Wave forecasting in ocean and coastal waters commonly relies on spectral models based on the spectral action balance equation. These models assume that different wave components are statistically independent and as a consequence cannot resolve wave interference due to statistical correlation between crossing waves, as may be found in, for instance, a focal zone. This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components. To this end, the quasi-coherent model (Smit & Janssen, J. Phys. Oceanogr., vol. 43, 2013, pp. 1741–1758) is extended to allow for wave–current interactions. The outcome is a generalized action balance model that predicts the evolution of the wave statistics over variable media, while preserving the effect of wave interferences. Two classical examples of wave–current interaction are considered to demonstrate the statistical contribution of wave interferences: (1) swell field propagation over a jet-like current and (2) the interaction of swell waves with a vortex ring. In both examples cross-correlation terms lead to development of prominent interference structures, which significantly change the wave statistics. Comparison with results of the SWAN model demonstrates that retention of cross-correlation terms is essential for accurate prediction of wave statistics in shear-current-induced focal zones.

In this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy–Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated by integrating the pressure along the pipeline. Through appropriate transformation, we show the difference between the Darcy–Weisbach equation and the improved model that should be treated as a Darcy–Weisbach model error, in multiplicative and additive form. This error increases when the overall pressure drop increases. This symptomatic phenomenon is discussed in detail. In addition, we also consider four methods of estimating the coefficient of friction, assess the impact of pressure difference on the estimated average flow velocity and, based on experimental data, we show the usefulness of new proposals in various applications.

Direct numerical simulation of the Navier–Stokes equations has been used to investigate the Taylor–Couette flow with an imposed pulsatile axial pressure gradient resulting in a spiral Poiseuille flow modulated by an oscillating forcing. Keeping the Reynolds and Taylor numbers constant, both the amplitude and frequency of the oscillating component are varied to span a small region of the phase space. In the narrow-gap geometry considered in this study, the base flow (spiral Poiseuille flow) is in the turbulent regime whereas the oscillating component is laminar. It has been found that the effect of the oscillation is to induce a global flow laminarization provided the frequency is sufficiently small (at constant amplitude) or the amplitude is sufficiently large (at constant frequency). The coupling between steady and oscillating components has been analysed with the help of long-time and phase-averaged statistics. The reverse transition mechanism has been associated to an anisotropic modification of the Reynolds stress tensor components, which has been shown to be caused by an alteration of the pressure–strain interaction.

We use a multiple-scale expansion to average the wave action balance equation over an ensemble of sea-surface velocity fields characteristic of the ocean mesoscale and submesoscale. Assuming that the statistical properties of the flow are stationary and homogeneous, we derive an expression for a diffusivity tensor of surface-wave action density. The small parameter in this expansion is the ratio of surface current speed to gravity wave group speed. For isotropic currents, the action diffusivity is expressed in terms of the kinetic energy spectrum of the flow. A Helmholtz decomposition of the sea-surface currents into solenoidal (vortical) and potential (divergent) components shows that, to leading order, the potential component of the surface velocity field has no effect on the diffusivity of wave action: only the vortical component of the sea-surface velocity results in diffusion of surface-wave action. We validate our analytic results for the action diffusivity by Monte Carlo ray-tracing simulations through an ensemble of stochastic velocity fields.

We study the equilibrium of two phases following gravity segregation under the influence of capillary heterogeneity. Such processes are important in a number of porous media applications, e.g. determining reservoir composition, secondary migration, gravity drainage enhanced oil recovery and CO$_{2}$ storage in aquifers. Solutions are derived for three-dimensional saturation distribution $S_{w}(x,y,z)$ and given as an analytical formula apart from a constant $P_{c}^{0}$ which is determined by numerical integration. The first solution assumes hydrostatic pressure and applies to cases without capillary entry pressure ($P_{c}(S_{w}=1)=0$). The solution can be used for validation of numerical simulations and we show a close match for a number of cases. A second analytical solution is derived, extending the first, to cases of random log-normally distributed permeability fields. A formula for ensemble average saturation solution is presented and a comparison to solutions of various realizations is discussed. When capillary entry pressure is present, the solution based on hydrostatic pressure may be inaccurate due to entry pressure trapping which occurs when regions of $S_{w}=1$ are present. Using numerical simulation, we extend the solution to include estimations of entry pressure trapping for a range of parameters and show its applicability. The comparison of analytical and numerical results helps illustrate and draw insight on the trapping mechanism.

The permanent precession of a baroclinic geophysical vortex is reproduced, under the quasi-geostrophic approximation, using three potential vorticity anomaly modes in spherical geometry. The potential vorticity modes involve the spherical Bessel functions of the first kind $\text{j}_{l}(\unicode[STIX]{x1D70C})$ and the spherical harmonics $\text{Y}_{l}^{m}(\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$, where $l$ is the degree, $m$ is the order, and $(\unicode[STIX]{x1D70C},\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ are the spherical coordinates. The vortex precession is interpreted as the horizontal and circular advection by a large-amplitude background flow associated with the spherical mode $c_{0}\text{j}_{0}(\unicode[STIX]{x1D70C})$ of the small-amplitude zonal mode $c_{2,0}\text{j}_{2}(\unicode[STIX]{x1D70C})\text{Y}_{2}^{0}(\unicode[STIX]{x1D703})$ tilted by a small-amplitude mode $c_{2,1}\text{j}_{2}(\unicode[STIX]{x1D70C})\text{Y}_{2}^{1}(\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$, where $\{c_{0},c_{2,0},c_{2,1}\}$ are constant potential vorticity modal amplitudes. An approximate time-dependent, closed-form solution for the potential vorticity anomaly is given. In this solution the motion of the potential vorticity field is periodic but not rigid. The vortex precession frequency $\unicode[STIX]{x1D714}_{0}$ depends linearly on the amplitudes $c_{0}$ and $c_{2,0}$ of the modal components of order 0, while the slope of the precessing axis depends on the ratio between the modal amplitude $c_{2,1}$ and $\unicode[STIX]{x1D714}_{0}$.

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.

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.

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 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.

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.

The stability of the jet in cross-flow is investigated using a complete set-up including the flow inside the pipe. First, direct simulations were performed to find the critical velocity ratio as a function of the Reynolds number, keeping the boundary-layer displacement thickness fixed. At all Reynolds numbers investigated, there exists a steady regime at low velocity ratios. As the velocity ratio is increased, a bifurcation to a limit cycle composed of hairpin vortices is observed. The critical bulk velocity ratio is found at approximately $R=0.37$ for the Reynolds number $Re_{D}=495$, above which a global mode of the system becomes unstable. An impulse response analysis was performed and characteristics of the generated wave packets were analysed, which confirmed results of our global mode analysis. In order to study the sensitivity of this flow, we performed transient growth computations and also computed the optimal periodic forcing and its response. Even well below this stability limit, at $R=0.3$, large transient growth ($10^{9}$ in energy amplification) is possible and the resolvent norm of the linearized Navier–Stokes operator peaks above $2\times 10^{6}$. This is accompanied with an extreme sensitivity of the spectrum to numerical details, making the computation of a few tens of eigenvalues close to the limit of what can be achieved with double precision arithmetic. We demonstrate that including the meshing of the jet pipe in the simulations does not change qualitatively the dynamics of the flow when compared to the simple Dirichlet boundary condition representing the jet velocity profile. This is in agreement with the recent experimental results of Klotz et al. (J. Fluid Mech., vol. 863, 2019, pp. 386–406) and in contrast to previous studies of Cambonie & Aider (Phys. Fluids, vol. 26, 2014, 084101). Our simulations also show that a small amount of noise at subcritical velocity ratios may trigger the shedding of hairpin vortices.

We present an investigation on the onset of Darcy–Bénard instability in a two-dimensional porous medium saturated with a non-Newtonian fluid and heated from below in the presence of a uniform horizontal pressure gradient. The fluid is taken to be of power-law nature with constant rheological index $n$ and temperature-dependent consistency index $\unicode[STIX]{x1D707}^{\ast }$. A two-dimensional linear stability analysis in the vertical plane yields the critical wavenumber and the generalised critical Rayleigh number as functions of dimensionless problem parameters, with a non-monotonic dependence from $n$ and with maxima/minima at given values of $\unicode[STIX]{x1D6FE}$, a parameter representing the effects of consistency index variations due to temperature. A series of experiments are conducted in a Hele-Shaw cell of aspect ratio $H/b=13.3{-}20$ to provide a verification of the theory. Xanthan Gum mixtures (nominal concentration from 0.10 % to 0.20 %) are employed as working fluids with a parameter range $n=0.55{-}0.72$ and $\unicode[STIX]{x1D707}_{0}^{\ast }=0.02{-}0.10~\text{Pa}~\text{s}^{n}$. The experimental critical wavenumber corresponding to incipient instability of the convective cells is derived via image analysis for different values of the imposed horizontal velocity. Theoretical results for critical wavenumber favourably compare with experiments, systematically underestimating their experimental counterparts by 10 % at most. The discrepancy between experiments and theory is more relevant for the critical Rayleigh number, with theory overestimating the experiments by a maximum factor less than two. Discrepancies are attributable to a combination of factors: nonlinear phenomena, possible subcritical bifurcations, and unaccounted-for disturbing effects such as approximations in the rheological model, wall slip, ageing and degradation of the fluid properties.

Although the process of hydrodynamic dispersion has been studied for many years, the description of solute spreading at early times has proved to be challenging. In particular, for some kinds of initial conditions, the solute evolution may exhibit a second moment that decreases (rather than increases, as is typically observed) in time. Most classical approaches would predict a negative effective hydrodynamic dispersion coefficient for such a situation. This creates some difficulties: not only does a negative dispersion coefficient lead to a violation of the second law of thermodynamics, but it also creates a mathematically ill-posed problem. We outline a set of four desirable qualities in a well-structured theory of unsteady dispersion as follows: (i) positivity of the dispersion coefficient, (ii) non-dependence upon initial conditions, (iii) superposability of solutions and (iv) convergence of solutions to classical asymptotic results. We use averaging to develop an upscaled result that adheres to these qualities. We find that the upscaled equation contains a source term that accounts for the relaxation of the initial configuration. This term decreases exponentially fast in time, leading to correct asymptotic behaviour while also accounting for the early-time solute dynamics. Analytical solutions are presented for both the effective dispersion coefficient and the source term, and we compare our upscaled results with averaged solutions obtained from numerical simulations; both averaged concentrations and spatial moments are compared. Error estimates are quantified, and we find good correspondence between the upscaled theory and the numerical results for all times.

We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

Quantifying accidental opaque discharges is a challenging task, since probing beyond their visible interfaces may be difficult or impossible. In this case, we show that the visible interface features near the jet exit can be used to gauge the flow. This work examines the interface in the near-field features of submerged homogeneous and immiscible turbulent jets. Experiments were carried out with water jets and immiscible silicone oil jets of two viscosities in a water tank. The jet Reynolds numbers are in the range of $Re\sim 4500{-}50\,000$ for homogeneous water jets and $Re\sim 3500{-}27\,000$ for silicone oil jets in water. The jet fluids are made visible by doping with fluorescent dye and excitation with directional illumination. The jet interfaces are continuous and convoluted for water jets, while convoluted and discontinuous with droplets and ligaments for oil jets. Direct flow visualization, schlieren photography, shadowgraph photography and particle image velocimetry are employed as appropriate. Interface length scales are characterized using various image processing techniques. Droplet sizes are quantified using Hough transformation. Interface length scales decrease with Reynolds number and increase gradually with distance from the exit plane for a given Reynolds number. These scales are isotropic for the homogeneous water jets and exhibit a streamwise-to-cross-stream ratio of approximately 1.3 for the oil jets. Interfacial tension, hence the Weber number, determines the average droplet size in the immiscible jets.

A planar jet issuing from a fully developed two-dimensional turbulent channel flow is studied, with a focus on the transverse flapping of the jet core. The streamwise and transverse velocities were measured with hot-wire anemometry using an X-type probe. The mean velocity field and the velocity covariances were first characterised to assess the undisturbed flow field. Periodic excitations were introduced from a slot mounted at the channel exit and the coherent fluctuating part of the signal was obtained by using a phase-locked averaging technique, where the periodic initial forcing was used as trigger. This enabled the eduction of the coherent structure associated with the introduced perturbation. Its amplitude was found to be directly proportional to the intensity of the initial forcing and, within a certain range of the initial forcing amplitude, the growth curves were identical as well as the spatial distribution of the extracted fluctuations. Parallel and non-parallel linear stability theory captures qualitatively and quantitatively the features of the educed coherent structure. The existence of the linear mode in the turbulent jet implies that the large-scale perturbations observed in natural (unforced) jets can be regarded as an incoherent set of linear modes.

The response of asymmetric and planar shock interactions to a continuous excitation of the lower incident shock is investigated numerically. Incident shock waves and centred expansion fans are generated by two wedges asymmetrically deflecting the inviscid free stream flow at Mach 3. The excitations mechanisms considered are (i) pitching of the lower wedge traversing the steady-state dual-solution domain (DSD) of regular interaction (RI) and Mach interaction (MI), (ii) a periodic (sinusoidal) oscillation of the lower wedge deflection with a mean value both within and outside of the steady-state DSD and (iii) a periodic (sinusoidal) streamwise oscillation of the lower wedge location with fixed wedge deflection. A detailed analysis of characteristic unsteady flow features, including the Mach stem growth, pressure evolution across the shock system and corresponding flow deflections and entropy rise, is presented with a focus on the bi-directional RI$\rightleftarrows$MI transition process. For fast pitching conditions, the MI pattern is maintained far inside the steady-state RI domain. The observed $\text{MI}\rightarrow \text{RI}$ transition limit as the rotational velocity decreases does not fully match steady-state theory, however. This is attributed to geometry-related effects. In the opposite case, $\text{RI}\rightarrow \text{MI}$ transition, good agreement with steady-state theoretical predictions is obtained for slow rotations, and a shock polar analysis applied in the (moving) frame of reference of the shock interaction location improves the agreement with fast pitching numerical data significantly. Furthermore, the MI pattern is found to be more robust against periodic perturbations than the corresponding RI configuration for mean flow conditions inside the steady-state DSD, which appears to be a consequence of the dynamics of the Mach stem during a period of excitation. This is not the case for mean flow conditions outside the steady-state DSD in the RI domain for which a periodic $\text{RI}\rightarrow \text{MI}\rightarrow \text{RI}$ alternation occurs instead.

Turbulent flows over dense canopies consisting of rigid filaments of small size are investigated using direct numerical simulations. The effect of the height and spacing of the canopy elements on the flow is studied. The flow is composed of an element-coherent, dispersive flow and an incoherent flow, which includes contributions from the background turbulence and from the flow arising from the Kelvin–Helmholtz-like, mixing-layer instability typically reported over dense canopies. For the present canopies, with spacings $s^{+}\approx 3{-}50$, the background turbulence is essentially precluded from penetrating within the canopy. As the elements are ‘tall’, with height-to-spacing ratios $h/s\gtrsim 1$, the roughness sublayer of the canopy is determined by their spacing, extending to $y\approx 2{-}3s$ above the canopy tips. The dispersive velocity fluctuations are observed to also depend mainly on the spacing, and are small deep within the canopy, where the footprint of the Kelvin–Helmholtz-like instability dominates. The instability is governed by the canopy drag, which sets the shape of the mean velocity profile, and thus the shear length near the canopy tips. For the tall canopies considered here, this drag is governed by the element spacing and width, that is, the planar layout of the canopy. The mixing length, which determines the length scale of the instability, is essentially the sum of its height above and below the canopy tips. The former remains roughly the same in wall units and the latter is linear with $s$ for all the canopies considered. For very small element spacings, $s^{+}\lesssim 10$, the elements obstruct the fluctuations and the instability is inhibited. Within the range of $s^{+}$ of the present canopies, the obstruction decreases with increasing spacing and the signature of the Kelvin–Helmholtz-like rollers intensifies. For sparser canopies, however, the intensification of the instabilities can be expected to cease as the assumption of a spatially homogeneous mean flow would break down. For the present, dense configurations, the canopy depth also has an influence on the development of the instability. For shallow canopies, $h/s\sim 1$, the lack of depth blocks the Kelvin–Helmholtz-like rollers. For deep canopies, $h/s\gtrsim 6$, the rollers do not perceive the bottom wall and the effect of the canopy height on the flow saturates. Some of the effects of the canopy parameters on the instability can be captured by linear analysis.

Turbulent superstructures, i.e. large-scale flow structures in turbulent flows, play a crucial role in many geo- and astrophysical settings. In turbulent Rayleigh–Bénard convection, for example, horizontally extended coherent large-scale convection rolls emerge. Currently, a detailed understanding of the interplay of small-scale turbulent fluctuations and large-scale coherent structures is missing. Here, we investigate the resolved kinetic energy and temperature variance budgets by applying a filtering approach to direct numerical simulations of Rayleigh–Bénard convection at high aspect ratio. In particular, we focus on the energy transfer rate between large-scale flow structures and small-scale fluctuations. We show that the small scales primarily act as a dissipation for the superstructures. However, we find that the height-dependent energy transfer rate has a complex structure with distinct bulk and boundary layer features. Additionally, we observe that the heat transfer between scales mainly occurs close to the thermal boundary layer. Our results clarify the interplay of superstructures and turbulent fluctuations and may help to guide the development of an effective description of large-scale flow features in terms of reduced-order models.