Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al., J. Fluid Mech., vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

In this work, we theoretically investigate the motion of a Taylor swimming sheet immersed in a viscosity-stratified fluid. The propulsion of the swimmer disturbs the surrounding fluid, which influences the transport of the stratifying agent described by the advection–diffusion equation. We employ a regular perturbation scheme to solve the coupled differential equations of motion up to the second order with the small parameter given by the ratio of the wave amplitude and the wavelength. The expression for the swimming velocity is linear in the magnitude of the viscosity gradient, while depending on the Péclet number in a non-monotonic way. Interestingly, we find that the Péclet number governs the propensity of the sheet to propel towards regions of favourable viscosities. In particular, for small Péclet numbers ($0<Pe<3$), the swimmer prefers regions of low viscosity, while for high Péclet numbers ($Pe>3$), the swimmer prefers regions of high viscosity. Our analysis shows that purely hydrodynamic effects might be responsible for the experimentally observed accumulation of swimmers near favourable viscosity regions. We find that viscosity gradients influence other motility characteristics of the swimmer, such as power expenditure and hydrodynamic efficiency, and provide analytical expressions for both.

Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh–Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number $0.025$ and Rayleigh and Hartmann numbers up to $10^{9}$ and $1400$, respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh–Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.

In nonlinear dynamics, there are three classic routes to chaos, namely the period-doubling route, the Ruelle–Takens–Newhouse route and the intermittency route. The first two routes have previously been observed in self-excited thermoacoustic systems, but the third has not. In this experimental study, we present evidence of the intermittency route to chaos in the self-excited regime of a prototypical thermoacoustic system – a laminar flame-driven Rijke tube. We identify the intermittency to be of type II from the Pomeau–Manneville scenario through an analysis of (i) the probability distribution of the quiescent epochs between successive bursts of chaos, (ii) the first return map, and (iii) the recurrence plot. By establishing the last of the three classic routes to chaos, this study strengthens the universality of how strange attractors arise in self-excited thermoacoustic systems, paving the way for the application of generic suppression strategies based on chaos control.

We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh–Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense, these states behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear state may provide an explanation for the strong zonal flows observed recently in experiments and simulations of rapidly rotating convection at high Rayleigh number.

Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulent flows. Through theoretical analyses, we find that there are two channels in the helicity cascade process, which differs dramatically from the traditional viewpoint. In this paper, we have conducted important research on the newly proposed dual-channel helicity cascade theory, including vortex dynamic processes, intermittent discrepancies, tensor geometries, etc. The first channel mainly originates from the vortex twisting process, and the second channel mainly originates from the vortex stretching process. Antisymmetric tensors are introduced to the derivations of dual-channel helicity cascade theory, and a complex rotation frame leads to a higher helicity transfer efficiency. By analysing data from direct numerical simulations of typical turbulent flows, we find that these two channels behave differently. The ensemble averages of helicity flux in different channels are equal in homogeneous and isotropic turbulence, while they are different in other types of turbulent flows. The intermittency of the second channel is stronger than that of the first channel. In addition, we find a novel mechanism of hindered or even inverse energy cascades, which could be attributed to the second-channel helicity flux.

Coasts are obstructions to the classical derivation of continuously stratified quasi-geostrophic equations, due to possible resonances between slow internal coastally trapped Kelvin waves and anticyclones. Deremble et al. (Ocean Model., vol. 119, 2017, pp. 1–12) proposed a coupled model between a quasi-geostrophic interior and boundary-layer Kelvin-wave dynamics. We revisit the derivation of this model, paying particular attention to conservation laws. We find that quasi-geostrophic energy is conserved, despite the existence of Kelvin-wave shocks in the boundary layer. The effect of those shocks is to change the global distribution of potential vorticity, and, consequently, the interior flow structure. In that respect, we show that there is an active control of the boundary region on the interior flow.

We consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If $t$ represents the time since the commencement of motion and $T$ the final time, then the optimum speed profile is $Ct^{1/4}(T-t)^{1/4}$, where $C$ is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves.

Double diffusion occurs when the fluid density depends on two components that diffuse at different rates (e.g. heat and salt in the ocean). Double diffusion can lead to an up-gradient buoyancy flux and drive motion at the expense of potential energy. Here, we follow the work of Lorenz (Tellus, vol. 7 (no. 2), 1955, pp. 157–167) and Winters et al. (J. Fluid Mech., vol. 289, 1995, pp. 115–128) for a single-component fluid and define the background potential energy (BPE) as the energy associated with an adiabatically sorted density field and derive its budget for a double-diffusive fluid. We find that double diffusion can convert BPE into available potential energy (APE), unlike in a single-component fluid, where the transfer of APE to BPE is irreversible. We also derive an evolution equation for the sorted buoyancy in a double-diffusive fluid, extending the work of Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193) and Nakamura (J. Atmos. Sci., vol. 53 (no. 11), 1996, pp. 1524–1537). The criterion we develop for a release of BPE can be used to analyse the energetics of mixing and double diffusion in the ocean and other multiple-component fluids, and we illustrate its application using two-dimensional simulations of salt fingering.

We generalise the classical Benjamin solution (Benjamin, J. Fluid Mech., vol. 31, 1968, pp. 209–248) modelling the flow in a horizontal duct of finite depth in situations where the flow contains a region spanning the depth of the duct, and a region in which the surface detaches from the ceiling of the duct as a free surface. It is shown that the Benjamin solution belongs to a one-parameter family of similar solutions, which are divided into two types: solutions that describe potential flows where the free surface of the fluid is deflected from the duct ceiling at a zero angle; and solutions that admit the formation of a vortex flow region in the vicinity of the point of fluid separation from the duct ceiling. It is shown that this one-parameter family of solutions is the limit of a two-parameter family of solutions in which part of the uniform flow energy is converted into energy of the small-scale fluid motion. Based on the local hydrostatic approximation, the applicability of the constructed solutions is discussed.

This work presents an experimental validation study of Isaacs’ incompressible unsteady-airfoil theory at Reynolds numbers above $10^{6}$, and explores the validity of the classical Kutta condition applied to surging flows. Harmonic variation of the free-stream velocity was produced by rotating choke vanes in an unsteady transonic wind tunnel, with time-resolved lift coefficients determined from surface pressure measurements on a NACA 0018 airfoil. Unsteady lift results demonstrate the same trends with reduced frequency and velocity amplitude ratio that are predicted by Isaacs’ theory. However, significant deviations of the lift magnitude and phase angle are observed. In order to understand the cause of these deviations, the background-oriented schlieren technique was used to visualize density gradients in the immediate vicinity of the airfoil trailing edge. The time-resolved background-oriented schlieren displacement field indicates oscillatory behaviour of the trailing-edge stagnation streakline, which violates the classical Kutta condition for this unsteady surging flow.

Liquid drop impact dynamics depends on the liquid–substrate interaction. In particular, when liquid–solid friction is decreased, the spreading of the impacting drop lasts longer. We characterise this effect by using two types of superhydrophobic surfaces, with similar wetting properties but different friction coefficients. It is found that, for large enough impact velocities, a reduced friction delays the buildup of a viscous boundary layer, and leads to an increase of the time required to reach the maximal radius of the impacting drop. An asymptotic analysis is carried out to quantify this effect, and agrees well with the experimental findings. Interestingly, this novel description complements the general picture of drop impact on solid surfaces, and more generally addresses the issue of drag reduction in the presence of slippage for non-stationary flows.

Classical and symmetrical horizontal convection is studied by means of direct numerical simulations for Rayleigh numbers $Ra$ up to 3 × 1012 and Prandtl numbers $Pr=0.1$, 1 and 10. For both set-ups, a very good agreement in global quantities with respect to heat and momentum transport is attained. Similar to Shishkina & Wagner (Phys. Rev. Lett., vol. 116, 2016, 024302), we find Nusselt number $Nu$ versus $Ra$ scaling transitions in a region $10^{8}\leqslant Ra\leqslant 10^{11}$. Above a critical $Ra$, the flow undergoes either a steady–oscillatory transition (small $Pr$) or a transition from steady state to a transient state with detaching plumes (large $Pr$). The onset of the oscillations takes place at $Ra\,Pr^{-1}\approx 5\times 10^{9}$ and the onset of detaching plumes at $Ra\,Pr^{5/4}\approx 9\times 10^{10}$. These onsets coincide with the onsets of scaling transitions.

We report a comparative experimental study of the reversal of the large-scale circulation in turbulent Rayleigh–Bénard convection in a quasi-two-dimensional corner-less cell where the corner vortices are absent and in a quasi-two-dimensional normal cell where the corner vortices are present. It is found that in the corner-less cell the reversal frequency exhibits a slow decrease followed by a fast decrease with increasing Rayleigh number $Ra$, separated by a transitional $Ra$ ($Ra_{t,r}$). The transition is similar to that in the normal cell, and $Ra_{t,r}$ is almost the same for both cells. Despite the similarities, the reversal frequency is greatly reduced in the corner-less cell. The reduction of the reversal frequency is more significant, in terms of both the amplitude and the scaling exponent, in the high-$Ra$ regime. In addition, we classified the reversals into main-vortex-led and corner-vortex-led, and found that both types exist in the normal cell while only the former exists in the corner-less cell. The frequency of main-vortex-led reversal in the normal cell is found to be in excellent agreement with the frequency of reversals in the corner-less cell. Our results reveal for the first time the quantitative role of the corner vortices in the occurrence of the reversals of the large-scale circulation.

In this paper, we report that reversals of large-scale circulation in two-dimensional Rayleigh–Bénard convection could be suppressed or enhanced by imposing local constant-temperature control on sidewalls. When the control area is away from the centre of the sidewalls, the control can successfully eliminate the flow reversal if the size of the control region is large enough. With a proper location, the width can be as small as 1 % of the system size. When the control region is located around the centre, the control may enhance the flow reversal. It may also stimulate the occurrence of a double-roll mode when the control is located in the centre. Explanations are also discussed based on the twofold effects of the control region on the nearby plumes and the concept of symmetry. The present work provides a new way to control the flow reversals in Rayleigh–Bénard convection through modifying sidewall boundary conditions.

In this simulation-based study, we investigate the surface roughness signature induced by internal solitary waves in oceans. We present the first-ever effort to directly capture the surface roughness signature with a deterministic two-layer model to avoid the singularity encountered in the traditional wave–current interaction theory. By capturing over four million wave components, the simulation resolves the surface wave and internal wave dynamics simultaneously. The surface signature characterized by a rough region followed by a smooth region travelling with an internal wave is quantified by the local wave geometry variation and the wave energy change. The surface wave dynamics are analysed in the wavenumber–frequency slope spectrum calculated in the frame moving with the internal wave. The asymmetric behaviours of right-moving and left-moving surface waves are found to contribute to the surface signature formation. Our results show that the formation of the surface signature is essentially an energy-conservative process and justify the use of the wave-phase-resolved two-layer model.

‘Ground effect’ refers to the enhanced performance enjoyed by fliers or swimmers operating close to the ground. We derive a number of exact solutions for this phenomenon, thereby elucidating the underlying physical mechanisms involved in ground effect. Unlike previous analytic studies, our solutions are not restricted to particular parameter regimes, such as ‘weak’ or ‘extreme’ ground effect, and do not even require thin aerofoil theory. Moreover, the solutions are valid for a hitherto intractable range of flow phenomena, including point vortices, uniform and straining flows, unsteady motions of the wing, and the Kutta condition. We model the ground effect as the potential flow past a wing inclined above a flat wall. The solution of the model requires two steps: firstly, a coordinate transformation between the physical domain and a concentric annulus; and secondly, the solution of the potential flow problem inside the annulus. We show that both steps can be solved by introducing a new special function which is straightforward to compute. Moreover, the ensuing solutions are simple to express and offer new insight into the mathematical structure of ground effect. In order to identify the missing physics in our potential flow model, we compare our solutions against new experimental data. The experiments show that boundary layer separation on the wing and wall occurs at small angles of attack, and we suggest ways in which our model could be extended to account for these effects.

A weakly nonlinear time-dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moderately different from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic ‘beat’. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude, allowing for the possibility of a superharmonic cascade.

The thermal protection system in atmospheric-entry and hypersonic-cruise vehicles are oftentimes designed to ablate during their operation, thus injecting a mixture of various gases with distinct properties into the boundary layer. Such outgassing affects the propagation of instabilities within the boundary layer that ultimately originates the transition to turbulence. This work uses linear stability theory, in combination with the e$^{N}$ method, to establish the underlying reason for the experimentally observed advancement/delay of transition in sharp slender hypersonic cones, when injecting lighter/heavier gases. Contrary to the current understanding and experimental correlations, this numerical analysis suggests that such a behaviour is not linked to the isolated effect of the injected gas’ molar weight, but to its combination with the blowing discontinuity, porosity and the appearance of a shocklet, consequence of the injected gas composition. The shocklet constitutes a density gradient that acts on second-mode instabilities like a thermoacoustic impedance.

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.