Hydraulic jumps, roll waves or bores in open channel flows are often treated as singularities by hydraulicians while slowly varying shallow water flows are described by continuous solutions of the Saint-Venant equations. Richard & Gavrilyuk (J. Fluid Mech., vol. 725, 2013, pp. 492–521) have enriched this model by introducing an equation for roller vorticity in a very elegant manner. This new model matches several experimental results that have resisted theoretical approaches for decades. This is the case of the roller of a stationary hydraulic jump as well as the oscillatory instability that the jump encounters when the Froude number is increased. The universality of their approach as well as its convincing comparisons with experimental results open the way for significant progress in the modelling of open channel flows.

We present an experimental and theoretical study of a thin, viscous fluid layer that flows radially under gravity from a point source into a denser inviscid fluid layer of uniform depth above a rigid horizontal surface. Near the source, the viscous layer lies in full contact with the surface, forming a vertical-shear-dominated viscous gravity current. At a certain distance from the source, the layer detaches from the surface to form a floating current whose dynamics are controlled by the viscous stresses due to longitudinal extension. We describe the dynamics of the grounded and floating components using distinct thin-layer theories. Separating the grounded and floating regions is the freely moving line of detachment, or grounding line, whose evolution we model by balancing the horizontal forces between the two regions. Using numerical and asymptotic analysis, we calculate the evolution of the system from a self-similar form at early times towards a steady state at late times. We use our solutions to illustrate how three-dimensional stresses within marine ice sheets, such as that of West Antarctica, can lead to stabilization of the grounding line. To assess the validity of the assumptions underlying our model, we compare its predictions with data from a series of laboratory experiments.

The Ekman flow, an exact solution of the Boussinesq equations with rotation, is a prototype flow for both atmospheric and oceanic boundary layers. The effect of stratification on the finite-amplitude longitudinal rolls developing in the Ekman flow and their three-dimensional stability is studied by means of linearized and nonlinear numerical simulations. Similarities and differences with respect to billows developing in the Kelvin–Helmholtz (KH) unidirectional stratified shear flow are discussed. Prandtl number effects are investigated as well as the role played by the buoyant-convective instability. For low Prandtl number, the amplitude of the saturated rolls vanishes at the critical bulk Richardson number, while at high Prandtl number, finite-amplitude rolls are found. The Prandtl number also affects how the growth rate of the secondary instability evolves as the Richardson number is increased. For low Prandtl number, the growth rate decreases as the Richardson number increases while it remains significant for large Prandtl number over the range of stratification studied. This behaviour is likely a result of the differing amplitudes of the roll vortices. Furthermore, the most unstable wave vector is much lower than for the secondary instability of KH billows. Examination of the energetics of the secondary instability shows that buoyant-convective instability is present locally at high Reynolds and Prandtl numbers but plays an overall minor role despite the presence in the base flow of statically unstable regions characterized by a high Richardson number.

The convective primary amplification of a forced two-dimensional perturbation initiates the formation of essentially two-dimensional large-scale vortices in a laminar separation bubble. These vortices are then shed from the bubble with the forcing frequency. Immediately downstream of their formation, the vortices get distorted in the spanwise direction and quickly disintegrate into small-scale turbulence. The laminar–turbulent transition in a forced laminar separation bubble is dominated by this vortex formation and breakup process. Using numerical and experimental data, we give an in-depth characterization of this process in physical space as well as in Fourier space, exploiting the largely periodic character of the flow in time as well as in the spanwise direction. We present evidence that a combination of more than one secondary instability mechanism is active during this process. The first instability mechanism is the elliptic instability of vortex cores, leading to a spanwise deformation of the cores with a spanwise wavelength of the order of the size of the vortex. Another mechanism, potentially an instability of flow in between two consecutive vortices, is responsible for three-dimensionality in the braid region. The corresponding disturbances possess a much smaller spanwise wavelength as compared to those amplified through elliptic instability. The secondary instability mechanisms occur for both fundamental and subharmonic frequency, respectively, even in the absence of continuous forcing, indicative of temporal amplification in the region of vortex formation.

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers $0. 3\leq {\mathrm{Fr} }_{0} \leq 40$ and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of ${\mathrm{Fr} }_{0} $. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of ${\mathrm{Fr} }_{0} $) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high ${\mathrm{Fr} }_{0} $ we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, ${\mathrm{Str} }_{top} $, based on experimental measures of the fountain top, defined such that ${\mathrm{Str} }_{top} = 1$ would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high-${\mathrm{Fr} }_{0} $ fountains we find ${\mathrm{Str} }_{top} \approx 0. 9$.

This paper describes an investigation of the linear, diffusive critical layer for shear flows whose inviscid neutral modes have an algebraic branch point. As examples of flows exhibiting such singular behaviour, we treat both stratified shear flows and non-axisymmetric modes on vortices. For the stratified case, the coupled vorticity and energy equations are solved numerically. In this way, the density perturbation, which is unbounded in the absence of diffusion, is determined directly. As an example featuring a vortex, we consider helical modes on a modified Lamb–Oseen vortex whose velocity profile is perturbed in such a way that linear instability is possible. Both the axial and azimuthal velocity perturbations in the critical layer are determined. A characteristic shared by all the above problems is that they involve eigenfunctions that are oscillatory in some region. For forced waves in a stably stratified shear flow, we consider a larger range of parameters than previous investigators. We also examine some experiments and find that the Reynolds stress is sensitive to the actual density profile in the region between a wavy wall providing the forcing and the critical layer. For the stratified shear flows without forcing, much smaller Richardson numbers are involved and the modes considered are over-reflecting. For an unbounded $\tanh y$ mixing layer, we show that the Reynolds stress for a neutral mode must jump across the critical layer. With the presence of a horizontal boundary beneath the shear layer, on the other hand, over-reflection can occur, with the Reynolds stress vanishing on either side of the critical layer. In all cases, the variation of the Reynolds stress across the critical layer is determined.

This paper reports a numerical study of coupled double diffusive convection and radiation in a differentially heated square enclosure filled with non-grey air–CO2 (or air–H2O) mixtures. The numerical procedure is based on a hybrid scheme with the multiple relaxation time lattice Boltzmann method and the finite difference method. The fluid velocity is determined by the D2Q9 multiple relaxation time model, and the energy equation is discretized by the finite difference method to compute the temperature field, while the radiative part of the energy equation is calculated by the discrete ordinates method combined with the spectral line-based weighted sum of grey gases model. Depending on the boundary conditions, aiding and opposing flows occur as the result of temperature and concentration gradients. The effects of various parameters, such as the molar fraction on the flow structure, thermal and concentration fields, are investigated for aiding and opposing cases. The numerical results show that, in the presence of non-grey radiation, the heat transfer is decreased and the mass transfer is slightly modified. The gas radiation modifies the structure of the velocity and thermal fields by generating inclined stratifications and promoting instabilities in opposing flows.

The paper presents an extension to ducted rotors of the nonlinear actuator disk theory of Conway (J. Fluid Mech., vol. 365, 1998, pp. 235–267) and it is exact for incompressible, axisymmetric and inviscid flows. The solution for the velocities and the Stokes stream function results from the superposition of ring vortices properly arranged along the duct surface and the wake region. Using a general analytical procedure the flow fields are given as a combination of one-dimensional integrals of expressions involving complete as well as incomplete elliptic integrals. The solution being exact, the proper shape of the slipstream whether converging or diverging is naturally accounted for, even for heavy loads. A semi-analytical method has been developed that enables the flow induced by an actuator disk housed in a contoured duct to be solved duly accounting for the nonlinear mutual interaction between the duct and the rotor. Non-uniform load distributions, rotor wake rotation and ducts of general shapes and thickness distribution can be dealt with. Thanks to its reduced numerical cost, the method is well suited for the design and/or analysis of ducted rotors for marine, wind and aeronautical applications.

A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier–Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical-layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially varying travelling waves. The leading modes effectively constitute a low-dimensional description of the turbulent flow, which is optimal in the sense of describing the resonant effects around the critical layer and which minimally predicts all types of structure. The approach is general for the full range of scales. By way of example, simple combinations of these modes are offered that predict hairpins and modulated hairpin packets. The example combinations are chosen to represent observed structure, consistent with the nonlinear triadic interaction for wavenumbers that is required for self-interaction of structures. The combination of the three leading response modes at streamwise wavenumbers $6, ~1, ~7$ and spanwise wavenumbers $\pm 6, ~\pm 6, ~\pm 12$, respectively, with phase velocity $2/ 3$, is understood to represent a turbulence ‘kernel’, which, it is proposed, constitutes a self-exciting process analogous to the near-wall cycle. Together, these interactions explain how the mode combinations may self-organize and self-sustain to produce experimentally observed structure. The phase interaction also leads to insight into skewness and correlation results known in the literature. It is also shown that the very large-scale motions act to organize hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally altering the shear profile. These energetic streamwise structures arise naturally from the resolvent analysis, rather than by a summation of hairpin packets. In addition, these packets are modulated through a ‘beat’ effect. The relationship between Taylor’s hypothesis and coherence is discussed, and both are shown to be the consequence of the localization of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin–Stuart (cat’s eye) vortices. Evidence for the theory is presented based on comparison with observations of structure in turbulent flow reported in the experimental and numerical simulation literature and with exact solutions reported in the transitional literature.

We analyse the steady-state convection–diffusion mixing of a solute by a creeping circulatory flow in a long sealed rectangular two-dimensional channel with impermeable sidewalls and fixed different solute concentrations at the two opposite edges. Solution circulation is due to a constant velocity slip along the sidewalls and a back flow along the channel axis. This simple model distils the essence of circulation in concentration polarization of an electrolyte solution under a DC electric current in a micro-channel sealed by an ion-selective element (a nano-channel or a cation exchange membrane). It is observed that in the slow circulation regime (small $Pe$ numbers) the solute flux through the channel is governed by the Taylor–Aris dispersion mechanism, i.e. the flux is driven by the cross-sectional average axial concentration gradient, whereas upon increase in $Pe$ this mechanism fails. The general question addressed is where the system goes after the breakdown of the Taylor–Aris dispersion regime. In order to find out the answer, the following specific questions have to be addressed. (1) How does the Taylor–Aris dispersion mechanism break down upon increase in $Pe$? (2) Why does it break down? (3) What is the role of the channel aspect ratio in this breakdown? The answers to these questions are obtained through analysing a hierarchy of suitable auxiliary model problems, including the unidirectional zero discharge channel flow and the circulatory analogue of plane-parallel Couette flow, for which most of the analysis is done. They may be summarized as follows. Upon increase in circulation velocity, the Taylor–Aris dispersion mechanism fails due to the formation of lateral non-uniformities of longitudinal solute concentration gradient driving the dispersion flux. These non-uniformities accumulate in protrusion-like disturbances of the solute concentration (wall fingers) emerging near the channel sidewall at the flow exit from the edge. Wall fingers propagate along the sidewalls with increase in $Pe$ and eventually reach the opposite channel edges, transforming into narrow surface convection layers. These layers, together with the edge diffusion layers, form a closed mass transport pattern carrying most of the mass flux through the channel with the bulk largely excluded from the transport. The formation of this pattern finalizes the transition from Taylor–Aris dispersion to the surface convection regime. For large circulation velocities, concentration distribution in the surface convection layers attains an oscillatory spiral structure reminiscent of thermal waves in heat conduction.

We describe the steady motion of a buoyant fluid migrating through a porous layer along a plane, inclined boundary from a localized well. We first describe the transition from an approximately radially spreading current near the source, to a flow which runs upslope, as it spreads in the cross-slope direction. Using the model, we predict the maximum injection rate for which, near the source, the flow does not fully flood the porous layer. We then account for the presence of a fracture on the boundary through which some of the flow can drain upwards, and calculate how the current is partitioned between the fraction that drains and the remainder which continues running upslope. The fraction that drains increases with the permeability of the fracture and also with the distance from the source, as the flow slows and has more time to drain. We introduce new scalings and some asymptotic solutions to describe both the flow near the fracture and the three-dimensional surface of the injected fluid as it spreads upslope. We extend the model to the case of multiple fractures, so that the current eventually drains away as it flows over successive fractures. We calculate the shape of the region that is invaded by the buoyant fluid and we show that this flow, draining through a series of discrete fractures, may be approximated by a flow that continuously drains through its upper boundary. The effective small uniform permeability of this upper boundary is given by ${k}_{b} \approx \int \nolimits {k}_{f} \hspace{0.167em} \mathrm{d} x/ {D}_{F} $, where $\int \nolimits {k}_{f} \hspace{0.167em} \mathrm{d} x$ is the integral of permeability across the width of the fracture and ${D}_{F} $ is the inter-fracture spacing. Finally, we discuss the relevance of the work for CO2 sequestration and we compare some simple predictions of the plume shape, volume and volume flux derived from our model with data from the Sleipner project, Norway for the plume of CO2 which developed in Horizon 1.

Statistical analysis of transitional boundary layers in pressure gradients is performed using the flow fields from direct numerical simulations of bypass transition. Laminar–turbulent discrimination separates the streaky laminar flow from turbulent regions. Individual streaks are identified and tracked in the flow field in order to obtain statistics of the amplitude of the streak population. An extreme value model is proposed for the distribution of streak amplitudes. It is also possible to differentiate those streaks which break down into turbulent spots from innocuous events. It is shown that turbulence onset is due to high-amplitude streaks, with streamwise perturbation velocity exceeding 20 % of the free stream speed. The resulting turbulent spots are tracked downstream. The current analysis allows for the measurement of the lateral spreading angles of individual spots and their spatial extent and volumes. It is demonstrated that the volumetric growth rate of turbulent spots is insensitive to pressure gradient.

The two-dimensional vortices characterizing the bottom boundary layer of both progressive and solitary waves, recently discovered by experimental flow visualizations and referred to as vortex tubes, are studied by numerical solution of the governing equations. In the case of progressive waves, the Reynolds numbers investigated belong to the subcritical range, according to Floquet linear stability theory. In such a range the periodic generation of strictly two-dimensional vortex structures is not a self-sustaining phenomenon, being the presence of appropriate ambient disturbances necessary to excite certain modes through a receptivity mechanism. In a physical experiment such disturbances may arise from several coexisting sources, among which the most likely is roughness. Therefore, in the present numerical simulations, wall imperfections of small amplitude are introduced as a source of disturbances for both types of wave, but from a macroscopic point of view the wall can be regarded as flat. The simulations show that even wall imperfections of small amplitude may cause flow instability and lead to the appearance of vortex tubes. These vortices, in turn, interact with a vortex layer adjacent to the wall and characterized by vorticity opposite to that of the vortex tubes. In a first stage such interaction gives rise to corrugation of the vortex layer and this affects the spatial distribution of the wall shear stress. In a second stage the vortex layer rolls up and pairs of counter-rotating vortices are generated, which leave the bottom because of the self-induced velocity.

In this paper direct numerical evidence of flow-induced incipient cavitation is presented through lattice Boltzmann simulations of multiphase flows with a non-ideal thermodynamic equation of state. Cavitation emerges spontaneously as a result of the underlying non-ideal interactions, with no need for any modelling criteria based on the fluid variables, such as pressure or stress tensor. The onset of cavitation is well captured by Joseph’s minimum tension criteria, (Joseph, J. Fluid Mech., vol. 366, 1998, pp. 367–378; Dabiri, Sirignano & Joseph, Phys. Fluids, vol. 19, 2007, 072112), complemented with surface tension corrections, as proposed by Brennen (Cavitation and Bubble Dynamics, Oxford University Press, 1995). The simulations also show that the cavitation number (${C}_{N} $) proves to be a poor predictor of the onset of cavitation. Finally, strong dependence of the bubble morphology on the surface tension is also highlighted.

Measurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers $R{e}_{\tau } \gt 20\hspace{0.167em} 000$, the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ∼100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.

Lagrangian coherent structures (LCS) of a turbulent boundary layer at ${\mathit{Re}}_{\theta } $ of 9800 are identified in a plane parallel to the wall at ${y}^{+ } = 50$. Three-component high-speed stereo particle image velocimetry measurements on a two-dimensional rectangular plane are used for the analysis. The velocity field is extended in the streamwise direction, using Taylor’s frozen field hypothesis. A computational approach utilizing the variational theory of hyperbolic Lagrangian coherent structures is applied to the domain and trajectories are computed using the extended field. The method identified both attracting and repelling Lagrangian coherent structures. There are no apparent differences in distribution of size, orientation and location of attracting and repelling structures. Hyperbolic behaviour appeared in the fluid at and around points of intersection between the attracting and repelling Lagrangian coherent structures. The network of curves identifying distinct regions of coherent flow patterns is displayed in observed relationship between the arrangement of Lagrangian coherent structures and various Eulerian fields.

The flow structure and turbulence in an open cavity shear layer has been investigated experimentally at a Reynolds number of $4. 0\times 1{0}^{4} $, with an emphasis on interactions of the unsteady pressure field with the cavity corners. A large database of time-resolved two-dimensional PIV measurements has been used to obtain the velocity distributions and calculate the pressure by spatially integrating the material acceleration at a series of sample areas covering the entire shear layer and the flow surrounding the corners. Conditional sampling, low-pass filtering and time correlations among variables enable us to elucidate several processes, which have distinctly different frequency ranges, that dominate the shear layer interactions with the corners. Kelvin–Helmholtz shear layer eddies have the expected Strouhal number range of 0.5–3.2. Their interactions with the trailing corner introduce two sources of vorticity fluctuations above the corner. The first is caused by the expected advection of remnants of the shear layer eddies. The second source involves fluctuations in local viscous vorticity flux away from the wall caused by periodic variations in the streamwise pressure gradients. This local production peaks when the shear layer vortices are located away from the corner, creating a lingering region with peak vorticity just above the corner. The associated periodic pressure minima there are lower than any other point in the entire flow field, making the region above the corner most prone to cavitation inception. Flapping of the shear layer and boundary layer upstream of the leading corner occurs at very low Strouhal numbers of ∼0.05, affecting all the flow and turbulence quantities around both corners. Time-dependent correlations of the shear layer elevation show that the flapping starts in the boundary layer upstream of the leading corner and propagates downstream at the free stream speed. Near the trailing corner, when the shear layer elevation is low, the stagnation pressure in front of the wall, the downward jetting flow along this wall, the fraction of shear layer vorticity entrained back into the cavity, and the magnitude of the pressure minimum above the corner are higher than those measured when the shear layer is high. However, the variations in downward jetting decay rapidly with increasing distance from the trailing corner, indicating that it does not play a direct role in a feedback mechanism that sustains the flapping. There is also low correlation between the boundary/shear layer elevation and the returning flow along the upstream vertical wall, providing little evidence that this returning flow affects the flapping directly. However, the characteristic period of flapping, ∼0.6 s, is consistent with recirculation time of the fluid within the cavity away from boundaries. The high negative correlations of shear/boundary layer elevation with the streamwise pressure gradient above the leading corner introduce a plausible mechanism that sustains the flapping: when the shear layer is low, the boundary layer is subjected to high adverse streamwise pressure gradients that force it to widen, and when the shear layer is high, the pressure gradients decrease, allowing the boundary layer to thin down. Flow mechanisms that would cause the flapping-induced pressure changes, and their relations to the flow within the cavity are discussed.

We present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette flow below the centrifugal instability threshold of circular Couette flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette flow (Abshagen et al., Phys. Fluids, vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.

A study on the axisymmetric near-contact motion of drops with tangentially mobile interfaces under the action of a body force in a quiescent fluid is described. A long-time asymptotic analysis is presented for small-deformation conditions. Under these conditions the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. According to our analysis, a hydrostatic dome does not form in the near-contact region at long times, in contrast to the assumption underlying all previous analyses of this problem. Instead, the shape of the film in the near-contact region results from the absence of tangential stresses acting on it. As a result, the long-time behaviour of the system is qualitatively different than previously predicted. According to the theory presented herein, the minimum film thickness (rim region) decays with time as ${h}_{m} \sim {t}^{- 4/ 5} $, and the thickness at the centre of the film decays as ${h}_{0} \sim {t}^{- 3/ 5} $, which is a faster decay than predicted by prior analyses based on a hydrostatic dome. Numerical thin-film simulations quantitatively confirm the predictions of our small-deformation theory. Boundary-integral simulations of the full two-drop problem suggest that the theory also describes qualitatively the long-time evolution under finite-deformation conditions.

We present an experimental investigation of the dynamics and flow coupling of convective turbulent flows in a cylindrical Rayleigh–Bénard convection (RBC) cell with two immiscible fluids, water and Fluorinert FC-77 electronic liquid (FC77). With the lighter water above FC77, the latter is under the condition of constant heat flux at its top and bottom boundaries. It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by ${\sim }\mathrm{\pi} $. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (the flow directions of the two LSCs are opposite to each other at the fluid–fluid interface) and viscous coupling (the flow directions of the two LSCs are the same at the fluid–fluid interface), are identified, with the former as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remains unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric.