Pressure-gradient-driven flows through sinusoidal channels have been studied. The analysis was carried out up to the formation of secondary nonlinear states and spanned a range of low and moderate Reynolds numbers. Direct numerical simulations were used to identify and determine the properties of steady as well as non-stationary, two-dimensional (2-D) and three-dimensional secondary flows. Our results indicate the existence of several distinct solution types. Two-dimensional, stationary flows with periodicity determined by the corrugation represent the first type. The second type is associated with the appearance of 2-D oscillatory flows arising from the onset of unstable travelling waves. Such oscillatory solutions are generally out of phase with the wall corrugation but could be in phase in special cases determined by the ratio of the critical disturbance wavelength and the channel corrugation wavelength. Consequently, several distinct types of time-dependent solutions are possible. The third type of solution results from the centrifugal effect caused by wall curvature and leads to three-dimensionalization of the flow through the onset of stationary streamwise vortices. Finally, various states resulting from the interaction of different solution types are possible. We examine those states and present a bifurcation diagram illustrating the formation of some of them. The results presented in this paper might help with the development of small-scale flow measurement and detection devices operating at low and moderate Reynolds numbers, as well as in the use of wall topographies for the intensification of mixing in flows with moderate, subturbulent Reynolds numbers.

We study the application of Taylor's frozen hypothesis to the pressure fluctuations in turbulent channels by means of spatio-temporal data from direct numerical simulations with large computational domains up to the friction Reynolds number $R{e_\tau } = 2000$. The applicability of the hypothesis is quantitatively verified by comparing the wavenumber and Taylor (frequency) premultiplied spectra of the pressure fluctuations at each distance y from the wall. Using the local mean velocity $U(y)$ for the hypothesis leads to a large difference between both spectra with a value of $O(50\,{\%})$ for its maximum from the wall to $y/h \approx 0.2$, where h is the channel half-depth. Alternatively, the convection velocity of the pressure fluctuations ${C_p}(y)$, originally defined by Del Álamo & Jiménez (J. Fluid Mech., vol. 640, 2009, pp. 5–26) as a function of y, is investigated and adopted for the hypothesis. It is nearly equal to $U(y)$ from ${y^ + } = 20$ to the channel centre, where ${y^ + } = y{u_\tau }/\nu $, in which ${u_\tau }$ and $\nu $ represent the friction velocity and kinematic viscosity, respectively. For ${y^ + } \le 20$, ${C_p}(y)$ is almost constant with a value of around $12{u_\tau }$. Applying ${C_p}(y)$ for the hypothesis decreases the difference between both spectra down to a value of $O(10\,{\%})$ for its maximum from the wall to $y/h \approx 0.2$. Finally, the difference between the pressure wavenumber and frequency premultiplied spectra near the wall is reduced further via applying a wavenumber-dependent convection velocity. This wavenumber-dependent convection velocity is the linear combination of the convection velocities of the turbulent structures associated with the pressure field weighted by their relative contributions to the pressure variance.

Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$, the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition (${\textit {Re}}_{cr-1}$) happens at around 180. At small $g^*$, 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$. Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A$'$ and subharmonic mode C$'$, of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$, the characteristics and the physical mechanisms of each 3-D mode are discussed in this study.

In this paper the multiscale dynamics of streamwise-rotating channel turbulence is studied through direct numerical simulations. Using the generalized Kolmogorov equation, we find that as rotation becomes stronger, the turbulence in the buffer layer is obviously reduced by the intense spatial turbulent convection. On the contrary, in other layers, the turbulence is strengthened mainly by the modified production peak, the intense spatial turbulent convection and the suppressed forward energy cascades. It is also discovered that under a system rotation, small- and large-scale inclined structures have different angles with the streamwise direction, and the difference is strengthened with increasing rotation rates. The multiscale inclined structures are further confirmed quantitatively through a newly defined angle based on the velocity vector. Through the budget balance of Reynolds stresses and the hairpin vortex model, it is discovered that the Coriolis force and the pressure–velocity correlation are responsible for sustaining the inclined structures. The Coriolis force directly decreases the inclination angles but indirectly induces inclined structures in a more predominant way. The pressure–velocity correlation term is related to the strain rate tensor. Finally, the anisotropic generalized Kolmogorov equation is used to validate the above findings and reveals that the multiscale behaviours of the inclined structures are mainly induced by the mean spanwise velocity gradients.

The scaling law of the structure function of Richtmyer–Meshkov (RM) turbulence is investigated both numerically and theoretically. High-fidelity simulations with a minimum-dispersion, adaptive-dissipation scheme are first performed. Results show that the mixing width experiences an exponential growth and the turbulent kinetic energy has a visible $-3/2$ spectrum. The scalar field exhibits a greater degree of intermittency than the velocity field, and also the small-scale statistics suffer a larger influence of large scales. Visible differences in the scaling law of the structure function among the RM turbulence and other types of turbulence are observed, which reveal the unique characteristic of RM turbulence. A phenomenological theory, which gives the spatial and temporal scaling laws of the structure functions of velocity and scalar of RM turbulence, is developed for the first time by introducing an external agent. The spatial scaling exponents of structure functions from simulation deviate from the Kolmogorov exponents, but are quite close to the RM-modified anomalous exponents. This demonstrates the validity of the present phenomenological theory. The temporal scaling exponents of structure functions first meet the RM-modified anomalous exponents, and then approach the Kolmogorov–Obukhov–Corrsin non-intermittent ones.

The effect of the initial condition upon the transport dynamics of miscible flowing fluids in a porous medium is investigated under viscosity and density contrasts. Such flows have attracted significant attention due to their importance in many fields of science and engineering, such as $\mathrm {CO}_2$ sequestration and aquifer remediation. Using high-resolution two-dimensional numerical simulations, we illustrate the impact of viscosity and density contrasts on the temporal evolution of the spreading and mixing quantities. We show that such impact depends on the initial shape of the source distribution where the solute is injected and on the intensity of the horizontal background flux. We find that rates of mixing are dependent on whether the solute is more or less viscous than the ambient fluid, a result usually not taken into consideration in studies on gravity fingering. At higher background flux, the effects due to horizontal viscous fingering dominate over gravitational fingering. Our computational analysis also suggests a non-trivial relationship between mixing and the length of the plume's interface under fingering instabilities. Finally, we show how a stratified permeability field can interact with these sources of instabilities and affect the transport behaviour of the plume.

An increased number of rogue waves, relative to standard distributions, can be induced by unidirectional waves passing over abrupt decreases in water depth. We investigate this phenomenon in a more general setting of multidirectional waves. We examine the influence of the directionality on the occurrence probability of rogue waves using laboratory experiments and fully nonlinear potential flow simulations. Based on the analysis of the statistics of random waves, we find that directional spreading reduces the formation probability of rogue waves relative to unidirectional seas. Nevertheless, for typical values of directional spreading in the ocean ($15^{\circ }\unicode{x2013}30^{\circ }$), our numerical results suggest that there is still a significant enhancement to the number of rogue waves just beyond the top of a depth discontinuity.

The present experimental study investigated the dynamics of single- and multi-port gaseous jet diffusion flames exposed to acoustic excitation via a standing wave situated in a closed waveguide at atmospheric pressure. High-speed imaging of the oscillatory flame was analysed via proper orthogonal decomposition (POD), revealing distinct signatures in both mode shapes and phase portraits for transitions in the acoustically coupled combustion process. For Reynolds numbers between 20 and 100, and for low to moderate forcing amplitudes, the flame exhibited sustained oscillatory combustion (SOC) that was highly coupled to the acoustic forcing. Frequency analysis of the temporal POD modes accurately recovered the forcing frequency and its higher harmonics. At higher forcing amplitudes, a multi-frequency response was observed, resulting from a combination of the forcing frequency and much lower frequency oscillations due to periodic lift-off and reattachment (PLOR) of the flame, preceding a transition to flame blow-off (BO). For both single- and triple-jet flames, transitions from SOC to PLOR to BO were characterized by significant alterations in primary modal energetic content, deflection and eventual smearing in phase portraits, and the development of additional frequencies in modal spectra, although transitional behaviour for the triple jet flames involved additional complexity in the dynamics due to its structure. These features provide the potential for the development of reduced-order models that can characterize and predict acoustically coupled combustion behaviour.

The purpose of this research was to provide further understanding of turbulent dynamics and heat transfer mechanisms in accelerating flows with thermophysical variations and pressure drops in micron tubes. Direct numerical simulations were conducted to investigate the turbulence to supercritical pressure ${\rm CO}_2$ in heated micron tubes with inner diameter $99.2~\mathrm {\mu }$m. In general, the turbulent heat transfer enhancement/deterioration at supercritical pressure is dominated by variations in thermophysical properties, buoyancy and thermal acceleration; however, the mechanism differs in micron tubes ($d^* < 100\ \mathrm {\mu }$m). The results showed that the pressure drop and scale effect made significant contributions to the development of turbulence flows heated at supercritical pressure in micron tubes, leading to the prominent property change and flow acceleration in the inlet fully developed turbulent flow. The deviation on temperature distribution because of pressure changes was non-negligible. The primary contribution of the acceleration was the decay of a boundary layer, which significantly suppressed the production of turbulence and decreased heat transfer. The acceleration had stabilizing effects on the ejection and sweep motions of the turbulent flow. The high-speed fluid contributed to a new disturbance scenario of the flow with a larger spanwise wavenumber superimposed on existing perturbations. The high-speed streak width in the quasilaminar region was approximately $150$–$160\nu /u_\tau$ in accelerating flow. In the micron tubes, the Reynolds stress events of quadrant Q4 contributed 60 % of the Reynolds stress, greater than those of quadrant Q2.

The maximum size and lifetime of an acoustically nucleated cavitation bubble is inversely proportional to the driving frequency and has achieved a limit of approximately 10 MHz. Smaller cavitation bubbles that are critical to microscopic applications require shorter lifetimes that correspond to higher oscillation frequencies. Here, we demonstrate that acoustic cavitation in the 100 MHz range and beyond can be achieved through wave propagation in a solid rather than in a liquid. The cavitation bubble is nucleated at a nano-sized fracture on a glass substrate, and its expansion is driven by a leaky Rayleigh wave, while the inertial collapse is induced by a trailing shock wave. As both waves travel at different velocities, the time interval between these two events is a function of the distance to the source. In this way, we demonstrate experimentally control of the lifetime of the bubbles in a range between 6 and 80 ns, corresponding to oscillation frequencies between 13 and 166 MHz. Our results agree with finite-volume fluid–structure interaction simulations.

The main objective of the present work is to explain the physical mechanisms occurring in droplet-laden homogeneous shear turbulence (HST) with a focus on the modulation of turbulence kinetic energy (TKE) caused by the droplets. To achieve such an objective, first, we performed direct numerical simulations (DNS) of HST laden with droplets of initial diameter approximately equal to twice the Taylor length scale of turbulence, droplet-to-fluid density and viscosity ratios equal to ten and a 5 % droplet volume fraction. We investigated the effects of shear number and Weber number on the modulation of TKE for $Sh \approx 2$ and $4$, and $0.02 \le {{We_{rms}}} \le 0.5$. Then, we derived the TKE equations for the two-fluid, carrier-fluid and droplet-fluid flow in HST and the relationship between the power of surface tension and the rate of change of total droplet surface area, providing the pathways of TKE for two-fluid incompressible HST. Our DNS results show that, for ${{We_{rms}}} = 0.02$, the rate of change of TKE is increased with respect to the single-phase cases, for ${{We_{rms}}} = 0.1$, the rate of change of TKE oscillates near the value for the single-phase cases and, for ${{We_{rms}}} = 0.5$, the rate of change of TKE is decreased with respect to the single-phase cases. Such modulation is explained from the analysis of production, dissipation and power of surface tension in the carrier-fluid and droplet-fluid flows. Finally, we explain the effects of droplets on the production and dissipation rate of TKE through the droplet ‘catching-up’ mechanism, and on the power of the surface tension through the droplet ‘shearing’ mechanism.