We describe an investigation of the effects of non-equilibrium thermochemistry on the interaction between a weak oblique shock and the strong bow shock formed by a blunt body in hypersonic flow. This type of shock-on-shock interaction, also known as an Edney type IV interaction, causes locally intense enhancement of the surface heat transfer rate. A supersonic jet is formed by the nonlinear interaction that occurs between the two shock waves and elevated heat transfer rates and surface pressures are produced by the impingement of the supersonic jet on the body. The current paper is motivated by previous studies suggesting that real gas effects would significantly increase the severity of the phenomenon.

Experiments are described in which a free-piston shock tunnel is used to produce shock interaction flows with significant gas dissociation. Surprisingly, the data that are obtained show no significant stagnation enthalpy dependence of the ratio of the peak heat transfer rates with and without shock interaction, in contrast to existing belief. The geometry investigated is the nominally two-dimensional flow about a cylinder with coplanar impinging shock wave. Holographic interferometry is used to visualize the flow field and to quantify increases in the stagnation density caused by shock interaction. Time-resolved heat transfer measurements are obtained from surface junction thermocouples about the model forebody.

An improved model is developed to elucidate the finite-rate thermochemical processes occurring in the interaction region. It is shown that severe heat transfer intensification is a result of a jet shock structure that minimizes the entropy rise of the supersonic jet fluid whereas strong thermochemical effects are promoted by conditions that maximize the entropy rise (and hence temperature). This dichotomy underlies the smaller than anticipated influence of real gas effects on the heat transfer intensification. The model accurately predicts the measured heat transfer rates.

Improved understanding of the influence of real gas effects on the shock interaction phenomenon reduces a significant element of risk in the design of hypersonic vehicles. The peak heat transfer rate for the Edney type IV interaction is shown to be well-correlated, in the weak impinging shock regime, by an expression of the form $(\skew1\hat q \,{-}\, 1) \,{\approx}\, 1 \,{+}\, \phi_0 (M_\infty-1)^{\phi_1}\delta_1^{\phi_2}$ for use in practical design calculations.

A systematic study has been undertaken to quantify the effect of jet temperature on the noise radiated by subsonic jets. Nozzles of different diameters were tested to uncover the effects of Reynolds number. All the tests were carried out at Boeing's Low Speed Aeroacoustic Facility, with simultaneous measurement of thrust and noise. It is concluded that the change in spectral shape at high jet temperatures, normally attributed to the contribution from dipoles, is due to Reynolds number effects and not dipoles. This effect has not been identified before. A critical value of the Reynolds number that would need to be maintained to avoid the effects associated with low Reynolds number has been estimated to be ${\sim}$400 000. It is well-known that large-scale structures are the dominant generators of noise in the peak radiation direction for high-speed jets. Experimental evidence is presented that shows the spectral shape at angles close to the jet axis from unheated low subsonic jets to be the same as from heated supersonic jets. A possible mechanism for the observed trend is proposed. When a subsonic jet is heated with the Mach number held constant, there is a broadening of the angular sector in which peak radiation occurs. Furthermore, there is a broadening of the spectral peak. Similar trends have been observed at supersonic Mach numbers. The spectral shapes in the forward quadrant and in the near-normal angles from unheated and heated subsonic jets also conform to the universal shape obtained from supersonic jet data. Just as for unheated jets, the peak frequency at angles close to the jet axis is independent of jet velocity as long as the acoustic Mach number is less than unity. The extensive database generated in the current test programme is intended to provide test cases with high-quality data that could be used for the evaluation of theoretical/semi-theoretical jet noise prediction methodologies.

Oceanic observations indicate that abyssal mixing tends to be localized to regions of rough topography. How localized mixing interacts with the ambient fluid in a stratified, rotating system is an open question. To gain insight into this complicated process laboratory experiments are used to explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a single vertically oscillating horizontal bar of finite horizontal extent, located at mid-depth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady-state height and collapses into the interior. The mixed-layer thickness, $h_m\,{\sim}\,\gamma ({\omega}/{N})^{1/2}$, is spatially uniform and independent of the Coriolis frequency $f$. $N$ is the initial buoyancy frequency, $\omega$ is the bar oscillation frequency, and $\gamma\,{\approx}\,1$ cm is an empirical constant determined by the bar geometry. Surprisingly, the export of mixed fluid does not occur as a boundary current along the tank perimeter. Rather, mixed fluid intrudes directly into the interior as a radial front of uniform height, advancing with a speed comparable to a gravity current. The volume of mixed fluid grows linearly with time, $V\,{\propto}\,({N}/{f})^{3/2}h_m^3 \textit{ft}$, and is independent of the lateral extent of the mixing bar. Entrainment into the turbulent zone occurs principally through horizontal flows at the level of the mixing that appear to eliminate export by a geostrophic boundary flow. The circulation patterns suggest a model of unmixed fluid laterally entrained at velocity $u_e \,{\sim}\,Nh_m $ into the open sides of a turbulent zone with height $h_{m}$ and a length, perpendicular to the boundary, proportional to $L_f \,{\equiv}\,\gamma ({\omega}/{f})^{1/2}$. Here $L_{f}$ is an equilibrium length scale associated with rotational control of bar-generated turbulence. The model flux of exported mixed fluid $Q\,{\sim}\,h_m L_f u_e$ is constant and in agreement with the experiments.

We show that the periodic boundary conditions typically applied in numerical simulations of vortex dynamics can lead to significantly incorrect results even when the vortex cores are small compared to the computational domain. This is demonstrated for two previously studied flows which capture significant flow physics: (i) an isolated vortex embedded in fine-scale turbulence; (ii) two antiparallel vortices of unequal strength undergoing reconnection. In case (i), periodicity, when invoked, results in strong, unphysical turbulence growth leading to vortex core transition, whereas the vortex remains totally intact during its interaction with the turbulence when periodicity is not invoked. In case (ii), the vortex interaction, including reconnection, is significantly distorted. These differences are due to the artificial zero circulation constraint, inherent in periodic simulations.

We reconstruct a kinematically admissible (volume-preserving) three-dimensional velocity field corresponding to the stationary helical vortex (SHV) mode which is observed in the Taylor–Couette–Poiseuille (TCP) system with a ratio of inner to outer cylinder radii of 0.5 and a length to annulus gap ratio of 16, starting from experimental data obtained via magnetic resonance imaging (MRI) for $\Rey \,{=}\, 11.14$ and $\Ta^{1/2} \,{=}\, 170$ in water. The goal of the present work is to provide a complete kinematic representation of a strongly nonlinear duct flow that is of importance in the fields of mixing and segregation, as well as in the study of the kinematic structure of three-dimensional flows. By a judicious choice of a set of global basis functions that exploit the helical symmetry of SHV, an analytical approximation of the streamfunction is obtained despite the coarse MRI data and the non-uniform distribution of measurement error. This approximation is given in terms of a truncated series of smooth functions that converges weakly in L$_2$, and the reconstruction method is directly applicable to three-dimensional incompressible flows that possess a continuous volume-preserving symmetry. The SHV flow structure consists of a pair of asymmetric counter-rotating helical cells in a double helix structure, foliated with invariant helically symmetric surfaces containing fibre-like fluid particle orbits wrapped around the inner cylinder. Imposing general topological constraints, juxtaposing SHV with neighbouring hydrodynamic modes such as the propagating Taylor vortex flow and direct numerical simulation help corroborate the validity of the reconstruction of the SHV flow field. The kinematically admissible flow field obeys the Navier–Stokes equations with 10% accuracy, which is consistent with experimental error, and has the same flow portrait as the numerically computed flow. Global analysis of the SHV mode indicates that it corresponds to a minimum in dissipation and mixing in comparison with a wide class of perturbed neighbouring modes; hence it is a candidate for the study of particle segregation. To our knowledge, the present study reports the first synthesis of a physically realizable complex open flow that can be represented by an integrable Hamiltonian system starting from point-wise experimental data and using solely kinematic constraints.

We investigate the response of a rotating stratified fluid to the local spin-up by a small rotating disk of radius $R$, with Rossby number $\hbox{\it Ro}\,{=}\,\omega_d/2\Omega$ around unity where $\omega_d$ is the rotating-disk vorticity and $\Omega$ the background rotation frequency. During an initial stage $\tau_{su}\,{=}\,O({E_k}^{-1/2} N^{-1})$ with Ekman number, $E_k\,{=}\,\nu/\Omega R^2$ ($\nu$ the kinematic viscosity and $N$ the buoyancy frequency), fluid ejected by the Ekman boundary layer mixes with ambient fluid, and forms an intermediate-density intrusion the radial spreading of which is arrested by background rotation. This flow resembles a concentric source–sink configuration with the sink represented by the Ekman layer above the disk and the source by the ejected fluid, which, by conservation of potential vorticity, leads to the formation of a cyclonic vortex embedded in an anti-cyclonic ring. In the next stage, the radial and axial diffusion of momentum dominate the flow evolution, and the flow is characterized by a balance between viscous dissipation of momentum and the amount of momentum applied by the rotating disk. Vorticity diffusion dominates the flow and smooths out the flow history when $E_k^{-1/2}(f/N)\,{<}\,3$, whereas the initial stage can be recognized as a separate flow stage when $E_k^{-1/2}(f/N)\,{>}\,3$. The stability of the density front is discussed.

We report laboratory and numerical experiments with the convective circulation that develops in a long channel driven by heating and cooling through opposite halves of the horizontal base. The problem is similar to that posed by Stommel (Proc. Natl Acad. Sci. vol. 48, 1962, p. 766) and Rossby (Deep-Sea Res. vol. 12, 1965, p. 9; Tellus vol. 50, 1998, p. 242), where flow forced by a linear temperature variation along the ocean surface or the base of a tank presented a demonstration of the smallness of sinking regions in the meridional overturning circulation of the oceans. In contrast to the previous experiments, we use small aspect ratio, larger Rayleigh numbers, piecewise uniform boundary conditions and an imposed input heat flux. The flow is characterized by a vigorous overturning circulation cell filling the box length and depth. A stable thermocline forms above the cooled base and is advected over the heated part of the base, where it is eroded from below by small-scale three-dimensional convection, forming a ‘convective mixed layer’. At the endwall, the convective mixing is overshadowed by a narrow but turbulent plume rising through the full depth of the box. The return flow along the top of the box is turbulent with large slowly migrating eddies, and occupies approximately a third of the total depth. Theoretical scaling laws give temperature differences, thermocline thickness and velocities that are in good agreement with the experimental data and two-dimensional numerical solutions. The measured and computed density structure is largely similar to the thermocline and abyssal stratification in the oceans.

The influence of viscosity variations on the density-driven instability of two miscible fluids in a vertical Hele-Shaw cell is investigated by means of a linear stability analysis. Dispersion relations are presented for different Rayleigh numbers, viscosity ratios and interfacial thickness parameters of the base concentration profile. The analysis employs the three-dimensional Stokes equations, and the results are compared with those obtained from the variable density and viscosity Hele-Shaw equations. While the growth rate does not depend on which of the two fluids is the more viscous, the maxima of the eigenfunctions are always seen to shift towards the less viscous fluid. For every parameter combination, the dominant instability mode is found to be three-dimensional. With increasing viscosity ratio, the instability is uniformly damped. For a fixed viscosity ratio, both the growth rate and the most unstable wavenumber increase monotonically with the Rayleigh number, until they asymptotically reach a plateau.

Surprising findings are obtained regarding the effects of varying the interface thickness. At higher viscosity ratios the largest growth rates and unstable wavenumbers are observed for intermediate thicknesses. This demonstrates that for variable viscosities thicker interfaces can be more unstable than their thinner counterparts, in contrast to the constant viscosity case. The reason behind this behaviour can be traced to the influence of the gap width on the vertical extent of the perturbation eigenfunctions. For thick interfaces, the eigenfunction can reside almost entirely within the interfacial region. In that way, the perturbation maximum is free to shift towards the less viscous fluid, i.e. into a locally more unstable environment. In contrast, for thin interfaces, the eigenfunction is forced to extend far into the viscous fluid, which leads to an overall stabilization. While the Hele-Shaw analysis also captures this ‘optimal’ growth for intermediate interface thicknesses, the growth rates differ substantially from those obtained from the full Stokes equations. Compared to the Hele-Shaw results, growth rates obtained from the modified Brinkman equation are seen to yield better quantitative agreement with the Stokes results.

In this study, estimates of inhomogeneous integral scales are derived from rapid distortion theory (RDT) for the case of wall-bounded high-Reynolds-number turbulence and from large-eddy simulation (LES) of a neutrally stratified atmospheric boundary layer (ABL). As for any inhomogeneous flow, integral scales in different directions are introduced. Downward integral scales are introduced since they differ from the usual vertical integral scales because of the presence of the wall. The study concentrates on the length scales based on the vertical velocity, which are the most affected by blocking by the wall, which is assumed to be horizontal.

It is shown from RDT that the asymptotic behaviour of the integral length scales for small heights depends crucially on the spectrum power law $-2p$. When $2p>1$ there is always one length scale which does not scale with the distance to the wall $z$. Only the downward integral scale is proportional to $z$ for any $2p$. These results show that the assumption, often made in studies of boundary layers, that all the lengths are proportional to $z$, is not compatible with the assumption of a spectrum decaying according to Kolmogorov's law, but rather with a spectrum following a $-1$ power law. It is an encouraging result since there is now widespread theoretical, experimental and numerical evidence that such a $-1$ power-law subrange exists in the spectra of high-Reynolds-number wall-bounded turbulence, for eddies larger than $z$. The RDT results allow an interpretation of the vertical profiles of the integral length scales computed from the LES outputs: above the third grid point, the vertical profiles of the integral length scales have a linear shape, as expected for high-Reynolds-number turbulence and $2p=1$. Very close to the surface, the upward integral length scales decreases with $z$ because of the fast decay of the spectrum ($2p>2$) from the LES subgrid model.

The longitudinal-to-transverse integral length scale ratio is computed using RDT and LES. This ratio is interpreted as the aspect ratio of elongated near-wall large eddies, which are ubiquitous features of LES of boundary layers in which shear plays an important role in the dynamics. The LES shows that the longitudinal-to-transverse integral length scale ratio is an increasing function of $z$, ranging between 1 and 3, which is of the order of magnitude of the published theoretical value of 3.5. From RDT, the evolution with $z$ of the longitudinal-to-transverse integral length scale ratio means either that the velocity shear $\beta$ decreases with $z$ and the spectral power law $2p$ varies in a non-trivial manner, or if both the RDT and LES are valid that the scale of the large eddies is proportional to $\beta z$ with $\beta$ varying from 1.3 to about 4.

Large-eddy simulations of a subsonic three-dimensional cavity flow with self-sustaining oscillations are carried out for a Reynolds number based on the length of the cavity equal to $7\,{\times}\,10^6$. Meticulous comparisons with available experimental data corresponding to the same configuration demonstrate a high level of accuracy. Special attention is paid to the mixing layer that develops over the cavity and two different zones are identified. The first one is dominated by Kelvin–Helmholtz instability, and the linear as well as quadratic energy transfers leading to the filling of velocity spectra are described. The Kelvin–Helmholtz instability also appears to be forced near the origin of the layer, and it is postulated that the small recirculation bubble located in this area is responsible for the forcing. Downstream of the first zone and up to the vicinity of the aft wall, the layer behaves very similarly to a free mixing layer by exhibiting a linear spreading. An influence of the recirculating flow inside the cavity upon the growth of the layer is nevertheless observed at downstream stations. Analysis of the pressure on the floor of the cavity reveals that the self-sustaining oscillation-related pressure modes (Rossiter modes) are independent of their spanwise location inside the cavity. On the contrary, Rossiter modes exhibit streamwise modulations and it is demonstrated that a very simple two-wave model is able to reproduce the spatial shape of the modes. Nonlinear interactions between Rossiter modes are encountered, as well as nonlinear interactions with low-frequency components. A joint time–frequency analysis shows a temporal modulation of the Rossiter mode levels at similar low frequencies, resulting in a special form of intermittency with competitive energy exchanges between modes.

The dynamic response of an initially spherical capsule subject to different externally imposed flows is examined. The neo-Hookean and Skalak et al. (Biophys. J., vol. 13 (1973), pp. 245–264) constitutive laws are used for the description of the membrane mechanics, assuming negligible bending resistance. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping-flow conditions are assumed to prevail. The capillary number $\varepsilon $ is the basic dimensionless number of the problem, which measures the relative importance of viscous and elastic forces. The boundary-element method is used with bi-cubic B-splines as basis functions in order to discretize the capsule surface by a structured mesh. This guarantees continuity of second derivatives with respect to the position of the Lagrangian particles used for tracking the location of the interface at each time step and improves the accuracy of the method. For simple shear flow and hyperbolic flow, an interval in $\varepsilon $ is identified within which stable equilibrium shapes are obtained. For smaller values of $\varepsilon $, steady shapes are briefly captured, but they soon become unstable owing to the development of compressive tensions in the membrane near the equator that cause the capsule to buckle. The post-buckling state of the capsule is conjectured to exhibit small folds around the equator similar to those reported by Walter et al. Colloid Polymer Sci. Vol. 278 (2001), pp. 123–132 for polysiloxane microcapsules. For large values of $\varepsilon $, beyond the interval of stability, the membrane has two tips along the direction of elongation where the deformation is most severe, and no equilibrium shapes could be identified. For both regions outside the interval of stability, the membrane model is not appropriate and bending resistance is essential to obtain realistic capsule shapes. This pattern persists for the two constitutive laws that were used, with the Skalak et al. law producing a wider stability interval than the neo-Hookean law owing to its strain hardening nature.

Tubeless and open siphons operate without conduits, in the open, supported only by extensional stresses. Here, we demonstrate that the addition of silica nanoparticles in modest concentrations (on the order of 1% by weight) to an aqueous Poly(ethylene oxide) (PEO) solution of a moderately low concentration (0.5% by weight) has a dramatic effect on the power of the siphon as well as on the ability of the siphon to completely clean substrates. These enhanced effects may have a partly fluid mechanical explanation, since they also occur when the siphon is laden with inert sub-millimetre particles (Wang & Joseph, J. Fluid Mech. vol. 480, 2003, p. 119). The extensional properties of PEO solutions are greatly enhanced when they are loaded with silica nanoparticles. The degradation of the PEO solution is suppressed by the addition of silica nanoparticles.

The shape evolution of small droplets attached to a conducting surface and subjected to relatively strong electric fields is studied both experimentally and numerically. The problem is motivated by the phenomena characteristic of the electrospinning of nanofibres. Three different scenarios of droplet shape evolution are distinguished, based on numerical solution of the Stokes equations for perfectly conducting droplets. (i) In sufficiently weak (subcritical) electric fields the droplets are stretched by the electric Maxwell stresses and acquire steady-state shapes where equilibrium is achieved by means of the surface tension. (ii) In stronger (supercritical) electric fields the Maxwell stresses overcome the surface tension, and jetting is initiated from the droplet tip if the static (initial) contact angle of the droplet with the conducting electrode is $\alpha_{s}\,{<}\,0.8\pi $; in this case the jet base acquires a quasi-steady, nearly conical shape with vertical semi-angle $\beta \,{\leq}\, 30^{\circ}$, which is significantly smaller than that of the Taylor cone ($\beta_{T}\,{=}\,49.3^{\circ}$). (iii) In supercritical electric fields acting on droplets with contact angle in the range $0.8\pi \,{<}\,\alpha_{s}\,{<}\,\pi $ there is no jetting and almost the whole droplet jumps off, similar to the gravity or drop-on-demand dripping. The droplet–jet transitional region and the jet region proper are studied in detail for the second case, using the quasi-one-dimensional equations with inertial effects and such additional features as the dielectric properties of the liquid (leaky dielectrics) taken into account. The flow in the transitional and jet region is matched to that in the droplet. By this means, the current–voltage characteristic $I\,{=}\,I(U)$ and the volumetric flow rate $Q$ in electrospun viscous jets are predicted, given the potential difference applied. The predicted dependence $I\,{=}\,I(U)$ is nonlinear due to the convective mechanism of charge redistribution superimposed on the conductive (ohmic) one. For $U\,{=}\,O(10kV)$ and fluid conductivity $\sigma \,{=}\,10^{-4}$ S m$^{-1}$, realistic current values $I\,{=}\,O(10^{2}nA)$ were predicted.