The flow structures and the acoustic feedback loops of underexpanded round jets are investigated by numerical simulations. The jets have a Mach number of 1 at the nozzle exit and a diameter-based Reynolds number of $2.5 \times {10^3}$. Three nozzle pressure ratios (NPRs) of 2.2, 2.4 and 2.6 are considered. The wavelengths of the screech tones are in good agreement with the experimental measurements on high-Reynolds-number jets in the literature. The screech tones are respectively at the A1 and B modes for the jets at NPRs of 2.2 and 2.6. Two screech tones at the A2 and B modes are identified in the jet at the NPR of 2.4 and the wavelet analyses conducted on the pressure fluctuations confirm that these two modes are contemporaneous. The amplitude and phase fields of fluctuating pressure at the screech frequencies are presented in the nozzle exit plane and azimuthal planes. The effective source locations of the screech tones are determined based on the distributions of the phase. The number of periods contained in the screech feedback loop is equal to the number of cells in the standing wave between the nozzle exit and the effective source. The screech frequencies estimated by the classical feedback model agree well with the numerical results at different modes. A modified model, in which the classical feedback model and the upstream-propagating acoustic wave mode of the jet are combined, shows that the screech feedback loops at the A1 and A2 modes are associated with the same acoustic wave mode. The modified model fails to estimate the screech frequencies at the B mode. Different feedback mechanisms lead to the coexistence of the A2 and B modes. The coherent structures corresponding to different screech modes are extracted by dynamic mode decomposition.

Molecular dynamics simulations with a repulsive Lennard-Jones potential are employed to understand the bifurcation scenario and the resulting patterns in compressible Taylor–Couette flow of a dense gas, with the inner cylinder rotating ($\omega _i>0$) and the outer one at rest ($\omega _o=0$). The steady-state flow patterns are presented in terms of a phase diagram in the ($\omega _i,\varGamma$) plane, where $\varGamma =h/\delta$ is the aspect ratio, $h$ is the height of the cylinders and $\delta =R_o-R_i$ is the gap between the outer and inner cylinders, and the underlying bifurcation scenario is analysed as a function of $\omega _i$ for different $\varGamma$. Considerable density stratification is found along both radial and axial directions in the Taylor-vortex regime of a dense gas, which makes the present system fundamentally different from its incompressible analogue. In the circular Couette flow regime, the stratifications remain small and the predicted critical Reynolds number for the onset of Taylor vortices matches well with that of its incompressible counterpart. The emergence of asymmetric Taylor vortices at $\varGamma >1$ is found to occur via saddle-node bifurcations, resulting in hysteresis loops in the bifurcation diagrams that are characterized in terms of the net circulation or the maximum radial velocity or the axial density contrast as order parameters. For $\varGamma \leq 1$ with reflecting axial boundary conditions, the primary bifurcation yields a single-vortex state which is connected to a two-roll branch via saddle-node bifurcations; however, changing to stationary (no-slip) endwalls yields a new state, which consists of two large symmetric vortices near the inner cylinder coexisting with an irregular pattern near the stationary outer cylinder. It is shown that the endwall conditions and the fluid compressibility play crucial roles on the genesis of asymmetric and stratified vortices and the related multiplicity of states in the Taylor-vortex regime of a dense gas.

In this work, we study the ascent dynamics of a liquid Taylor drop formed from a lock-exchange configuration in a closed vertical pipe. We focus on the buoyancy-driven motion of an elongated drop surrounded by a denser fluid when viscous forces dominate over inertial and surface tension effects. While gaseous Taylor bubbles have been studied extensively, a liquid Taylor drop moving in a closed pipe is less well understood. We formulate an analytical model for estimating the ascent speed and drop thickness from first principles. First, we use a lubrication approximation to solve for the velocity profiles in the two fluids. Then, we analyse the mechanical energy balance of the whole system, including the effect of viscous dissipation, to understand how the ascent speed and drop thickness scale with the viscosity ratio. We show that a drop with density ratio $\mathcal {R}$ reaches a stationary state with a uniform dimensionless thickness of $\sqrt {2}/{2}$ in the absence of dissipation and $\sqrt {2\mathcal {R}}/{2}$ in the dissipative regime. Through a comparison with existing experimental data, we demonstrate that our model correctly predicts the ascent speed of a Taylor drop if the material properties of the fluids and the geometry of the conduit are known. Our theoretical framework can be generalized to an isolated Taylor drop rising in a vertical pipe.

Direct numerical simulations (DNS) are used to examine a spatially developing non-equilibrium three-dimensional turbulent boundary layer (3DTBL) over a flat plate. The present flow is a ‘shear-driven’ 3DTBL owing to a sudden imposition of a surface spanwise velocity ${W_S}$. Particular attention is given to the effects of cross-flow and Reynolds number. In the DNS, three values of the inlet momentum thickness Reynolds number, $R{e_{{\theta _0}}} = 300$, 600 and 900, are used with several values of ${W_S}$. The present largest ${W_S}$ is twice the free-stream velocity ${U_0}$, comparable to the maximum value of the spinning cylinder experiment by Lohmann (Trans. ASME I: J. Fluids Engng, vol. 98, 1976, pp. 354–363). After imposing ${W_S}$, the mean streamwise vorticity ${\overline \varOmega _x}$ increasingly propagates away from the wall where there is close relationship between a deficit of mean streamwise velocity and inviscid skewing (i.e. three-dimensionality). At a downstream station of a 3DTBL, near-plateaus appear in the skin friction coefficients where the magnitudes depend intrinsically on ${W_S}$. The approach to the collateral state is, however, slow for mean streamwise velocity $\overline U$ where the Reynolds shear stress $\overline {uv}$ extracts energy from the mean flow inefficiently. As the Reynolds number increases, the mean velocity magnitude ${Q_r}$ tends to show the log law but with a larger von Kármán constant than in a two-dimensional turbulent boundary layer. Instantaneously, toppling u structures dominate owing to cross-flow and become more prominent with increasing Re. Statistically, the latter spanwise length scale increases linearly with respect to y below y/δ99 = 0.2, which indicates that cross-flow yields a self-similar behaviour.

A liquid droplet hovering on a hot solid surface is commonly referred to as a Leidenfrost droplet. In this study, we discover that a Leidenfrost droplet spontaneously performs a series of distinct oscillations as it shrinks during the span of its life. The oscillation first starts out erratically, followed by a stage with stable frequencies, and finally turns into periodic bouncing with signatures of a parametric oscillation and occasional resonances. The last bouncing stage exhibits nearly perfect collisions. We showed experimentally and theoretically the enabling effects of each oscillation mode and how the droplet switches between such modes. We finally show that these spontaneous oscillation modes and the conditions for transitioning between modes are universal for all tested combinations of liquids and surfaces.

The migration of dense fluid through a saturated, layered porous medium leads to two end-member examples of buoyancy-driven flow, namely plumes and gravity currents. Herein we develop an integrated theoretical model to study this scenario for the special case where the boundary between the permeable layers, in a two-layered porous medium, is inclined at an angle to the horizontal. Far from being a routine detail, the inclination of the permeability jump leads to a symmetry-breaking: up- and downdip flows have different volume fluxes and travel different distances, possibly substantially different distances, before becoming arrested at the point where plume inflow balances basal draining. Our model predicts these associated run-out lengths and the transient approach thereto. Predictions are validated with measurements from similitude laboratory experiments, in which the upper and lower layers are comprised of glass beads of different diameters. Experiments are conducted for a range of inclination angles and also a range of plume source conditions. The experimental data suggest a complicated structure for the gravity currents, whose boundaries are blurred by dispersion in a manner not captured by our (sharp interface) model. This observation has particular significance in predicting the lateral spread of contaminated fluid through real geological formations, particularly in instances where for example groundwater contamination is of particular concern.

Coordinated laboratory experiments and computational simulations are conducted that explore the collective vertical migration of a swarm of inertial swimmers through a stably stratified density interface. Values of the governing parameters such as the swimmer- and swarm-scale Reynolds numbers, the Richardson number, as well as the animal number density in the swarm closely match each other in the simulations and experiments. In addition to intense mixing at the swimmer scale, the experiments and simulations demonstrate that the hydrodynamic interaction of the individual swimmers produces a spatially coherent source of thrust that results in the formation of a swarm-scale jet in the direction opposite to the migration. The jet velocity is seen to increase monotonically with the animal number density, at a sublinear rate. For steadily moving dilute swarms, the jet velocity is well predicted by a simple analytical model that assumes spatially uniform jet and swimmer velocities. Experimental measurements demonstrate effective diffusivity values up to three orders of magnitude larger than the molecular value. Numerical results are consistent with these observations, although they employ a larger molecular diffusivity and, hence, yield a lower ratio. The effective diffusivity is seen to increase linearly with the volume fraction of the swimmers. A continuum model is proposed for the generation of the swarm-scale jet, based on an idealization of the swarm as a self-propelled porous sphere. This model suggests that large swarms generate most of their mixing through the coherent swarm-scale jet, rather than by processes at the scale of individual swimmers.

The so-called moist-convective shallow-water model, which incorporates moist convection in a simple albeit self-consistent way is used to analyse how intense localized vortices, with distributions of horizontal velocity and relative vorticity close to those observed in tropical cyclones (TC), evolve and interact with topography on the $\beta$-plane at low latitudes. Instabilities of such TC-like vortices are studied first in the $f$-plane approximation, and their development, interplay with beta-gyres and the role they play in vorticity redistribution and intensification are then analysed along the vortex trajectories on the $\beta$-plane, both in dry and moist-convective environments. Interactions of the vortices with an idealized topography in the form of zonal and meridional ridges and islands of elliptic form and the role of moist convection in these processes are then investigated, revealing rich vortex-dynamics patterns. The results can be helpful in crude analyses and predictions of the evolution of the barotropic component of TC, of their trajectories over the ocean and during landfall and of related condensation/precipitation patterns.

Ekman layers over a rough surface are studied using direct numerical simulation. The roughness takes the form of periodic two-dimensional bumps whose non-dimensional amplitude is fixed at a small value ($h^+=15$) and whose mean slope is gentle. The neutral Ekman layer is subjected to a stabilizing cooling flux for approximately one inertial period ($2{\rm \pi} /f$) to impose the stratification. The Ekman boundary layer is in a transitionally rough regime and, without stratification, the effect of roughness is found to be mild in contrast to the stratified case. Roughness, whose effect increases with the slope of the bumps, changes the boundary layer qualitatively from the very stable (Mahrt, Theor. Comput. Fluid Dyn., vol. 11, issue 3–4, 1998, pp. 263–279) regime, which has a strong thermal inversion and a pronounced low-level jet, in the flat case to the stable regime, which has a weaker thermal inversion and stronger surface-layer turbulence, in the rough cases. The flat case exhibits initial collapse of turbulence which eventually recovers, albeit with inertial oscillations in turbulent kinetic energy. The roughness elements interrupt the initial collapse of turbulence. In the quasi-steady state, the thickness of the turbulent stress profiles and of the near-surface region with subcritical gradient Richardson number increase in the rough cases. Analysis of the turbulent kinetic energy (TKE) budget shows that, in the surface layer, roughness counteracts the stability-induced reduction of TKE production. The flow component, coherent with the surface undulations, is extracted by a triple decomposition, and leads to a dispersive component of near-surface turbulent fluxes. The significance of the dispersive component increases in the stratified cases.

In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218–220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the generalized Taylor dispersion (GTD) theory and the Fokker–Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker–Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.

In order to elucidate the physical connection between the propulsive performance and the unsteadiness of jet flow, the transient development of the impulse and thrust of laminar starting jets with finite fluid discharged is investigated numerically for cases with different velocity programmes and jet stroke ratios. The simulation quantitatively demonstrates that the impulse and thrust generated are highly sensitive to the jet kinematics and its near-wake dynamics. The momentum flux contribution to the jet impulse is found to be significant and is associated closely with the jet kinematics. On the other hand, although the over pressure effect at the jet initiation stage has been identified previously as the main reason for the enhanced propulsive performance of the starting jet, the current results indicate that its contribution is in fact weakened by the negative local pressure, induced by the formation of the leading vortex ring as well as jet development during the deceleration stage. Contrary to the effects of the leading vortex ring, the stopping vortex formed near the nozzle exit plane during the jet deceleration stage is found to contribute positively to the pressure impulse production, albeit it is relatively small. By augmenting the over pressure effect and mitigating the negative-pressure effect, the cases with the fast acceleration and slow deceleration velocity programme is capable of producing the maximum pressure impulse, leading to additional impulse production over what would be expected from the jet momentum flux alone.

We carry out direct numerical simulation combined with adhesive discrete element calculations to investigate collision-induced breakage of agglomerates in homogeneous isotropic turbulence. The adopted method tracks the dynamics of individual particles while they are travelling alone through the fluid and while they are colliding with other particles. Based on extensive simulation runs, an adhesion parameter $Ad_n$ is constructed to quantify the possibility of occurrence of sticking, rebound and breakage events. The collision-induced breakage rate is then formulated based on the Smoluchowski equation and a breakage fraction. The breakage fraction, defined as the fraction of collisions that result in breakage, is then analytically estimated by a convolution of the probability distribution of collision velocity and a universal transfer function. It is shown that the breakage rate decreases exponentially as the adhesion parameter $Ad_n$ increases for doublets and scales as linear functions of the agglomerate size, with the slope controlled by $Ad_n$. These results allow one to estimate the breakage rate for early stage agglomerates of arbitrary size. Moreover, the role of the flow structure on the collision-induced breakage is also examined. Violent collisions and breakages are more likely caused by particles ejected rapidly from strong vortices and happen in straining sheets. Our results extend the findings of shear-induced fragmentation, forming a more complete picture of breakage of agglomerates in turbulent flows.

A dual-step cylinder is a canonical geometry commonly encountered in many practical flows. It consists of a large diameter cylinder ($D$) attached coaxially to the mid-span of a small diameter cylinder ($d$). This work provides a comprehensive description of the flow development, classifies common wake regimes and considers the associated structural loading on a dual-step cylinder. The influence of the aspect ratio of the large diameter cylinder ($L/D$) and diameter ratio ($D/d$) is studied experimentally for a Reynolds number of $Re_D = 2100$, $1.33\leq D/d \leq 4$ and $0.2\leq L/D \leq 5$. The flow evolution and structural loading are quantified via a combination of flow visualization, Laser Doppler velocimetry, particle image velocimetry measurements and multi-component force balance measurements. Through a detailed analysis of the results, six distinct flow regimes are identified based on observed changes in the flow development downstream of the large diameter cylinder. The findings are distilled into a map of flow regimes that provides a framework for analysis of the dual-step cylinder wakes and incorporates limiting cases of this geometry, namely, uniform circular cylinders, cantilevered cylinders, cylinders with two free ends, coin-like cylinders and single-step cylinders. The identified flow regimes are also related to changes in structural loading.

A control volume based analytical method for calculating the efficiency $\eta$ of flapping foil power generators was developed for single and tandem foil configurations. Ignoring unsteady effects and non-uniform pressures resulted in theoretical limits identical to the Betz ($\eta =16/27$ for a single turbine) and Newman ($\eta =16/25$ for tandem turbines) limits. Inclusion of unsteady flow and non-uniform pressure distributions produced theoretical efficiency maxima in excess of these limits. Simulation of single and tandem foil cases to determine the magnitude of these effects showed that the Betz limit would not be exceeded by a single foil system in practice, but that it is conceivable that a tandem foil system could exceed the Newman limit due to the strong unsteady vortex wake of the upstream turbine entraining additional energy into the path of the downstream turbine and maintaining pressures in the wake below ambient.

The present study concerns a temporally developing parallel natural convection boundary layer with Prandtl number $\textit {Pr} = 0.71$ over an isothermally heated vertical plate. Three-dimensional direct numerical simulations (DNS) with different initial conditions were carried out to investigate the turbulent statistical profiles of mean velocity and temperature up to ${\textit {Gr}}_\delta =7.7\times 10^7$, where $Gr_\delta$ is the Grashof number based on the boundary layer thickness $\delta$. By virtue of DNS, we have identified a constant heat flux layer (George & Capp, Intl J. Heat Mass Transfer, vol. 22, issue 6, 1979, pp. 813–826; Hölling & Herwig, J. Fluid Mech., vol. 541, 2005, pp. 383–397) and a constant forcing layer in the near-wall region. In the close vicinity of the wall ($y^+<5$) a laminar-like sublayer has developed, and the temperature profile follows the linear relation, consistent with the studies of spatially developing flows (Tsuji & Nagano, Intl J. Heat Mass Transfer, vol. 31, issue 8, 1988, pp. 1723–1734); whereas such a linear relation cannot be observed for the velocity profile due to the extra buoyancy. Similar to earlier studies (Ng et al., J. Fluid Mech., vol. 825, 2017, pp. 550–572) we show that this buoyancy effect would asymptotically become zero if the ${\textit {Gr}}_\delta$ is sufficiently large. Further away from the wall ($y^+>50$), there is a log-law region for the mean temperature profile as reported by Tsuji & Nagano (1988). In this region, the turbulent length scale which characterises mixing scales linearly with the distance from the wall once ${\textit {Gr}}_\delta$ is sufficiently large. By taking the varying buoyancy into consideration with the robust mixing length model, a modified log-law for the mean velocity profile for $y^+>50$ is proposed. The effect of the initialization is shown to persist until relatively high ${\textit {Gr}}_\delta$ as a result of slow adjustment of the buoyancy (temperature) profile. Once these differences are accounted for, we find excellent agreement with our two DNS cases and with the spatially developing data of Tsuji & Nagano (1988). In the limit of higher ${\textit {Gr}}_\delta$ the velocity profile is expected to become asymptotic to momentum-dominated behaviour as buoyancy becomes increasingly weak in comparison with shear in the near-wall region.