The transport of motile micro-organisms exhibits rich and complex phenomena, of significance to various biological and environmental applications. For dilute suspensions of gyrotactic algae dispersing in vertical pipe flows, previous studies obtained only approximate values for the overall drift and dispersivity in the longitudinal direction, using two-step averaging methods with the Pedley–Kessler (PK) model and the generalized Taylor dispersion (GTD) model. These two-step methods impose restrictive assumptions: both the swimming Péclet number and the variation of shear rates relative to swimming must be sufficiently small. Thus, it is difficult to analyse the gyrotactic dispersion process in the ‘breakdown’ parameter region. Following a recent study of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1–34), this paper applies the integrated and precise one-step GTD method to study the overall dispersion process and performs a quantitative test for the applicability of two-step methods. An appropriate function basis for series expansions in the GTD method is proposed to deal with reflective boundary conditions imposed at the tube wall. Detailed results for Chlamydomonas nivalis are presented to illustrate the influence of the gyrotactic focusing on the overall dispersion process, for both downwelling and upwelling flows. The overall drift above the mean flow increases monotonically with the flow rate. However, the overall dispersivity will first decrease, then increase, and finally saturate as the flow rate increases, due to a combined effect of gyrotaxis, swimming and convection. Shear alignments of prolate cells will weaken the focusing, and thus reduce the drift and enhance the dispersivity. The predictions by two-step methods with the PK and GTD models are found to be successful inside their required parameter region. Within the ‘breakdown’ region, the two-step GTD method still gives reasonable results for the local distribution and the drift, but fails in the predictions of dispersivity.

A numerical model, based on the two-phase incompressible Navier–Stokes equations, is used to study transmission of regular water waves by a thin floating plate in two dimensions. The model is shown to capture the phenomenon of waves overwashing the plate, and the generation of turbulent bores on the upper plate surface. It is validated against laboratory experimental measurements, in terms of the transmitted wave field and overwash depths, for a set of incident wave periods and steepness values. Corresponding simulations are performed for a thick plate that does not experience overwash, which are validated using experiments where an edge barrier prevents thin-plate overwash. The model accurately reproduces (i) the linear relationship between the transmitted and incident amplitudes for the thick plate, and (ii) the decrease in proportion of incident-wave transmission for the thin plate, as incident steepness increases. Model outputs are used to link the decreasing transmission to wave-energy dissipation in the overwash, particularly where bores collide, and in the surrounding water, particularly at the plate ends. It is shown that most energy dissipation occurs in the overwash for the shortest incident waves tested, and in the surrounding water for the longer incident waves. Further, evidence is given that overwash suppresses plate motions, and causes asymmetry in plate rotations.

We present an experimental investigation of steady particle-driven gravity currents with Reynolds numbers in the range 500–1600, and with the ratio of the initial current speed to the fall speed of the particles, $S=u_{0}/u_{fall}$, in the range $5<S<160$. We identify three regimes: (i) For $S<10$, the particles settle close to the source at a velocity corresponding to their fall speed, consistent with the observation of sedimenting fronts in classical settling column experiments. (ii) In the range $10<S<40$, a steady gravity current develops within the tank. The experiments show that the depth of the gravity current gradually decreases away from the source and dye added to the source liquid appears above the gravity current along its entire length, suggesting that there is a sedimentation front, so that the volume and momentum fluxes of the current gradually decrease with distance from the source. We find that as $S$ increases, the descent speed of the sedimentation front decreases relative to the fall speed of the particles, and the run-out length of the gravity current increases. We note that the density of the interstitial fluid corresponds to the density of the ambient fluid, so that any reduction in buoyancy of the gravity current is attributed to the sedimentation of particles on the floor of the tank and we do not observe lofting of the interstitial fluid. (iii) For $40<S<160$, the gravity currents reach the end of our experimental tank and we no longer observe a sedimentation front. For these experiments, it appears that the entrainment at the top of the current begins to match the sedimentation and so the current depth does not change significantly over the scale of the tank, but a larger scale experimental system would be needed to explore the full run-out behaviour for these larger values of $S$. For the intermediate case, $10<S<40$, we develop a model for the conservation of volume, momentum and buoyancy fluxes in the current, accounting for the sedimentation front and the release of fluid at the top surface of the gravity current, and we compare this with our new experimental data.

Steep wave passage around vertical circular cylinders is associated with an additional force peak occurring after the main peak: the secondary load cycle. The secondary load cycle for a focused wave group typical of offshore wind turbine foundations at 33 m full-scale water depth is investigated in scale 1 : 50. Ensemble-averaged force, front face pressures and free surface elevation measurements are used as the basis for the investigation. A two-phase free-surface Reynolds-averaged Navier–Stokes solver is validated against generic cases of turbulent flow over a wall, wave-boundary layer flow for a Reynolds number, $Re$, of $1\times 10^{4}<Re<1\times 10^{7}$, two-dimensional (2-D) drag on a cylinder for $1\times 10^{2}<Re<2.5\times 10^{5}$ and 2-D oscillatory flow for three combinations of $Re=\{5.8\times 10^{4},9\times 10^{4},1.7\times 10^{5}\}$ and Keulegan–Carpenter number, $KC=\{6,12,18\}$, respectively. The solver is next applied to reproduce ensemble-averaged experimental results of the focused wave group and a good match for the inline force and free surface elevation is found along with a good match for the measured front face pressures. The numerical solution for the focused wave is next analysed in detail to explain the cause of the secondary load cycle. We find that the secondary load cycle is confined to an upper region ranging from just above the still water level to 1.5 cylinder diameters below. By a further break down of the pressure field into contributions from the individual terms of the vertical Navier–Stokes equation, we find that the local force peak in the secondary load cycle is mainly caused by suction effects around the still water level on the back side, contributed through the material time derivative of the vertical velocity, $\text{D}\unicode[STIX]{x1D70C}u_{z}/\text{D}t$. The suction occurs due to the rapid decrease of water level below the generated water column at the back of the cylinder, which at this time has only just begun its downward motion. The first force local minimum in the secondary load cycle is aided by the hydrostatic pressure from the water column while the second local minimum of the secondary load cycle is aided by wash-down effects on the front side. Finally, the role of the observed vortices behind the cylinder is discussed and compared to reference computations with slip conditions. The results confirm findings from earlier slip boundary studies that the global force history through the secondary load cycle is not strongly affected by the boundary layer. The source of vortices behind the cylinder, observed in both sets of computations is discussed.

We consider the two-dimensional steady channel flow of a rarefied gas over a backward facing step in the limit of large Knudsen numbers. The free-molecular problem is solved analytically for both diffuse and specular-reflecting channel boundaries, and the solutions are validated through comparison with direct simulation Monte Carlo calculations. Prescribing the density and temperature differences between the inlet and outlet external equilibrium conditions, the results for the density- and temperature-drop-driven flows are analysed and contrasted, revealing higher flow velocities and mass flow rates in the former. While the flow rate is unaffected by the step geometry in the specular case, it increases with the step size in the diffuse-reflecting set-up. At conditions where small flow velocities occur, flow detachment is observed in the form of streamlines connecting the step edge stagnation points. Considering the problem at finite Knudsen numbers, the collisionless-flow regime breaks down at higher Knudsen numbers for lower gas speed flows, followed by the occurrence of step flow separation and recirculation.

The dynamical connection between topographic control and wave excitation aloft is investigated theoretically and numerically in the idealized setting of two-dimensional stratified flow over an isolated ridge. We consider a constant far upstream inflow with uniform stratification except for a sharp density step located above the height of the ridge crest. Below this step, the stratification is sufficiently strong that the low level flow is blocked upstream and a hydraulically controlled flow spills over the crest. Above the density step, the flow supports upward radiating waves. In the inviscid limit, a bifurcating isopycnal separates the hydraulically controlled overflow from the wave field aloft. We show that, depending on the height of the density step, the sharp interface can either remain approximately flat, above the controlled downslope flow, or plunge in the lee of the obstacle as part of the controlled overflow itself. Whether the interface plunges or not is a direct consequence of hydraulic control at the crest. The flow above the crest responds to the top of the sharp density step as if it were a virtual topography. We find that a plunging interface can excite a wave field aloft that is approximately six times as energetic, with 15 % higher pressure drag, than that in a comparable flow in which the interface remains approximately flat.

Macroscopic vortex rings are generated thermally in superfluid 4He, between 1.28 and 1.95 K, by applying a brief voltage pulse to a resistive heater located below a circular vertical tube 5 mm in diameter and 20 mm high. The rings form above the tube and propagate upward with velocities of the order of $10~\text{mm}~\text{s}^{-1}$, resulting in Reynolds numbers up to $10^{5}$. We visualize their cross-section, of size comparable with the tube diameter, by capturing the motions of relatively small solid deuterium particles, previously dispersed in the quiescent bath of superfluid 4He. We employ particle positions and velocities to compute the Lagrangian pseudovorticity, which can be seen as a measure of the ring strength and which allows us to identify and track these objects. We thus obtain time-dependent sizes, positions and velocities of the vortex rings. We show that, in the range of investigated parameters, these rings behave as if they were turbulent vortex rings moving in classical viscous fluids, at least in the direction of ring propagation. The outcome reinforces the view that the study of turbulent flows of superfluid 4He is not only interesting in its own right, but that it can also contribute to our current understanding of fluid turbulence in general.

We examine the dynamics of a thin film composed of a non-evaporative silicone oil (high surface tension) with trace amounts of an evaporative silicone oil (low surface tension) over an air bubble. An evaporating thin liquid film is formed atop a capillary-pinned air bubble by squeezing then holding the bubble against the air–silicone oil interface. Despite the simplicity of the system, complex oscillatory dynamical behaviour has been observed. Through interferometric experiments and numerical simulations, we show that as the bubble is moved towards the opposite interface, a dimple forms and during the subsequent holding period the dimple spontaneously oscillates. The evaporation-driven solutal–thermal Marangoni flow thickens the film and capillarity subsequently discharges the dimple. Solutal and thermal Marangoni flows both contribute to film thickening and as the local concentration of the non-evaporative species increases, the strength of the Marangoni flows increases. The oscillation frequency and waveform depend on initial composition and the maximum dimple volume. We suggest that these oscillatory solutions and the associated mechanism are a partial explanation for the film stabilization in multicomponent oils, reported experimentally in a recent publication (Chandran Suja et al., Proc. Natl Acad. Sci., vol. 115, 2018, pp. 7919–7924).

The interaction between a planar shock wave propagating in air and a polygonal bubble (composed of two triangles) containing two different gases is studied numerically. Studying the interaction between an oncoming shock wave with front- and rear-facing triangles containing light and heavy gases is of great importance in understanding the complex shock wave propagation, interaction and hydrodynamic instabilities as well as their effect on mitigating or enhancing the colliding shock/blast wave. Two different cases were studied: in the first case, the front triangle contained sulfur hexafluoride (SF6) and the rear one contained helium (He); while in the second case, He is in the front and SF6 in the rear triangle. As the speed of sound in He is significantly higher than that in SF6 and in air, different flow fields were evolved. When SF6 is placed in the front triangle, the shock wave transmitted through the SF6 is reflected back from the interface separating the two gases and starts propagating downstream; over the He segment of the bubble, the incident shock wave (in the open air) is already seen over the He section and it submits compression waves into the He gas. These compression waves travel upstream and downstream; in their upstream movement they generate compression waves into the ambient air ahead of the incident shock wave. The part moving downstream will hit the interface separating SF6 and He, resulting in a complex wave pattern. A completely different wave pattern is visible when He is placed in the front triangle. Now the fastest shock is the transmitted shock wave in the He section; it reaches the membrane separating the two gases well before the incident shock wave reaches this location. Unlike the previous case, now the resulting flow in the rear triangle of the bubble is affected not only by the incident shock wave but also by the transmitted compression waves from the helium section. Furthermore, when helium is placed in the front section of the bubble, the compression waves in the He impacts the rear triangle of the bubble (containing SF6) almost like a planar shock wave. This is different from the previous case where SF6 was in the front section; then the shock wave impacting on the rear bubble containing He had a completely different shape due to its propagation into the SF6 bubble. This resulted in completely different peak pressures.

The receptivity of an under-expanded supersonic impinging jet flow at a sharp nozzle lip to acoustic impulse disturbances is investigated as a function of geometric and flow parameters. The under-expanded supersonic jets emanate from an infinite-lipped nozzle, i.e. the nozzle exit is a circular hole in a flat plate. Two specific cases have been investigated corresponding to nozzle-to-wall distances of $h=2d$ and $5d$, where $d$ is the jet diameter, at a nozzle pressure ratio of 3.4 and a Reynolds number of 50 000. Receptivity in this study is defined as originally coined by Morkovin (Tech. Rep. AFFDL TR, 1969, pp. 68–149; see also Reshotko, AGARD Special Course on Stability and Transition of Laminar Flow, N84-33757 23-34) as the internalisation of an external disturbance into the initial condition that either initiates or sustains a vortical fluid dynamic instability. Notionally, receptivity can be considered as a transfer function between the external disturbance and the initial conditions of the vortical instability. In the case of under-expanded supersonic impinging jet flow subjected to an acoustic disturbance, this transfer function is located at the nozzle lip and, thus, is amenable to an impulse response analysis using the linearised compressible three-dimensional Navier–Stokes equations. In this study, the transfer function at the nozzle lip is defined as the ratio of the output flow energy to the input acoustic energy of the acoustic disturbance. The sensitivity of this transfer function to the angular acoustic disturbance location, its azimuthal mode number and Strouhal number has been investigated for the two under-expanded supersonic impinging jet flow cases. It is found that for both the $h=2d$ and $5d$ cases, acoustic disturbances located at angles greater than $80^{\circ }$ from the jet centreline, with Strouhal numbers in the range between 0.7 and 6.5, have the highest receptivity for all azimuthal mode numbers investigated, except the azimuthal mode number 2 in the case of $h=5d$. The case with $h=5d$ is found to also have high receptivity to acoustic disturbances located at angles between $15^{\circ }$ and $50^{\circ }$ from the jet centreline for acoustic disturbances of all azimuthal mode numbers.

The modification of fluid turbulence due to suspended particles is analysed using direct numerical simulations for the fluid turbulence and discrete particle simulations where the point-particle approximation is used for the particle force on the fluid. Two values of the Reynolds number based on the channel width $h$ and the average gas velocity $\bar{u}$, $(\unicode[STIX]{x1D70C}_{f}\bar{u}h/\unicode[STIX]{x1D702}_{f})=3300$ and 5600 are considered, where $\unicode[STIX]{x1D70C}_{f}$ and $\unicode[STIX]{x1D702}_{f}$ are the gas density and viscosity. The particle Reynolds number based on the root mean square of the difference in the particle and fluid velocities is in the range 4–15. The particle volume fraction is small, in the range $0{-}3.5\times 10^{-3}$, the mass loading is varied in the range 0–13.5 and the particle Stokes number (ratio of particle relaxation time and fluid integral time) is varied in the range 1–420. Multiple models for the force on the particles are examined, the Stokes drag law, the Schiller–Naumann correlation, a correction to determine the ‘undisturbed’ fluid velocity at the particle centre, the lift force and wall corrections. In all cases, as the particle volume fraction is systematically increased, there is a discontinuous decrease in the turbulence intensities at a critical volume fraction. The mean square velocities and the rate of production of turbulent energy decrease by 1–2 orders of magnitude when the volume fraction is increased by $10^{-4}$ at the critical volume fraction. There is no compensatory increase in the particle fluctuating velocities or the energy dissipation rate due to the drag force on the particles, and there is a significant decrease in the total fluid energy dissipation rate at the critical volume fraction. This shows that the turbulence collapse is due to a catastrophic reduction in the turbulent energy production rate. This is contrary to the current understanding that turbulence attenuation is caused by the enhanced dissipation due to particle drag.

A growing body of studies supports the existence of Townsend’s wall-attached eddies in wall turbulence under the condition of sufficiently high Reynolds numbers. In the present work, we uncover the signature of Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence. To this end, we use a three-dimensional clustering methodology to identify the wall-attached structures of intense streamwise and spanwise velocity fluctuations in turbulent channel flows at four Reynolds numbers ($Re_{\unicode[STIX]{x1D70F}}=186$, 358, 547 and 934). The statistical properties of the structures, such as their geometric self-similarity, population density and statistical moments, are investigated and compared with the predictions of the attached-eddy model. Particular attention is paid to the asymmetries between high- and low-speed wall-attached streaky structures, and we show that the former are a closer representation of the wall-attached eddies. This observation is ascribed to the differences between the sweep and ejection events associated with the streaks. We also examine the Reynolds-number effects on the statistical properties of the structures, and find that the signature of attached eddies can be observed within the Reynolds-number range under scrutiny. Our approach paves the way to cost-efficient model development and flow prediction using computationally more affordable simulations at low Reynolds numbers.

The flow-induced vibration of a sphere elastically mounted in the cross-flow direction with imposed feedback rotation was investigated experimentally. The application of rotation provides a means to exercise control over the vibration response of axisymmetric three-dimensional objects. Both the rotational amplitude, which was imposed in proportion to sphere transverse displacement, and the phase of the control signal were varied over a broad parameter space comprising: a non-dimensionalised proportional gain ($0.5\leqslant K_{p}^{\ast }\leqslant 2$); rotation phase ($0^{\circ }\leqslant \unicode[STIX]{x1D719}_{rot}\leqslant 360^{\circ }$), which is the phase between the applied sphere rotation and the transverse displacement; and reduced velocity ($3\leqslant$$U^{\ast }\leqslant 20$). The corresponding Reynolds number range was ($3900\lesssim Re\lesssim 25\,800$). The structural vibration, fluid forces and wake structure were examined to characterise the effect of the imposed rotation. It was found that the rotation not only altered the magnitude of the vibration response, either amplifying or attenuating the response depending on operating conditions, but it also altered the reduced velocity at which vibrations commenced, the vibration frequency and periodicity and significantly altered the phase between the transverse fluid force and displacement. It was possible to almost completely suppress the vibration in the mode I, mode II and mode III transition regimes for imposed rotation over the ranges $90^{\circ }\lesssim$$\unicode[STIX]{x1D719}_{rot}\lesssim 180^{\circ }$, $15^{\circ }\lesssim$$\unicode[STIX]{x1D719}_{rot}\lesssim 135^{\circ }$ and $0^{\circ }\lesssim$$\unicode[STIX]{x1D719}_{rot}\lesssim 120^{\circ }$, respectively. In particular, this could be achieved at effective rotation rates well below those required by using open-loop control (Sareen et al., J. Fluid Mech., vol. 837, 2018, pp. 258–292). Past the peak of mode II, a ‘galloping-like’ response, similar to that reported by Vicente-Ludlam et al. (J. Fluid Mech., vol. 847, 2018, pp. 93–118) for the circular cylinder, was observed with an increase in vibration amplitude of up to 368 % at the highest reduced velocity tested ($U^{\ast }=20$). Particle image velocimetry measurements revealed a change in the timing and spatial position of the streamwise vortex structures with imposed rotation. Contrary to what has been observed for the circular cylinder, however, no de-synchronisation between vortex shedding and sphere motion was observed.

Vortex breakdown (VB) in swirling jets can be classified as either a bubble (BVB) or a conical (CVB) form based on the shape of its recirculation zone. The present study investigates the hysteresis features of these forms in laminar swirling jets using direct numerical simulations. It is established here that BVB and CVB are bistable forms in a large swirl range and for a Reynolds number of 200 (based on jet radius and centreline velocity). Considerable differences were observed in the length scales associated with the two, with the approximate recirculation zone diameters of the BVB and CVB being 1 and 15 jet diameters, respectively. Additionally, two types of BVB were observed, identified as a two-celled BVB with spiral tail and an asymmetric BVB. The former is characterized by an almost steady bubble with a two-celled structure. By contrast, the entire bubble envelope oscillated in a non-axisymmetric fashion for the latter. These two types of BVB themselves were found to coexist in a small swirl range. A global linear stability analysis was used to show that two different unstable single helical modes are associated with these two types. In comparison to using the base flow, a stability analysis performed on the mean flow was found to predict the coherent features of asymmetric BVB observed in the simulations more precisely. This study highlights the rich variety of VB flow states that coexist in various ranges of swirl strengths and the significance of hysteresis effects in laminar swirling jets.

We derive the upper limit for power extraction from an open-channel flow with lateral bypass representing tidal power or run-of-river plants for the complete range of blockage $\unicode[STIX]{x1D70E}$, Froude number $Fr_{2}$ and turbine head $H_{T}$. For this, a generic turbine model is used: a momentum and energy sink distributed over the geometric blocking $\unicode[STIX]{x1D70E}$ of the channel allowing lateral bypass. It is indicated that existing models neglect important aspects of the free-surface deformation due to the energy extraction, yielding unphysical behaviour at high blockage, high Froude number or high turbine head. The asymptotic validity of existing theories for $\unicode[STIX]{x1D70E}\rightarrow 0$, $Fr_{2}\rightarrow 0$, $H_{T}\rightarrow 0$ becomes evident: firstly, by comparing existing theories with the presented general theory; and secondly, by the experimental validation of the existing and presented theories. The accompanying systematic experimental study comprises a wide range of blockage ratios, $0.25\leqslant \unicode[STIX]{x1D70E}\leqslant 1.0$, of downstream Froude numbers, $0.2\leqslant Fr_{2}\leqslant 0.5$, and of different turbine heads, $H_{T}$, measured in multiples of the specific energy $E_{0}$ of the undisturbed flow. The subsequent model-based optimisation allows an indication of the optimal turbine head $H_{T,opt}/E_{0}$ as well as the maximal obtainable coefficient of performance $C_{P,opt}$ as a function of $\unicode[STIX]{x1D70E}$ and $Fr_{2}$ or downstream water depth $h_{2}/E_{0}$, respectively. The theory reveals points of operation in which there is a surge wave in the tailwater. The new physical insight and optimisation results may serve for plant design and operation, as well as for investment decisions.

We revisit the optimal heat transport problem for Rayleigh–Bénard convection in which a rigorous upper bound on the Nusselt number, $Nu$, is sought as a function of the Rayleigh number, $Ra$. Concentrating on the two-dimensional problem with stress-free boundary conditions, we impose the time-averaged heat equation as a constraint for the bound using a novel two-dimensional background approach thereby complementing the ‘wall-to-wall’ approach of Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662). Imposing the same symmetry on the problem, we find correspondence with their maximal result for $Ra\leqslant Ra_{c}:=4468.8$ but, beyond that, the results from the two approaches diverge. The bound produced by the two-dimensional background field approaches that produced by the one-dimensional background field from below as the length of computational domain $L\rightarrow \infty$. On lifting the imposed symmetry, the optimal two-dimensional temperature background field reverts to being one-dimensional, giving the best bound $Nu\leqslant 0.055Ra^{1/2}$ compared to $Nu\leqslant 0.026Ra^{1/2}$ in the non-slip case. We then show via an inductive bifurcation analysis that introducing two-dimensional temperature and velocity background fields (in an attempt to impose the time-averaged Boussinesq equations) is also unable to lower the bound. This then exhausts the background approach for the two-dimensional (and by extension three-dimensional) Rayleigh–Bénard problem with the bound remaining stubbornly $Ra^{1/2}$ while data seem more to scale like $Ra^{1/3}$ for large $Ra$. Finally, we show that adding a velocity background field to the formulation of Wen et al. (Phys. Rev. E., vol. 92, 2015, 043012), which is able to use an extra vorticity constraint due to the stress-free condition to lower the bound to $Nu\leqslant O(Ra^{5/12})$, also fails to further improve the bound.

Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of the velocity fields by a Péclet number $Pe$ proportional to their root-mean-square rate of strain, the schemes are applied to compute two-dimensional flows optimizing convective enhancement of diffusive heat transfer, i.e. the Nusselt number $Nu$ up to $Pe\approx 10^{5}$. The resulting transport exhibits a change of scaling from $Nu-1\sim Pe^{2}$ for $Pe<10$ in the linear regime to $Nu\sim Pe^{0.54}$ for $Pe>10^{3}$. Optimal fields are observed to be approximately separable, i.e. products of functions of the wall-parallel and wall-normal coordinates. Analysis employing a separable ansatz yields a conditional upper bound ${\lesssim}Pe^{6/11}=Pe^{0.\overline{54}}$ as $Pe\rightarrow \infty$ similar to the computationally achieved scaling. Implications for heat transfer in buoyancy-driven Rayleigh–Bénard convection are discussed.

Three-dimensional numerical simulations are performed to investigate the dynamics of deep-ocean convection. Organized structures of denser fluid moving downwards, known as plumes, are formed during the initial evolution. We propose a scaling for the diameter and velocity of these plumes based on surface flux magnitude $B_{0}$ and the thermal/eddy diffusivity. Rotation effects are found to be negligible during this initial evolution. At a later time $t>2\unicode[STIX]{x03C0}/f$, where $f$ is the Coriolis parameter, the flow comes under the influence of rotation, which stabilizes the flow by inhibiting the conversion of potential energy to turbulent kinetic energy. At moderate to low rotation rates, the dense fluid plummets and spreads laterally as a gravity current along the bottom boundary. However, at high rotation rates, the flow reaches a quasi-geostrophic state (before the dense fluid reaches the bottom boundary) with an approximate balance between the pressure gradient and the Coriolis forces. We also see the formation of baroclinic vortices and a rim current at the interface of the mixed and surrounding fluids at high rotation rates. A quantitative analysis of the root-mean-square velocities reveals that higher rotation rates result in lower turbulence intensities. Closure of the turbulent kinetic energy budget is also achieved with an approximate balance between the buoyancy flux and the dissipation rate.

To study the variation of the stagnation point position of the flow impinging obliquely on a moving flat plate, we follow the mathematical approach of Dorrepall (J. Fluid Mech., vol. 163, 1986, p. 141) and obtain the analytical solution of the flow. Based on the solution, we derive an equation governing the variation of stagnation point position with both the plate velocity as well as the impinging angle. Results show that, when the plate is stationary, the stagnation point will stay in upstream if the flow is non-orthogonal, as concluded by previous studies. As soon as the plate starts to move, the stagnation point will move from upstream to downstream when the plate velocity increases beyond a small critical value, no matter whether the flow is orthogonal or non-orthogonal.

We tackle the question of how anisotropy in flows subject to background rotation favours structures elongated along the rotation axis, especially in turbulent flows. A new, wave-free mechanism is identified that challenges the current understanding of the process. Inertial waves propagating near the rotation axis (Staplehurst et al. J. Fluid Mech., vol. 598, 2008, pp. 81–105; Yarom & Sharon, Nat. Phys., vol. 10(7), 2014, pp. 510–514) are generally accepted as the most efficient mechanism to transport energy anisotropically. They have been shown to transfer energy to large anisotropic, columnar structures. Nevertheless, they cannot account for the formation of simpler steady anisotropic phenomena such as Taylor columns. Here, we experimentally show that more than one mechanism involving the Coriolis force may promote anisotropy. In particular, in the limit of fast rotation, that is at low Rossby number, anisotropy favouring the direction of rotation of the average of a turbulent flow arises neither because of inertial waves nor following the same mechanism as in steady Taylor columns, but from an interplay between the Coriolis force and average advection.