A series of laboratory experiments were conducted to investigate the characteristics of a dense gravity current flowing down an inclined slope into a quiescent two-layer stratification. The presence of the pycnocline causes the gravity current to split and intrude into the ambient at two distinct levels of neutral buoyancy, as opposed to the classical description of gravity currents in stratified media as being either a pure underflow or interflow. The splitting behaviour is observed to be dependent on the Richardson number ($Ri_{\unicode[STIX]{x1D70C}}$) of the gravity current, formulated as the ratio of the excess density and the ambient stratification. For low $Ri_{\unicode[STIX]{x1D70C}}$, underflow is more dominant, while at higher $Ri_{\unicode[STIX]{x1D70C}}$ interflow is more dominant. As $Ri_{\unicode[STIX]{x1D70C}}$ increases, however, we find that the splitting behaviour eventually becomes independent of $Ri_{\unicode[STIX]{x1D70C}}$. Additionally, we have also identified two different types of waves that form on the pycnocline in response to the intrusion of the gravity current. An underflow-dominated regime causes a pycnocline displacement where the speed of the wave crest is locked to the gravity current, whereas an interflow-dominated regime launches an internal wave that moves much faster than the gravity current head or interfacial intrusion.

Mach reflection in steady supersonic flow with two incident shock waves that reflect at the same point on the reflecting surface has been studied recently. Under some conditions we have pre-Mach reflection, where the first incident shock wave produces Mach reflection, the reflected shock wave of which intersects the second incident shock wave, leading to a type I shock interference structure. In this study, we find that a critical condition exists to have a double solution of this shock interference, i.e. we may either have type I interference or type II interference. However, numerical simulation shows that, for inverted Mach reflection, the double solution domain is below the theoretical one and for usual Mach reflection, the double solution domain is above the theoretical one. This discrepancy is found to be due to secondary Mach waves on the initial segment of the slipline of the Mach reflection, thus demonstrating for the first time a case where the transition criterion is modified by secondary Mach waves developed over the primary flow structure.

A spatially developing turbulent boundary layer subject to a space- and time-dependent pressure gradient is analysed via large-eddy simulation. The unsteadiness is prescribed by imposing an oscillating suction–blowing velocity profile at the top boundary of the computational domain. The alternating favourable and adverse pressure gradients cause the flow to separate and reattach to the wall periodically. A range of reduced frequencies $k$ was investigated, spanning from a very rapid flutter-like motion to a slow, quasi-steady flapping. The Reynolds number based on the boundary-layer displacement thickness $\delta _o^{*}$ at the inflow plane is $Re_*=1000$. Both time- and phase-averaged fields are analysed and results are compared with steady conditions. The reduced frequency $k$ has a significant effect on the transient flow-separation process. For high $k$ the separation bubble does not grow as thick as in the corresponding steady case, but the length of the bubble remains comparable; hysteresis is observed in the near-wall region. As $k$ is reduced, a threshold is met at which the separation bubble grows in the wall-normal direction. However, the length of the bubble is significantly reduced again when compared with the steady case. At this frequency, the region of slow-moving fluid generated by the flow reversal is advected downstream, causing a decorrelation between the forcing (the imposed free-stream velocity) and the velocity and pressure downstream of the separation bubble. Moreover, hysteresis effects are shifted away from the wall. At the lowest frequency a quasi-steady solution is approached; however, transient effects are still present in the backflow region.

We develop a model to predict the fragmentation limit of drops colliding off-centre. The prediction is excellent over a wide range of liquid properties and it can be used without adjusting any parameter. The so-called stretching separation is attributed to the extension of the merged drop above a critical aspect ratio of 3.25. The evolution of this aspect ratio is influenced by the liquid viscosity and can be interpreted via an energy balance. This approach is then adapted to drop–jet collisions, which we model as consecutive drop–drop collisions. The fragmentation criterion is similar to that observed for drop–drop collisions, while the evolution of the stretched jet aspect ratio is modified to account for the different flow fields and geometry.

We investigate the spatial organization and temporal dynamics of large-scale, coherent structures in turbulent Rayleigh–Bénard convection via direct numerical simulation of a 6.3 aspect-ratio cylinder with Rayleigh and Prandtl numbers of $9.6\times 10^7$ and $6.7$, respectively. Fourier modal decomposition is performed to investigate the structural organization of the coherent turbulent motions by analysing the length scales, time scales and the underlying dynamical processes that are ultimately responsible for the large-scale structure formation and evolution. We observe a high level of rotational symmetry in the large-scale structure in this study and that the structure is well described by the first four azimuthal Fourier modes. Two different large-scale organizations are observed during the duration of the simulation and these patterns are dominated spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. Studies of the transition between these two large-scale patterns, radial and vertical variations in the azimuthal energy spectra, as well as the spatial and modal variations in the system's correlation time are conducted. Rotational dynamics are observed for individual Fourier modes and the global structure with strong similarities to the dynamics that have been reported for unit aspect-ratio domains in prior works. It is shown that the large-scale structures have very long correlation time scales, on the order of hundreds to thousands of free-fall time units, and that they are the primary source for a horizontal inhomogeneity within the system that can be observed during a finite, but a very long-time simulation or experiment.

A neural-network-based large eddy simulation is performed for flow over a circular cylinder. To predict the subgrid-scale (SGS) stresses, we train two fully connected neural network (FCNN) architectures with and without fusing information from two separate single-frame networks (FU and nFU, respectively), where the input variable is either the strain rate (SR) or the velocity gradient (VG). As the input variables, only the grid-filtered variables are considered for the SGS models of G-SR and G-VG, and both the grid- and test-filtered variables are considered for the SGS models of T-SR and T-VG. The training data are the filtered direct numerical simulation (fDNS) data at $Re_d=3900$ based on the free-stream velocity and cylinder diameter. Using the same grid resolution as that of the training data, the performances of G-SR and G-VG (grid-filtered inputs) and T-SR-FU and T-VG-FU (grid- and test-filtered inputs with fusion) are better than those of the dynamic Smagorinsky model and T-SR-nFU and T-VG-nFU (grid- and test-filtered inputs without fusion). These FCNN-based SGS models are applied to untrained flows having different grid resolutions from that of training data. Although the performances of G-SR and G-VG are degraded, T-SR-FU and T-VG-FU still provide good performances. Finally, T-SR-FU and T-VG-FU trained at $Re_d = 3900$ are applied to higher-Reynolds-number flows ($Re_d = 5000$ and 10 000) and their results are also in good agreements with those of fDNS and previous experiment, indicating that adding the test-filtered variables and fusion increases the prediction capability even for untrained Reynolds number flows.

Self-propulsion of chemically active droplets and phoretic disks has been studied widely; however, most research overlooks the influence of disk shape on swimming dynamics. Inspired by experimentally observed prolate composite droplets and elliptical camphor disks, we employ simulations to investigate the phoretic dynamics of an elliptical disk that emits solutes uniformly in the creeping flow regime. By varying the disk's eccentricity $e$ and the Péclet number $Pe$, we distinguish five disk behaviours: stationary, steady, orbiting, periodic and chaotic. We perform a linear stability analysis (LSA) to predict the onset of instability and the most unstable eigenmode when a stationary disk transitions spontaneously to steady self-propulsion. In addition to the LSA, we use an alternative approach to determine the perturbation growth rate, illustrating the competing roles of advection and diffusion. The steady motion features a transition from a puller-type to a neutral-type swimmer as $Pe$ increases, which occurs as a bimodal concentration profile at the disk surface shifts to a polarized solute distribution, driven by convective solute transport. An elliptical disk achieves an orbiting motion through a chiral symmetry-breaking instability, wherein it repeatedly follows a circular path while simultaneously rotating. The periodic swinging motion, emerging from a steady motion via a supercritical Hopf bifurcation, is characterized by a wave-like trajectory. We uncover a transition from normal diffusion to superdiffusion as eccentricity $e$ increases, corresponding to a random-walking circular disk and a ballistically swimming elliptical counterpart, respectively.

In Rayleigh–Bénard convection, it has been found that the amount of heat passing through the fluid has a power-law dependence on the imposed temperature difference. Modifying this dependence, either enhancing or reducing the heat transfer capability of fluids, is important in many scientific and practical applications. Here, we present a simple means to control the vertical heat transfer in Rayleigh–Bénard convection by injecting heat through one lateral side of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates the large-scale circulation, and increases the heat transfer rate in the vertical direction. Our numerical and theoretical studies demonstrate how a classical Rayleigh–Bénard convection responds to such a perturbation when the system is near or well above the onset of convection.

Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow ridges are common in arid regions. Here, we consider the initial instability and the ultimate fate of buoyancy-driven convection that could lead to such patterns. Specifically, we look at convection in a deep porous medium with a constant throughflow boundary condition on a horizontal surface, which resembles the situation found below an evaporating salt lake. The system is scaled to have only one free parameter, the Rayleigh number, which characterises the relative driving force for convection. We then solve the resulting linear stability problem for the onset of convection. Further exploring the nonlinear regime of this model with pseudo-spectral numerical methods, we demonstrate how the growth of small downwelling plumes is itself unstable to coarsening, as the system develops into a dynamic steady state. In this mature state we show how the typical speeds and length scales of the convective plumes scale with forcing conditions, and the Rayleigh number. Interestingly, a robust length scale emerges for the pattern wavelength, which is largely independent of the driving parameters. Finally, we introduce a spatially inhomogeneous boundary condition – a modulated evaporation rate – to mimic any feedback between a growing salt crust and the evaporation over the dry salt lake. We show how this boundary condition can introduce phase locking of the downwelling plumes below sites of low evaporation, such as at the ridges of salt polygons.

We report for the first time on triadic resonances in a rotating convection system. Using direct numerical simulations, we find that convective modes in a rotating spherical fluid can excite a pair of inertial modes whose frequencies and wavenumbers match the triadic resonance conditions. Depending on the structures of the convective modes, triadic resonances can lead to the growth of either a pair of modes with lower frequencies and wavenumbers, or a pair of modes with higher frequencies and wavenumbers, providing a possible mechanism for the bi-directional energy cascade. Increased thermal forcing leads to fully developed turbulence, which also exhibits wave-like motions, and is reminiscent of the energy spectrum of inertial wave turbulence. Our results suggest that the interaction of inertial waves plays an important role in rotating convection, which is of great importance in understanding the dynamics of planetary and stellar interiors.

Active and passive controls for drag reduction in flow around a cylinder are obtained by computing the sensitivity of drag with respect to surface velocity perturbations and roughness, respectively. Both controls are concentrated around the separation line and localized in the spanwise direction, producing suction effects to the separating boundary layers. In the wake, the control induces localized vertical displacements and streamwise stretches of the upper and lower vorticity sheets, and subsequently delay the vortex shedding and push the local pressure minimum away from the cylinder. Instead of suppressing separation and recirculation as commonly observed in two-dimensional controls, the present three-dimensional control extends the recirculation zone to produce a virtual surface converting the bluff body flow to a streamlined body flow. Through this mechanism, the control reduces drag by 20 % at maximum control velocity 2 % of the free-stream velocity (or momentum coefficient $10^{-4}$) at Reynolds number $Re=190$. The control is much more efficient than the previously tested spanwise uniform suction or periodic suction/blowing, both requiring maximum control velocity above 8 % (or momentum coefficient above $10^{-3}$) to achieve similar drag reduction effects. The power savings ratio, defined as the ratio of the control-reduced drag power and the maximum input power, is above 20, up to $Re=1000$, the highest Reynolds number considered in this work. This ratio reduces slightly to 17.8 when the control is simplified to spanwise localized suction around the separation lines in order to facilitate practical implementations.