hypothesis that the endothelial surface glycocalyx forms the primary size selective structure to solutes in microvascular permeability.

We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.

This paper is focused on the investigation of vortex rings evolving in a tube. A new theoretical model for a confined axisymmetric vortex ring is developed. The predictions of this model are shown to be in agreement with available experimental data and numerical simulations. The model combines the viscous vortex ring model, developed by Kaplanski & Rudi (Phys. Fluids, vol. 17, 2005, 087101), with Brasseur’s (PhD thesis, Stanford University) approach to deriving a wall-induced streamfunction correction. Using the power-law assumption for the time variation of the viscous length of the vortex ring, the time variations of the main integral characteristics, circulation, kinetic energy and translational velocity are obtained. Direct numerical simulation (DNS) is used to test the range of applicability of the model and to investigate new physical features of confined vortex rings recently reported in the experimental study by Stewart et al. (Exp. Fluids, vol. 53, 2012, pp. 163–171). The model is shown to lead to a very good approximation of the spatial distribution of the Stokes streamfunction, obtained by DNS. The vortex signature and the time evolution of the energy of the vortex are also accurately predicted by the model. A procedure for fitting the model with realistic vortex rings, obtained by DNS, is suggested. This opens the way to using the model for practical engineering applications.