This paper reports results obtained with two-dimensional numerical simulations of viscous incompressible flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities; a so-called double cavity. Based on time series recorded at discrete probe points inside the double cavity, different flow regimes are identified when the Reynolds number and the intercavity distance are varied. The transition from steady to chaotic flow behaviour can in general be summarized as follows: steady (fixed) point, period-1 limit cycle, intermediate regime (including quasi-periodicity) and torus breakdown leading to toroidal chaos. The analysis of the intracavity vorticity reveals a ‘carousel’ pattern, creating a feedback mechanism, that influences the shear-layer oscillations and makes it possible to identify in which regime the flow resides. A relation was found between the ratio of the shear-layer frequency peaks and the number of small intracavity structures observed in the flow field of a given regime. The properties of each regime are determined by the interplay of three characteristic time scales: the turnover time of the large intracavity vortex, the lifetime of the small intracavity vortex structures and the period of the dominant shear-layer oscillations.

A numerical investigation on the stalled flow characteristics of a NACA0021 aerofoil with a sinusoidal wavy leading edge (WLE) at chord-based Reynolds number $Re_{\infty }=1.2\times 10^{5}$ and angle of attack $\unicode[STIX]{x1D6FC}=20^{\circ }$ is presented in this paper. It is observed that laminar separation bubbles (LSBs) form at the trough areas of the WLE in a collocated fashion rather than uniformly/periodically distributed over the span. It is found that the distribution of LSBs and their influence on the aerodynamic forces is strongly dependent on the spanwise domain size of the simulation, i.e. the wavenumber of the WLE used. The creation of a pair of counter-rotating streamwise vortices from the WLE and their evolution as an interface/buffer between the LSBs and the adjacent fully separated shear layers are discussed in detail. The current simulation results confirm that an increased lift and a decreased drag are achieved by using the WLEs compared to the straight leading edge (SLE) case, as observed in previous experiments. Additionally, the WLE cases exhibit a significantly reduced level of unsteady fluctuations in aerodynamic forces at the frequency of periodic vortex shedding. The beneficial aerodynamic characteristics of the WLE cases are attributed to the following three major events observed in the current simulations: (i) the appearance of a large low-pressure zone near the leading edge created by the LSBs; (ii) the reattachment of flow behind the LSBs resulting in a decreased volume of the rear wake; and, (iii) the deterioration of von-Kármán (periodic) vortex shedding due to the breakdown of spanwise coherent structures.

Inviscid, unsteady simulations of the roll up of the start-up vortex issuing from a semi-infinite plate are compared with previous simulations of the viscous flow. The inviscid equations were solved by a lumped-vortex method, the two-dimensional, incompressible Navier–Stokes equations in the vorticity–streamfunction formulation modelled the viscous problem. The purpose is to verify whether the irregular behaviour found by the inviscid solution well approximates the unstable evolution of the viscous spiral vortex in the limit of infinitely large time (or equivalently Reynolds number).

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process.

Two-dimensional direct numerical simulation and Floquet stability analysis have been performed at moderate Keulegan–Carpenter number ($KC$) and low Reynolds number ($Re$) for a square cross-section cylinder with its face normal to the oscillatory flow. Based on the numerical simulations a map of flow regimes is formed and compared to the map of flow around an oscillating circular cylinder by Tatsuno & Bearman (J. Fluid Mech., vol. 211, 1990, pp. 157–182). Two new flow regimes have been observed, namely A$^{\prime }$ and F$^{\prime }$. The regime A$^{\prime }$ found at low $KC$ is characterised by the transverse convection of fluid particles perpendicular to the motion; and the regime F$^{\prime }$ found at high $KC$ shows a quasi-periodic feature with a well-defined secondary period, which is larger than the oscillation period. The Floquet analysis demonstrates that when the two-dimensional flow breaks the reflection symmetry about the axis of oscillation, the quasi-periodic instability and the synchronous instability with the imposed oscillation occur alternately for the square cylinder along the curve of marginal stability. This alternate pattern in instabilities leads to four distinct flow regimes. When compared to the vortex shedding in otherwise unidirectional flow, the two quasi-periodic flow regimes are observed when the oscillation frequency is close to the Strouhal frequency (or to half of it). Both the flow regimes and marginal stability curve shift in the $(Re,KC)$-space compared to the oscillatory flow around a circular cylinder and this shift appears to be consistent with the change in vortex formation time associated with the lower Strouhal frequency of the square cylinder.

High-incidence lift generation via flow reattachment is studied. Different reattachment mechanisms are distinguished, with dynamic manoeuvres and tip vortex downwash being separate mechanisms. We focus on the latter mechanism, which is strictly available to finite wings, and isolate it by considering steadily translating wings. The tip vortex downwash provides a smoother merging of the flow at the trailing edge, thus assisting in establishing a Kutta condition there. This decreases the strength/amount of vorticity shed from the trailing edge, and in turn maintains an effective bound circulation resulting in continued lift generation at high angles of attack. Just below the static lift-stall angle of attack, strong vorticity is shed at the trailing edge indicating an increasingly intermittent reattachment/detachment of the instantaneous flow at mid-span. Above this incidence, the trailing-edge shear layer increases in strength/size representing a negative contribution to the lift and leads to stall. Lastly, we show that the mean-flow topology is equivalent to a vortex pair regardless of the particular physical flow configuration.

Steady methane/air laminar premixed flames stabilised on a cylindrical bluff body subjected to a continuous rotation are analysed using joint direct numerical simulations (DNS) and experiments. DNS are carried out using a 19 species scheme for methane/air combustion and a lumped model to predict the cylinder temperature. Rotation of the cylinder induces a symmetry breaking of the flow, and leads to two distinct flame branches in the wake of the cylinder. DNS are validated against experiments in terms of flame topologies and velocity fields. DNS are then used to analyse flame structures and thermal effects. The location and structure of the two flames are differently modified by rotation and heat transfer: a superadiabatic flame branch stabilises close to the hot cylinder and burns preheated fresh gases while a subadiabatic branch is quenched over a large zone and anchors far downstream of the cylinder. Local flame structures are shown to be controlled to first order by the local enthalpy defect or excess due to heat transfer between the cylinder and the flow. An analysis of the local wall heat flux around the cylinder shows that, for low rotation speeds, the superadiabatic flame branch contributes to wall heat fluxes that considerably exceed typical values found for classical flame/wall interactions. However, for high rotation speeds, fluxes decrease because the cylinder is surrounded by a layer of burned gases that dilute incoming reactants and shield it from the flame.

We simulate shear flow past a stationary monolayer of spherical particles embedded in a flat gas–liquid interface. This problem is relevant to the understanding of the microhydrodynamics of particle-laden interfacial structures, including particle-laden drops, bubbles and foams. The combination of the free-shear condition at the gas–liquid interface and the no-slip condition at the particle surfaces gives rise to a velocity slip at the particle-laden interface. We study the characteristics of the flow near the monolayer, focusing on slip velocity, slip length and interfacial shear stress. Two microstructures are compared: a square array, and a reticulated array mimicking a percolating network of aggregated particles. We demonstrate that the scaling laws for the dependence of the slip length on solid area fraction developed for flow past superhydrophobic microstructured surfaces apply to the case of interfacial particles. The calculated slip lengths are in general smaller that those reported for microstructured superhydrophobic surfaces. This difference, which is due to the significant protrusion of the spherical particles in the liquid, can be accounted for in the case of the square array by an approximate argument. For a given area fraction, the reticulated array yields a larger slip length than the square array. We analyse the hydrodynamic forces acting on the particles, and the corresponding tangential stress exerted by the bulk ‘subphase’.

This paper presents both linear and nonlinear analyses of extreme responses for a multi-body wave energy converter (WEC) in severe sea states. The WEC known as M4 consists of three cylindrical floats with diameters and draft which increase from bow to stern with the larger mid and stern floats having rounded bases so that the overall system has negligible drag effects. The bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion would be damped to absorb power in operational conditions. A range of focussed wave groups representing extreme waves were tested on a scale model without hinge damping, also representing a more general system of interconnected cylindrical floats with multi-mode forcing. Importantly, the analysis reveals a predominantly linear response structure in hinge angle and weakly nonlinear response for the beam bending moment, while effects due to drift forces, expected to be predominantly second order, are not accounted for. There are also complex and violent free-surface effects on the model during the excitation period driven by the main wave group, which generally reduce the overall motion response. Once the main group has moved away, the decaying response in the free-vibration phase decays at a rate very close to that predicted by simple linear radiation damping. Two types of nonlinear harmonic motion are demonstrated. During the free-vibration phase, there are only double and triple frequency Stokes harmonics of the linear motion, captured using a frequency doubling and tripling model. In contrast, during the excitation phase, these harmonics show much more complex behaviour associated with nonlinear fluid loading. Although bound harmonics are visible in the system response, the overall response is remarkably linear until temporary submergence of the central float (‘dunking’) occurs. This provides a strong stabilising effect for angular amplitudes greater than ${\sim}30^{\circ }$ and can be treated as a temporary loss of part of the driving wave as long as submergence continues. With an experimentally and numerically derived response amplitude operator (RAO), we perform a statistical analysis of extreme response for the hinge angle based on wave data at Orkney, well known for its severe wave climate, using the NORA10 wave hindcast. For storms with spectral peak wave periods longer than the RAO peak period, the response is controlled by the steepness of the sea state rather than the wave height. Thus, the system responds very similarly under the most extreme sea states, providing an upper bound for the most probable maximum response, which is reduced significantly in directionally spread waves. The methodology presented here is relevant to other single and multi-body systems including WECs. We also demonstrate a general and potentially important reciprocity result for linear body motion in random seas: the averaged wave history given an extreme system response and the average response history given an extreme wave match in time, with time reversed for one of the signals. This relationship will provide an efficient and robust way of defining a ‘designer wave’, for both experimental testing and computationally intensive computational fluid dynamics (CFD), for a wide range of wave–structure interaction problems.

The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al., J. Fluid Mech., vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS. LS consist of evolving the Langevin equations for pair separation and relative velocity, which is statistically equivalent to solving the classical Fokker–Planck form of the pair PDF equation. Langevin simulations of particle-pair dispersion were performed using three closure forms of the diffusivity – i.e. the one containing the time integral of the Eulerian two-time correlation of the seen fluid relative velocities and the two analytical diffusivity expressions. In the first closure form, the two-time correlation was computed using DNS of forced isotropic turbulence laden with stationary particles. The two analytical closure forms have the advantage that they can be evaluated using a model for the turbulence energy spectrum that closely matched the DNS spectrum. The three diffusivities are analysed to quantify the effects of the approximations made in deriving them. Pair relative-motion statistics obtained from the three sets of Langevin simulations are compared with the results from the DNS of (moving) particle-laden forced isotropic turbulence for $St_{\unicode[STIX]{x1D702}}=10,20,40,80$ and $Re_{\unicode[STIX]{x1D706}}=76,131$. Here, $St_{\unicode[STIX]{x1D702}}$ is the particle Stokes number based on the Kolmogorov time scale and $Re_{\unicode[STIX]{x1D706}}$ is the Taylor micro-scale Reynolds number. Statistics such as the radial distribution function (RDF), the variance and kurtosis of particle-pair relative velocities and the particle collision kernel were computed using both Langevin and DNS runs, and compared. The RDFs from the stochastic runs were in good agreement with those from the DNS. Also computed were the PDFs $\unicode[STIX]{x1D6FA}(U|r)$ and $\unicode[STIX]{x1D6FA}(U_{r}|r)$ of relative velocity $U$ and of the radial component of relative velocity $U_{r}$ respectively, both PDFs conditioned on separation $r$. The first closure form, involving the Eulerian two-time correlation of fluid relative velocities, showed the best agreement with the DNS results for the PDFs.

We present the linear stability properties and nonlinear evolution of two-dimensional plane Couette flow for a statically stable Boussinesq three-layer fluid of total depth $2h$ between two horizontal plates driven at constant velocity $\pm \unicode[STIX]{x0394}U$. Initially the three layers have equal depth $2h/3$ and densities $\unicode[STIX]{x1D70C}_{0}+\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$, $\unicode[STIX]{x1D70C}_{0}$ and $\unicode[STIX]{x1D70C}_{0}-\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$, such that $\unicode[STIX]{x1D70C}_{0}\gg \unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$. At finite Reynolds and Prandtl number, we demonstrate that this flow is susceptible to two distinct primary linear instabilities for sufficiently large bulk Richardson number $Ri_{B}=g\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}h/(\unicode[STIX]{x1D70C}_{0}\unicode[STIX]{x0394}U^{2})$. For a given bulk Richardson number $Ri_{B}$, the zero phase speed ‘Taylor’ instability is always predicted to have the largest growth rate and to be an inherently two-dimensional instability. An inherently viscous instability, reminiscent of the ‘Holmboe’ instability, is also predicted to have a non-zero growth rate. For flows with Prandtl number $Pr=\unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}=1$, where $\unicode[STIX]{x1D708}$ is the kinematic viscosity, and $\unicode[STIX]{x1D705}$ is the diffusivity of the density distribution, we find that the most unstable Taylor instability, maximized across wavenumber and $Ri_{B}$, has a (linear) growth rate which is a non-monotonic function of Reynolds number $Re=\unicode[STIX]{x0394}Uh/\unicode[STIX]{x1D708}$, with a global maximum at $Re=700$ over 50 % larger than the growth rate as $Re\rightarrow \infty$. In a fully nonlinear evolution of the flows with $Re=700$ and $Pr=1$, the two interfaces between the three density layers diffuse more rapidly than the underlying instabilities can grow from small amplitude. Therefore, we investigate numerically the nonlinear evolution of the flow at $Re=600$ and $Pr=300$, and at $Re=5000$ and $Pr=70$ in two-dimensional domains with streamwise extent equal to two wavelengths of the Taylor instability with the largest growth rate. At both sets of parameter values, the primary Taylor instability undergoes a period of identifiable exponential ‘linear’ growth. However, we demonstrate that, unlike the so-called ‘Kelvin–Helmholtz’ instability that it superficially resembles, the Taylor instability’s finite-amplitude state of an elliptical vortex in the middle layer appears not to saturate into a quasiequilibrium state, but is rapidly destroyed by the background shear. The decay process reveals $Re$-dependent secondary processes. For the $Re=600$ simulation, this decay allows the development to finite amplitude of the co-existing primary ‘viscous Holmboe wave instability’, which has a substantially smaller linear growth rate. For the $Re=5000$ simulation, the Taylor instability decay induces a non-trivial modification of the mean velocity and density distributions, which nonlinearly develops into more classical finite-amplitude Holmboe waves. In both cases, the saturated nonlinear Holmboe waves are robust and long-lived in two-dimensional flow.

Coupling is considered between fluid flow and a freely moving body shorter than the development length in an oncoming boundary layer or channel flow but longer than the flow thickness. The body lies within the core of the flow. The coupling occurs between the inviscid-dominated displacement and the viscous–inviscid pressure, the latter acting to move the body. This interaction can be unstable. It is found however that three factors serve to stabilise the interaction as each one alters the decisive balance of angular momentum. One is a 10 % shift forward in the position of the centre of mass. The second is a degree of flexibility in the body shape by means of its response to the induced pressure force. Third is a slight streamwise movement of the body which is sufficient to modify the viscous–inviscid pressure response and again produce stabilisation. The effects are largely independent of the lateral position of the body.

We establish through numerical simulation conditions for optimal undulatory propulsion for a single fish, and for a pair of hydrodynamically interacting fish, accounting for linear and angular recoil. We first employ systematic two-dimensional (2-D) simulations to identify conditions for minimal propulsive power of a self-propelled fish, and continue with targeted 3-D simulations for a danio-like fish; all at Reynolds number 5000. We find that the Strouhal number, phase angle between heave and pitch at the trailing edge, and angle of attack are principal parameters. For 2-D simulations, imposing a deformation based on measured displacement for carangiform swimming provides, at best, efficiency of 35 %, which increases to 50 % for an optimized motion; for a 3-D fish, the efficiency increases from 22 % to 34 %. Indeed, angular recoil has significant impact on efficiency, and optimized body bending requires maximum bending amplitude upstream of the trailing edge. Next, we turn to 2-D simulation of two hydrodynamically interacting fish. We find that the upstream fish benefits energetically only for small distances. In contrast, the downstream fish can benefit at any position that allows interaction with the upstream wake, provided its body motion is timed appropriately with respect to the oncoming vortices. For an in-line configuration, one body length apart, the efficiency of the downstream fish can increase from 50 % to 60 %; for an offset arrangement it can reach 80 %. This proves that in groups of fish, energy savings can be achieved for downstream fish through interaction with oncoming vortices, even when the downstream fish lies directly inside the jet-like flow of an upstream fish.

We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number ($Re\approx 0.8\times 10^{5}$) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, $\unicode[STIX]{x1D70E}_{D}$, that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing $\unicode[STIX]{x1D70E}_{D}$ leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using $\unicode[STIX]{x1D70E}_{D}$ in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm.

The present paper describes the effect of drag reduction of circular cylinders due to a porous coating on their leeward sides. To investigate the coating effect, experiments were conducted in a wind tunnel of Goettingen type. Systematic drag measurements were carried out for different cylinder configurations and flow velocities. The drag measurements were complemented by pressure and particle image velocimetry (PIV) flow field measurements around selected cylinders. The Reynolds numbers were varied in the subcritical range of $3\times 10^{4}<Re<1.4\times 10^{5}$. The results show that a thin porous layer on the leeward side, either incorporated in the cylinder shape or applied on the cylinder surface, leads to an increase of base pressure on the leeward side of the cylinder. It causes a reduction of drag and dampens oscillation amplitudes when compared to a cylinder without coating. Results obtained for different configurations with varying key parameters (coating angles, layer thicknesses and pore sizes of the porous material) clearly indicate the drag-reducing and amplitude-damping potential of leeward coating. The amount of drag reduction and amplitude damping depends on the combination of key parameters. It was demonstrated that the lowered drag coefficients $c_{d}$ were almost constant in the tested range of Reynolds numbers. A maximum reduction of drag of 13.2 % was measured. In addition, the results revealed a strong reduction of the pressure fluctuations around cylinders with a leeward coating due to the shift of the vortex region further downstream.

A turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at $Re_{\unicode[STIX]{x1D70F}}\approx 3900$. The three velocity components resulting from this experiment reveal a pronounced spanwise periodicity in all single-point velocity statistics. Consistent with previous hot-wire studies over similar-type riblets, we observe a weak time-average secondary flow in the form of $\unicode[STIX]{x1D6FF}$-filling streamwise vortices. The observed differences in the surface and secondary flow characteristics, compared to other heterogeneous-roughness studies, may suggest that different mechanisms are responsible for the flow modifications in this case. Observations of instantaneous velocity fields reveal modified and rearranged turbulence structures. The instantaneous snapshots also suggest that the time-average secondary flow may be an artefact arising from superpositions of much stronger instantaneous turbulent events enhanced by the surface texture. In addition, the observed instantaneous secondary motions seem to have promoted a free-stream-engulfing behaviour in the outer layer, which would indicate an increase turbulent/non-turbulent flow mixing. It is overall demonstrated that the presence of large-scale directionality in transitional surface roughness can cause a modification throughout the entire boundary layer, even when the roughness height is 0.5 % of the layer thickness.

We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metric is the averaged deviation of the vorticity from its spatial mean over the Eulerian vortex, normalized by the instantaneous material leakage from the Eulerian vortex. The metric offers a model- and frame-independent tool for uncovering the instantaneous Eulerian signature of long-lived Lagrangian vortices. Using satellite-derived ocean velocity data, we show that Lagrangian vortex-persistence predictions by our metric significantly outperform those inferred from other customary Eulerian diagnostics, such as the potential vorticity gradient and the Okubo–Weiss criterion.

The role of the global curvature on the structure and propagation of cylindrical detonations is studied allowing and without allowing the development of cellular structures through two-dimensional (2-D) and 1-D simulations, respectively. It is shown that as the detonation transitions from being overdriven to the Chapman–Jouguet (CJ) state, its structure evolves from no cell, to growing cells and then to diverging cells. Furthermore, the increased dimension of the average structure of the cellular cylindrical detonation, coupled with the curved transverse wave, leads to bulk un-reacted pockets as the cells grow, and consequently lower average propagation velocities as compared to those associated with smooth fronts. As the global detonation front expands and its curvature decreases, the extent of the un-reacted pockets diminishes and the average velocity of the cellular cylindrical detonation eventually degenerates to that of the smooth fronts. Consequently, the presence of cellular instability renders detonation more difficult to initiate for weakly unstable detonations.

A numerical investigation of vortex-induced rotations (VIRs) of a rigid square cylinder, which is free to rotate in the azimuthal direction in a two-dimensional uniform cross-flow, is presented. Two-dimensional simulations are performed in a range of Reynolds numbers between 45 and 150 with a fixed mass and moment of inertia of the cylinder. The parametric investigation reveals six different dynamic responses of the square cylinder (expanding on those reported by Zaki et al. (J. Fluids Struct., vol. 8, 1994, pp. 555–582)) and their coupled vortex patterns at low Reynolds numbers. In each characteristic regime, moment generating mechanisms are elucidated with investigations of instantaneous flow fields and surface pressure distributions at chosen time instants in a period of rotation response. Our simulation results also elucidate that VIRs significantly influence the statistics of drag and lift force coefficients: (i) the onset of a rapid increases of the two coefficients at $Re=80$ and (ii) their step increases in the autorotation regime.

Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.