An experimental analysis of the vortex-induced vibrations of a hanging string with variable tension along its length is presented in this paper. It is shown that standing waves develop along the hanging string. First, the evolution of the Strouhal number $\mathit{St}$ with the Reynolds number $\mathit{Re}$ follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers ( $32\lt \mathit{Re}\lt 700$ ). Second, the extracted mode shapes are self-similar: a rescaling of the spanwise coordinate by a self-similarity coefficient allows all of them to collapse onto a unique function. The self-similar behaviour of the spatial distribution of the vibrations along the hanging string is then explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. This linear stability analysis finally provides an accurate description of the mode shapes and of the evolution of the self-similarity coefficient with the flow speed.

We present a depth-integrated equation for the mechanics of propagation of low-frequency hydroacoustic waves due to a sudden bottom displacement associated with earthquakes. The model equation can be used for numerical prediction in large-scale domains, overcoming the computational difficulties of three-dimensional models and so creating a solid base for tsunami early warning systems.

Miscible thermals are formed by instantaneously releasing a finite volume of buoyant fluid into stagnant ambient. Their subsequent motion is then driven by the buoyancy convection. The gross characteristics (e.g. overall size and velocity) of a thermal have been well studied and reported to be self-similar. However, there have been few studies concerning the internal structure. Here, turbulent miscible thermals (with initial density excess of 5 % and Reynolds number around 2100) have been investigated experimentally through a large number of realizations. The vorticity and density fields were quantified separately by particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques. Ensemble-averaged data of the transient development of the miscible thermals are presented. Major outcomes include: (i) validating Turner’s assumption of constant circulation within a buoyant vortex ring; (ii) measuring the vorticity and density distributions within the miscible thermal; (iii) quantifying the effect of baroclinicity on the generation and destruction of vorticity within the thermal; and (iv) identifying the significantly slower decay rate of the peak density as compared to the mean.

Direct numerical simulations are used to investigate potential enstrophy in stratified turbulence with small Froude numbers, large Reynolds numbers, and buoyancy Reynolds numbers ( $R{e}_{b} $ ) both smaller and larger than unity. We investigate the conditions under which the potential enstrophy, which is a quartic quantity in the flow variables, can be approximated by its quadratic terms, as is often done in geophysical fluid dynamics. We show that at large scales, the quadratic fraction of the potential enstrophy is determined by $R{e}_{b} $ . The quadratic part dominates for small $R{e}_{b} $ , i.e. in the viscously coupled regime of stratified turbulence, but not when $R{e}_{b} \gtrsim 1$ . The breakdown of the quadratic approximation is consistent with the development of Kelvin–Helmholtz instabilities, which are frequently observed to grow on the layerwise structure of stratified turbulence when $R{e}_{b} $ is not too small.

We investigate the optimal morphologies for fast and efficient anguilliform swimmers at intermediate Reynolds numbers, by combining an evolution strategy with three-dimensional viscous vortex methods. We show that anguilliform swimmer shapes enable the trapping and subsequent acceleration of regions of fluid transported along the entire body by the midline travelling wave. A sensitivity analysis of the optimal morphological traits identifies that the width thickness in the anterior of the body and the height of the caudal fin are critical factors for both speed and efficiency. The fastest swimmer without a caudal fin, however, still retains 80 % of its speed, showing that the entire body is used to generate thrust. The optimal shapes share several features with naturally occurring morphologies, but their overall appearances differ. This demonstrates that engineered swimmers can outperform biomimetic swimmers for the criteria considered here.

We present a theoretical and experimental study of viscous gravity currents introduced at the surface of a denser inviscid fluid layer of finite depth inside a vertical Hele-Shaw cell. Initially, the viscous fluid floats on the inviscid fluid, forming a self-similar, buoyancy-driven current resisted predominantly by the viscous stresses due to shear across the width of the cell. Once the viscous current contacts the base of the cell, the flow can be considered in two regions: a grounded region in which the current lies in full contact with the base; and a floating region. The subsequent advance of the grounding line separating these regions is shown to be controlled by the thickening of the current associated with balancing the local shear stresses. An understanding of the flow transitions is developed using asymptotic and numerical analysis of a model based on lubrication theory.

A novel method to create a discontinuous gaseous interface with a minimum-surface feature by the soap film technique is developed for three-dimensional (3D) Richtmyer–Meshkov instability (RMI) studies. The interface formed is free of supporting mesh and the initial condition can be well controlled. Five air/SF6 interfaces with different amplitude are realized in shock-tube experiments. Time-resolved schlieren and planar Mie-scattering photography are employed to capture the motion of the shocked interface. It is found that the instability at the linear stage in the symmetry plane grows much slower than the predictions of previous two-dimensional (2D) impulsive models, which is ascribed to the opposite principal curvatures of the minimum surface. The 2D impulsive model is extended to describe the general 3D RMI. A quantitative analysis reveals a good agreement between experiments and the extended linear model for all the configurations including both the 2D and 3D RMIs at their early stages. An empirical model that combines the early linear growth with the late-time nonlinear growth is also proposed for the whole evolution process of the present configuration.

The halting scale of the inverse energy cascade and the partition between kinetic and potential energy are considered for the case of forced quasigeostrophic turbulence in the regime of intermediate Rossby deformation length, for which the deformation length is comparable to the energy-containing scales of the flow. Phenomenological estimates for the halting scale and equilibrated energy of the forced–dissipative system with a simple representation of large-scale thermal damping are tested against numerical integrations and are found to poorly describe the numerically obtained dependence on damping coefficient; a modified scaling law is proposed that more accurately describes the dependence. The scale-selective nature of the damping leads to a large-scale spectral bottleneck that steepens the energy spectrum, consistent with previous studies of hypodiffusive dissipation. It is found that, across the parameter range considered, the blocking is largely insensitive to the ratio of deformation radius to the energy-containing scales.

Flow through axisymmetric and eccentric sinuous stenoses is investigated numerically, for Reynolds numbers up to 400. The eccentricity consists of an offset of the stenosis throat. A range of stenosis eccentricity is tested; the wake flow is found to be highly sensitive to small eccentricities in the stenosis geometry, even with stenosis offsets of the order of the machining precision of experimental test-sections. Comparisons are made between the numerically simulated flow through stenoses with small eccentricities and results from the literature of non-axisymmetric flows through nominally axisymmetric geometries. The effect of distortion to the inlet Poiseuille velocity profile is also investigated and found to have a significantly less severe effect on the downstream wake flow than geometric eccentricity.

We conduct a series of laboratory experiments to study the mixing of an initially linear stratification in turbulent Taylor–Couette flow. We vary the inner radius, ${R}_{1} $ , and rotation rate, $\Omega $ , relative to the fixed outer cylinder, of radius ${R}_{2} $ , as well as the initial buoyancy frequency ${N}_{0} = \sqrt{(- g/ \rho )\partial \rho / \partial z} $ . We find that a linear stratification spontaneously splits into a series of layers and interfaces. The characteristic height of these layers is proportional to ${U}_{H} / {N}_{0} $ , where ${U}_{H} = \sqrt{{R}_{1} { \mathrm{\Delta} }_{R} } \Omega $ is a horizontal velocity scale, with ${ \mathrm{\Delta} }_{R} = {R}_{2} - {R}_{1} $ the gap width of the annulus. The buoyancy flux through these layers matches the equivalent flux through a two-layer stratification, independently of the height or number of layers. For a strongly stratified flow, the flux tends to an asymptotic constant value, even when multiple layers are present, consistent with Woods et al. (J. Fluid Mech., vol. 663, 2010, pp. 347–357). For smaller stratification the flux increases, reaching a maximum just before the layers disappear due to overturning of the interfaces.

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Voronoï analysis enables us to distinguish quantitatively between two typical preferential clustering configurations: a regular lattice arrangement and irregular clustering. The bubble data are obtained from direct numerical simulations using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio $\chi $ , plays a significant role in determining which type of clustering is realized: nearly spherical bubbles form a regular lattice arrangement, while more deformed bubbles show irregular clustering. Remarkably, this criterion for the clustering morphology holds for different diameters of the bubbles, surface tensions and viscosities of the liquid in the studied parameter regime. The mechanism of this clustering behaviour is most likely connected to the amount of vorticity generated at the bubble surfaces.

The hydrodynamic stability of plane Poiseuille flow of superfluid is studied using modal and non-modal analysis. Two modes of instability are predicted, in normal mode stability analysis of the normal fluid, one caused by viscosity similar to the classical mode and another due to mutual friction between superfluid and normal fluid. The mutual friction mode occurs at high wavenumbers, which are stable wavenumbers in classical plane Poiseuille flow. A high superfluid vortex line density alone is not enough to induce instability in normal fluid; a localization of vortex lines is shown to play a major role. The extent of vortex line concentration required to cause instability depends on the density itself. Non-modal instability analysis shows that oblique waves are stronger than streamwise waves, unlike the scenario in classical plane Poiseuille flow.

At finite Dukhin numbers, where Smoluchowski’s formula is inapplicable to thin-double-layer electrophoresis, the mobility of non-spherical particles is generally anisotropic. We consider bodies of revolution of otherwise arbitrary shape, where a uniformly applied electric field results in a rectilinear motion in the plane spanned by the field direction and the particle symmetry axis, as well as (for particles lacking fore–aft symmetry) rigid-body rotation about an axis perpendicular to that plane. Focusing upon slender particles, where the ratio $\epsilon $ of cross-sectional and longitudinal scales is asymptotically small, the translational and rotational mobilities are obtained as quadratures which depend upon the lengthwise distribution of the scaled cross-sectional width and the force densities associated with rigid-body motion. These mobility expressions approach finite limits as $\epsilon \rightarrow 0$ , yielding closed-form expressions for specific particle geometries.

A Janus swimmer is any force-free, torque-free organism, particle or micro-robot operating at low Reynolds numbers and having contiguous regions of its boundary on which different boundary conditions are in play. In this paper we study a ‘slip–stick’ Janus swimmer theoretically within a two-dimensional model. The boundary of the swimmer is split into two zones: its motion is driven by an imposed tangential stress on a portion of the boundary with the complement taken to be a no-slip surface. The Stokes flow generated by the swimmer, and its swimming speed, are determined in closed analytical form as a function of the angle over which the stress actuation is active.

Simple stochastic models and direct nonlinear numerical simulations of three-dimensional internal waves are combined in order to understand the strong horizontal particle dispersion at second-order in wave amplitude that arises when small-amplitude internal waves are exposed to weak dissipation. This is contrasted with the well-known results for perfectly inviscid internal waves, in which such dispersion arises only at fourth-order in wave amplitude.

High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations ${u}^{\prime } $ . Prior work has shown that the variance of ${u}^{\prime } $ exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the $2p$ -order moments, raised to the power $1/ p, $ also follow logarithmic behaviour according to $\langle \mathop{({u}^{\prime + } ){}^{2p} \rangle }\nolimits ^{1/ p} = {B}_{p} - {A}_{p} \ln (z/ \delta )$ , where ${u}^{\prime + } $ is the velocity fluctuation normalized by the friction velocity, $\delta $ is an outer length scale and ${B}_{p} $ are non-universal constants. The slopes ${A}_{p} $ in the logarithmic region appear quite insensitive to Reynolds number, consistent with universal behaviour for wall-bounded flows. The slopes differ from predictions that assume Gaussian statistics, and instead are consistent with sub-Gaussian behaviour.

The stabilization of a swept-wing boundary layer by distributed surface roughness elements is studied by performing direct numerical simulations. The configuration resembles experiments studied by Saric and coworkers at Arizona State University, who employed this control method in order to delay transition. An array of cylindrical roughness elements are placed near the leading edge to excite subcritical cross-flow modes. Subcritical refers to the modes that are not critical with respect to transition. Their amplification to nonlinear amplitudes modifies the base flow such that the most unstable cross-flow mode and secondary instabilities are damped, resulting in downstream shift of the transition location. The experiments by Saric and coworkers were performed at low levels of free stream turbulence, and the boundary layer was therefore dominated by stationary cross-flow disturbances. Here, we consider a more complex disturbance field, which comprises both steady and unsteady instabilities of similar amplitudes. It is demonstrated that the control is robust with respect to complex disturbance fields as transition is shifted from 45 to 65 % chord.

We investigate numerically, in spherical geometry, the interaction of stratification with precession. Both stable stratification and unstable stratification are studied. In the parameter regime we are concerned with, stable stratification suppresses the precessional instability, whereas unstable stratification and precession can either stabilize or destabilize each other at different precession rates.

In this paper we study the self-propulsion of a dumbbell micro-robot submerged in a viscous fluid. The micro-robot consists of two rigid spherical beads connected by a rod or a spring; the rod/spring length changes periodically. The constant density of each sphere differs from the density of the fluid, while the whole micro-robot has neutral buoyancy. An effective oscillating gravity field is created via rigid-body oscillations of the fluid. Our calculations show that the micro-robot undertakes both translational and rotational motion. Using an asymptotic procedure containing a two-time method and a distinguished limit, we obtain analytic expressions for the averaged self-propulsion velocity and averaged angular velocity. The important special case of zero angular velocity represents rectilinear self-propulsion with constant velocity. In particular, we have shown that: (a) no unidirectional oscillations of a fluid result in self-propulsion; and (b) for the oscillations of a fluid in two directions rectilinear motion of a micro-robot can be achieved.

The breakup of droplets due to creeping motion in a confined microchannel geometry is studied using three-dimensional numerical simulations. Analogously to unconfined droplets, there exist two distinct breakup phases: (i) a quasi-steady droplet deformation driven by the externally applied flow; and (ii) a surface-tension-driven three-dimensional rapid pinching that is independent of the externally applied flow. In the first phase, the droplet relaxes back to its original shape if the externally applied flow stops; if the second phase is reached, the droplet will always break. Also analogously to unconfined droplets, there exist two distinct critical conditions: (i) one that determines whether the droplet reaches the second phase and breaks, or it reaches a steady shape and does not break; and (ii) one that determines when the rapid autonomous pinching starts. We analyse the second phase using stop–flow simulations, which reveal that the mechanism responsible for the autonomous breakup is similar to the end-pinching mechanism for unconfined droplets reported in the literature: the rapid pinching starts when, in the channel mid-plane, the curvature at the neck becomes larger than the curvature everywhere else. The same critical condition is observed in simulations in which we do not stop the flow: the breakup dynamics and the neck thickness corresponding to the crossover of curvatures are similar in both cases. This critical neck thickness depends strongly on the aspect ratio, and, unlike unconfined flows, depends only weakly on the capillary number and the viscosity contrast between the fluids inside and outside the droplet.