This contribution is a remake of the one published under the same title by Reynolds (Nord. Hydrol., vol. 7, 1976, pp. 161–183). As in that paper, attention is given to the latest developments in the field of river morphodynamics and, in particular, on the formation of bed patterns. Stimulated by the work by Kidanemariam and Uhlmann (J. Fluid Mech., vol. 750, 2014, R2) the opportunity is taken to examine the most recent developments in terms of sediment transport models.

The scales of fast-swimming sharks contain riblet structures with microgrooves, aligned in the direction of fluid flow, that result in water moving efficiently over the surface. In previous studies, these riblet structures have shown a drag reduction of up to 10 % when compared with a smooth, flat surface. These studies have suggested two prevalent drag-reduction mechanisms which involve the effect of vortices and turbulence fluctuations. To further explore relevant mechanisms and study the effect of riblet geometry and flow properties on drag, vortices and turbulence fluctuations, various shark-skin-inspired riblet structures were created using computational models in which velocity, viscosity, spacing, height and thickness parameters were independently modified. A relevant mechanism of drag reduction is discussed to relate riblet parameters and flow properties to drag change and vortex size. Modelling information will lead to a better understanding of riblets and allow for optimum drag-reducing designs for applications in marine, medical and industrial fields.

The space–time characteristics of a compliant wall in a turbulent channel flow are investigated using direct numerical simulation (DNS). The compliant wall is modelled as a homogeneous plane supported by spring-and-damper arrays and is passively driven by wall-pressure fluctuations. The frequency/wavenumber spectra and convection velocities of the wall-pressure fluctuations, wall displacement and wall velocity are obtained from the present simulation. As the spring, damping, and tension coefficients decrease, the wall becomes softer and the wall displacement and velocity fluctuations increase. For a relatively stiff compliant wall (i.e. large spring, damping and streamwise tension coefficients), there are few changes in the skin-friction drag and near-wall turbulence structures. However, when a compliant wall is soft (i.e. small spring, damping and streamwise tension coefficients), the wall moves in the form of a large-amplitude quasi-two-dimensional wave travelling in the downstream direction. This wave is generated by the resonance of the wall property and the near-wall flow is significantly activated by this wall motion. The power spectra of wall variables show distinct peaks near the resonance frequencies. The convection velocities of the wall motion and wall-pressure fluctuations become smaller with a softer wall.

It is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

In this article, a two-layer vertical equilibrium model for the injection of carbon dioxide into a low-pressure porous reservoir containing methane and water is developed. The dependent variables solved for include pressure, temperature and $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathrm{CO}}_2$–${\mathrm{CH}}_4$ interface height. In contrast to previous two-layer vertical equilibrium models in this context, the compressibility of all material components is fully accounted for. Non-Darcy effects are also considered using the Forchheimer equation. The results show that, for a given injection scenario, as the initial pressure in the reservoir decreases, both the pressure buildup and temperature change increase. A comparison was conducted between a fully coupled non-isothermal numerical model and a simplified model where fluid properties are held constant with temperature. This simplified model was found to provide an excellent approximation when using the injection fluid temperature for calculating fluid properties, even when the injection fluid was as much as $\pm 15\, ^\circ \mathrm{C}$ of the initial reservoir temperature. The implications are that isothermal models can be expected to provide useful estimates of pressure buildup in this context. Despite the low viscosity of ${\mathrm{CO}}_2$ at the low pressures studied, non-Darcy effects were found to be of negligible concern throughout the sensitivity analysis undertaken. This is because the ${\mathrm{CO}}_2$ density is also low in this context. Based on these findings, simplified analytic solutions are derived, which accurately calculate both the pressure buildup and temperature decline during the injection period.

A new model to account for the presence of the test-section wall in wind-turbine or propeller measurements is proposed. The test section, here assumed to be cylindrical, is modelled by means of axisymmetric source panels, while the wind turbine (or the propeller) is modelled with a simplified vortex model (Segalini & Alfredsson, J. Fluid Mech., vol. 725, 2013, pp. 91–116). Combining both models in an iterative scheme allows the simulation of the effect of the test-section wall on the flow field around the rotor. Based on this novel approach, an analysis of the flow modification due to blockage is conducted together with a comparison of actuator-disk theory results. Glauert’s concept of equivalent unconfined turbine is reviewed and extended to account for the angular velocity of the rotor. It is shown that Glauert’s equivalent free-stream velocity concept is beneficial and can correct most of the systematic error introduced by the presence of the test-section wall, although some discrepancies remain, especially in the power coefficient. The effect of the confinement on the wake structure is also discussed in terms of wake expansion/contraction, pitch of the tip vortices and forces at the rotor.

Air curtains are used to reduce the heat and mass exchange across open doorways. Their sealing ability is assessed in terms of the effectiveness $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E$, the fraction of the exchange flow prevented by the air curtain compared to an unobstructed open door. Previous work has studied air-curtain effectiveness when the doorway is the only means of ventilating a space. In this paper, we examine the effects of additional displacement ventilation on the dynamics of the air curtain and the resulting changes in its effectiveness. The main controlling parameter is the deflection modulus $D_{m}$, which is the ratio between the momentum flux of the air curtain and the transverse forces due to the displacement ventilation. For a relatively warm interior, we find that, for small values of $D_{m}$, the air curtain is drawn inside the space by the ventilation flow. For large values of $D_{m}$, the flow through the doorway is controlled by the air curtain. A smooth transition occurs between these two regimes, and we estimate the $D_{m}$ value for the onset of this transition. Our model provides a quantitative prediction of $E(D_{m})$ in the ventilation-driven regime, and gives a qualitative description of the other two regimes. Laboratory experiments were conducted to test the proposed model. The experimental data were compared to theoretical predictions, and good agreement was found.

In this study we undertook various calculations of the turbulent flow around a building in close proximity to neighbouring obstacles, with the aim of gaining an understanding of the velocity and the surface-pressure variations with respect to the azimuth angle of wind direction and the gap distance between the obstacles. This paper presents the effects of flow interference among consecutive cubes for azimuth angles of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta = 0$, 15, 30, and $45^{\circ }$ and gap distances of $G = 0.5{h}, 1.0{h}, 1.5{h}$, and $\infty $ (i.e. a single cube), where $h$ is the cube height, placed in a turbulent boundary layer. A transient detached eddy simulation (DES) was carried out to calculate the highly complicated flow domain around the three wall-mounted cubes to observe the fluctuating pressure, which substantially contributes to the suction pressure when there is separation and reattachment around the leading and trailing edges of the cubes. In addition, the results indicate that an increasing azimuth angle increases the pressure variation on the centre cube of the three parallel-aligned cubes. The mean pressure variation can even change from negative to positive on the side face. Owing to interference effects, the mean pressure coefficient of the centre cube of the three parallel-aligned cubes was generally lower than the coefficient of the single cube and tended to increase depending on the gap distance. Furthermore, when the three consecutive cubes are in a tandem arrangement, the gap distance has little influence on the first cube but results in significant interference effects on the second and third cubes.

Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon.

We report our systematic development of a general and exact theory for diagnosis of total force and moment exerted on a generic body moving and deforming in a calorically perfect gas. The total force and moment consist of a longitudinal part (L-force) due to compressibility and irreversible thermodynamics, and a transverse part (T-force) due to shearing. The latter exists in incompressible flow but is now modulated by the former. The theory represents a full extension of a unified incompressible diagnosis theory of the same type developed by J. Z. Wu and coworkers to compressible flow, with Mach number ranging from low-subsonic to moderate-supersonic flows. Combined with computational fluid dynamics (CFD) simulation, the theory permits quantitative identification of various complex flow structures and processes responsible for the forces, and thereby enables rational optimal configuration design and flow control. The theory is confirmed by a numerical simulation of circular-cylinder flow in the range of free-stream Mach number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_{\infty }$ between 0.2 and 2.0. The L-drag and T-drag of the cylinder vary with $M_{\infty }$ in different ways, the underlying physical mechanisms of which are analysed. Moreover, each L-force and T-force integrand contains a universal factor of local Mach number $M$. Our preliminary tests suggest that the possibility of finding new similarity rules for each force constituent could be quite promising.

An experimental study of turbulence generated by a low-blockage space-filling fractal square grid was performed using cinematographic stereoscopic particle image velocimetry in a water tunnel. All fluctuating velocity gradients were measured and their statistics were computed at three different stations along the streamwise direction downstream of the grid: in the production region, at the location of peak turbulence intensity and in the non-equilibrium decay region. The usual signatures of these statistics are only found in the decay region, where a well-defined $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2/3$ power-law dependence of the second-order structure function on two-point distance is also present. However, this $2/3$ exponent is well defined over a wide range of scales even at the peak location, where the statistics of the fluctuating velocity-gradient tensor are very unusual. There, as at the production region station, the $Q\text {--}R$ teardrop shape is not yet fully developed, vortex stretching only slightly dominates over compression and they both fluctuate very widely, reaching very high low-probability values. In these two stations, there is also only marginal preference between sheet-like and tube-like velocity-gradient structures as seen by the sign of the second eigenvalue of the strain-rate tensor. Yet, there are subregions of the flow in the production region where the $2/3$ exponent is present and where the $Q\text {--}R$ teardrop shape is as undeveloped as for the entire data set at this station.

We report on the influence of a quasi-one-dimensional periodic forcing on the pattern selection process in Rayleigh–Bénard convection (RBC). The forcing was introduced by a lithographically fabricated periodic texture on the bottom plate. We study the convection patterns as a function of the Rayleigh number ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ra}$) and the dimensionless forcing wavenumber ($q_f$). For small $\mathit{Ra}$, convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing $\mathit{Ra}$, these rolls give way to more complex patterns, due to a secondary instability. The forcing wavenumber $q_f$ was varied in the experiment over the range of $0.6q_c<q_f<1.4q_c$, with $q_c$ being the critical wavenumber of the unforced system. We investigate the stability of straight rolls as a function of $q_f$ and report patterns that arise due to a secondary instability.

This paper looks at the two-layer ocean model from a wave-turbulence (WT) perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It is already well known that in two-layers, energy is transferred via triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale, where barotropization takes place, and from there to the large-scale barotropic modes via an inverse transfer. However, by applying WT theory, we find that energy is transferred via dominant $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\{+--\}$ triads with one barotropic component and two baroclinic components, and that the direct transfer of energy is local and the inverse energy transfer is non-local. We study this non-locality using scale separation and obtain a system of coupled equations for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. Using the frequency resonance condition, we show that in the presence of the beta-effect this transfer is mostly anisotropic and mostly to the zonal component.

The interaction between two separated flow regions was studied for the fundamental problem of a shock wave–boundary layer interaction (SBLI) within a rectangular inlet. One motivation is that the inlet of an engine on a supersonic aircraft may contain separation zones on the sidewalls and the bottom wall; if one region separates first it can alter the flow on the other wall and lead to engine unstart. In our work an oblique shock wave was generated by a wedge suspended from the upper wall of a Mach 2.75 wind tunnel. Stereo particle image velocimetry (PIV) measurements were recorded in 25 planes that include all three possible orthogonal orientations. The lateral velocity and vorticity measurements help to explain the underlying flow structure and these quantities were not measured previously for this problem. It is concluded that the sidewall and bottom wall separation zones interact due to an underlying flow structure that is similar to the two types of 3-D separation patterns previously described by Tobak & Peake (Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 61–85). Separation first occurs at an upstream location where the shock interacts with the sidewall. Lateral velocities direct flow toward the centreline to cause separation on the bottom wall. This causes significant curvature of the shock wave, so that even the region near the tunnel centreline cannot be explained by conventional 2-D concepts. A number of critical points (saddle points, nodes, focus points) were identified. Results are consistent with the general ideas of Burton & Babinsky (J. Fluid Mech., vol. 707, 2012, pp. 287–306) and help to provide details of how the sidewalls redistribute the adverse pressure gradient in space.

A technique of particle image velocimetry is employed to characterize the three-dimensional flow structure on a wing subjected to simultaneous pitch-up and rotational motions. Distinctive vortical structures arise, relative to the well-known patterns on a wing undergoing either pure pitch-up or pure rotation. The features associated with these simultaneous motions include: stabilization of the large-scale vortex generated at the leading edge, which, for pure pitch-up motion, rapidly departs from the leading-edge region; preservation of the coherent vortex system involving both the tip vortex and the leading-edge vortex (LEV), which is severely degraded for pure rotational motion; and rapid relaxation of the flow structure upon termination of the pitch-up component, whereby the relaxed flow converges to a similar state irrespective of the pitch rate. Three-dimensional surfaces of iso-$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{Q}$ and helicity are employed in conjunction with sectional representations of spanwise vorticity, velocity and vorticity flux to interpret the flow physics.

Experiments have been performed on the disturbance of a high-Reynolds-number turbulent boundary layer by three forward steps with sizes close to 3.8, 15 and 60 % of the boundary layer thickness. Particular attention is focused on the impact of the steps on the fluctuating surface pressure field. Measurements were made from 5 boundary layer thicknesses upstream to 22 boundary layer thicknesses downstream of the step, a distance equivalent to over 600 step heights for the smallest step size. Flow speeds of 30 and $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}60\ \mathrm{m}\ {\mathrm{s}}^{-1}$ were studied, corresponding to boundary layer momentum thickness Reynolds numbers of 15 500 and 26 600 and step size Reynolds numbers from 6640 to 213 000. The steps produce a disturbance to the boundary layer pressure spectrum that scales on step size and decays remarkably slowly with distance downstream. When normalized on step height and free-stream velocity, the disturbance is self-similar and appears to develop almost independently of the enveloping boundary layer. The disturbance is still clearly visible at 150 step heights downstream of the mid-size step. Pressure correlations show the disturbance to be characterized by organized quasiperiodic motions that become visible well downstream of reattachment. The coherence and scale of these motions, as seen in the wall pressure correlations, scales on the step height and thus their visibility relative to the boundary layer grows rapidly as the step size is increased.

The noise of flow over tandem cylinders at $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_D= 22\, 000$ and its reduction using single dielectric barrier discharge (SDBD) plasma actuators are simulated numerically both to confirm and extend experimental results. The numerical approach is based on large-eddy simulation (LES) for the turbulent flow field, a semi-empirical plasma actuation model, and Lighthill’s theory for acoustic calculation. Excellent agreement between LES and experimental results is obtained for both the baseline flow and flow with plasma control in terms of wake velocity profiles, turbulence intensity, and frequency spectra of pressure fluctuations on the downstream cylinder. The validated flow-field results allow an accurate acoustic analysis based on Lighthill’s equation, which is solved using a boundary-element method. The effectiveness of plasma actuators for reducing noise is clearly demonstrated. In the baseline flow, the acoustic field is dominated by the interaction between the downstream cylinder and the upstream wake. Through suppression of vortex shedding from the upstream cylinder, the interaction noise is reduced drastically by the plasma flow control, and the vortex-shedding noise from the downstream cylinder becomes equally important. At a free-stream Mach number of 0.2, the peak sound pressure level is reduced by approximately 16 dB. This suggests the viability of plasma actuation for active aeroacoustic control of airframe noise.

We investigate three-dimensional (laminar) boundary layers that include a spanwise scale comparable to the boundary-layer thickness. A forcing of short spanwise scales requires viscous dissipation to be retained in the two-dimensional cross-section, perpendicular to the external flow direction, and in this respect the flows are related to previous work on corner boundary layers. We use two examples to highlight the main features of this category of boundary layer: (i) a flat plate of narrow (spanwise) width, and (ii) a narrow (spanwise) gap cut into an otherwise infinite flat plate; in both cases the plate is aligned with a uniform oncoming stream. We find that a novel feature arises in connection with the external flow; the presence of a narrow gap/plate (or indeed any comparable short-scale feature of long streamwise extent) necessarily modifies the streamwise mass flux in that vicinity, which in turn induces an associated boundary-layer transpiration on the same short spanwise length scale. This (short-scale) transpiration region leads to a half-line-source/sink correction to the outer inviscid, irrotational flow. Crucially, the volumetric flux associated with this line-source/sink must be explicitly included as part of the computational procedure for the leading-order boundary layer, and as such there is a weak interaction between the outer (inviscid) flow and the boundary layer. This is a generic feature of boundary layers that are forced through the presence of short-scale spanwise variations.

The dynamic transition from combustion noise to combustion instability was investigated experimentally in two laboratory-scale turbulent combustors (namely, swirl-stabilized and bluff-body-stabilized backward-facing-step combustors) by systematically varying the flow Reynolds number. We observe that the onset of combustion-driven oscillations is always presaged by intermittent bursts of high-amplitude periodic oscillations that appear in a near-random fashion amidst regions of aperiodic low-amplitude fluctuations. These excursions to periodic oscillations last longer in time as operating conditions approach instability and finally the system transitions completely into periodic oscillations. A continuous measure to quantify this bifurcation in dynamics can be obtained by defining an order parameter as the probability of the signal amplitude exceeding a predefined threshold. A hysteresis zone was observed in the bluff-body-stabilized configuration that was absent in the swirl-stabilized configuration. The recurrence properties of the dynamics of intermittent burst oscillations were quantified using recurrence plots and the distribution of the aperiodic phases was examined. From the statistics of these aperiodic phases, robust early-warning signals of an impending combustion instability may be obtained.

Localized patches of turbulence frequently occur in geophysics, such as in the atmosphere and oceans. The effect of rotation, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\boldsymbol{\Omega}$, on such a region (a ‘turbulent cloud’) is governed by inhomogeneous dynamics. In contrast, most investigations of rotating turbulence deal with the homogeneous case, although inhomogeneous turbulence is more common in practice. In this paper, we describe the results of $512^3$ direct numerical simulations (DNS) of a turbulent cloud under rotation at three Rossby numbers ($\mathit{Ro}$), namely 0.1, 0.3 and 0.5. Using a spatial filter, fully developed homogeneous turbulence is vertically confined to the centre of a periodic box before the rotation is turned on. Energy isosurfaces show that columnar structures emerge from the cloud and grow into the adjacent quiescent fluid. Helicity is used as a diagnostic and confirms that these structures are formed by inertial waves. In particular, it is observed that structures growing parallel to the rotation axis (upwards) have negative helicity and those moving antiparallel (downwards) to the axis have positive helicity, a characteristic typical of inertial waves. Two-dimensional energy spectra of horizontal wavenumbers, $k_{\perp }$, versus dimensionless time, $2 \varOmega t$, confirm that these columnar structures are wavepackets which travel at the group velocities of inertial waves. The kinetic energy transferred from the turbulent cloud to the waves is estimated using Lagrangian particle tracking to distinguish between turbulent and ‘wave-only’ regions of space. The amount of energy transferred to waves is 40 % of the initial at $\mathit{Ro}=0.1$, while it is 16 % at $\mathit{Ro}=0.5$. In both cases the bulk of the energy eventually resides in the waves. It is evident from this observation that inertial waves can carry a significant portion of the energy away from a localized turbulent source and are therefore an efficient mechanism of energy dispersion.