The evolution of turbulent spots in a flat plate boundary layer is examined using time-resolved tomographic particle image velocimetry (Tomo-PIV) experiments and direct numerical simulation (DNS). The characteristics of flow structures are examined using timelines and material surfaces. Both the numerical and experimental results reveal a notable behaviour in the developmental process of turbulent spots: the development of low-speed streaks at the spanwise edges of turbulent spots, followed by the subsequent formation of hairpin vortices. The behaviour of these low-speed streaks is further investigated using timelines and material surfaces generated for a series of regions and development times. The results indicate that these low-speed streaks exhibit characteristic wave behaviour. The low-speed streaks are observed to lift up as three-dimensional (3-D) waves, with high-shear layers forming at the interface of these waves. These induced high-shear layers become unstable and evolve into vortices, which contribute to the expansion of the turbulent spot. These findings show the significant role of 3-D waves in the development of turbulent spots, supporting the hypothesis that 3-D waves serve as initiators of vortices at the bounding surface of a turbulent spot.

The greatest challenge in pressure reconstruction from the measured velocity fields is that the error of material acceleration is significantly contaminated due to error propagation. Particularly for flows with moving boundaries, accurate boundary velocities are difficult to obtain due to error propagation, and a complex boundary processing technique is needed to treat the moving boundaries. The present work proposes a machine-learning-based method to determine the pressure for incompressible flows with moving boundaries. The proposed network consists of two neural networks: one network, named the boundary network, is used to track the Lagrangian boundary points; the other physics-informed neural network, named the flow network, is adopted to approximate the flow fields. These two networks are coupled by imposing boundary conditions. We further propose a new dynamic weight strategy for the loss terms to guarantee convergence and stability. The performance of the proposed method is validated by two examples: the flow over an oscillating cylinder and the flow around a swimming fish. The proposed method can accurately determine the pressure fields and boundary motion from synthetic particle image velocimetry (PIV) flow fields. Moreover, this method can also predict the boundary and pressure at a given instant without supervised data. Finally, this method was applied to reconstruct the pressure from the two-dimensional and three-dimensional PIV velocities of the left ventricle. All of the results indicate that the proposed method can accurately reconstruct the pressure fields for flows with moving boundaries and is a novel method for surface pressure estimation.

Reflection of a rightward-moving shock over a steady oblique shock, equivalent to a shock-on-shock interaction, is typically studied with post-formed shock waves. Law, Felthun and Skews (Shock Waves, vol. 13, 2003, pp. 381–394) reported post-formed expansion fan (PFEF) reflection for second-family incident shock. Here, we show that PFEF reflection also exists for first-family incident shock. We derive the critical condition for PFEF reflection in the shock speed Mach number and incident shock angle plane. Our findings indicate PFEF emergence near type post-I region. Numerical simulations reveal that PFEF with rising incident angle can intersect the incident shock, triple point or Mach stem, echoing the Hillier (J. Fluid Mech., vol. 575, 2007, pp. 399–424) three-type classification of shock–expansion fan interactions. The complex shock reflection pattern is essentially composed of an upstream structure linked to the moving shock wave, and a downstream structure linked to the unperturbed oblique shock wave. Under the conditions investigated, the upstream structure is characterized by a Mach reflection of the incident shock over the wall, potentially featuring a triple point formed within the Mach stem. Below this triple point, there is a curved segment of the Mach stem that is close to the wall. As the inclined angle increases, the curved shock may expand and interact with the incident shock, leading to an asymmetric regular reflection, which is a phenomenon that has not been observed previously. The downstream structure is a double $\lambda$ shock structure, with the lower shock resulting from the generation of recompression shock waves.

Local shearing motions in turbulence form small-scale shear layers, which are unstable to perturbations at approximately 30 times the Kolmogorov scale. This study conducts direct numerical simulations of passive-scalar mixing layers in a shear-free turbulent front to investigate mixing enhancements induced by such perturbations. The initial turbulent Reynolds number based on the Taylor microscale is $ Re_\lambda = 72$ or 202. The turbulent front develops by entraining outer fluid. Weak sinusoidal velocity perturbations are introduced locally, either inside or outside the turbulent front, or globally throughout the flow. Perturbations at this critical wavelength promote small-scale shear instability, complicating the boundary geometry of the scalar mixing layer at small scales. This increases the fractal dimension and enhances scalar diffusion outward from the scalar mixing layer. Additionally, the promoted instability increases the scalar dissipation rate and turbulent scalar flux at small scales, facilitating faster scalar mixing. The effects manifest locally; external perturbations intensify mixing near the boundary, while internal perturbations affect the entire turbulent region. The impact of perturbations is consistent across different Reynolds numbers when the amplitudes normalised by the Kolmogorov velocity are the same, indicating that even weaker perturbations can enhance scalar mixing at higher Reynolds numbers. The mean scalar dissipation rate increases by up to 50 %, even when the perturbation energy is only 2.5 % of the turbulent kinetic energy. These results underscore the potential to leverage small-scale shear instability for efficient mixing enhancement in applications such as chemically reacting flows.

Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time, that artificial numerical noise in direct numerical simulation (DNS) of turbulence is approximately equivalent to thermal fluctuation and/or stochastic environmental noise. This confers physical significance on the artificial numerical noise of DNS of the Navier–Stokes equations. As a result, DNS on a fine mesh should correspond to turbulence under small internal/external physical disturbance, whereas DNS on a sparse mesh corresponds to turbulent flow under large physical disturbance. The key point is that all of them have physical meanings and so are correct in terms of their deterministic physics, even if their statistics are quite different. This is illustrated herein. Our paper provides a positive viewpoint regarding the presence of artificial numerical noise in DNS.

We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at the other. Clarke et al. (Phys. Rev. Fluids, vol. 9, 2024, 073101) recently conducted a thorough investigation of this model using methods of computational dynamical systems; inter alia, they showed that the filament first loses stability via a supercritical double-Hopf bifurcation, with periodic ‘planar-beating’ states (unstable) and ‘whirling’ states (stable) simultaneously emerging at the critical follower-force value. We complement their numerical study by carrying out a weakly nonlinear analysis close to this unconventional bifurcation, using the method of multiple scales. The main outcome is an ‘amplitude equation’ governing the slow modulation of small-magnitude oscillations of the filament in that regime. Analysis of this reduced-order model provides insights into the onset of spontaneous dynamics, including the creation of the nonlinear whirling states from particular superpositions of linear planar-beating modes as well as the selection of whirling over planar beating in three-dimensional scenarios.

A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning.

Particle-laden horizontal turbulent pipe flow is studied experimentally in the two-way coupling regime with a focus on delineating the effects of particle-to-fluid density ratio $\rho _{p}/\rho _{f}=1$ and 1.05 on the fluid and particle statistics. Particle volume fraction $\phi _{v}$ up to $1\,\%$ and viscous Stokes numbers ranging from $St^+ \approx 1.2$ to $St^+ \approx 3.8$ are investigated at friction Reynolds number $Re_\tau \approx 195$ using time-resolved two-dimensional particle image and tracking velocimetry. Substantial differences are observed between the statistics of neutrally buoyant (i.e. $\rho _{p}/\rho _{f}=1$) and denser (i.e. $\rho _{p}/\rho _{f}=1.05$) settling particles (with settling velocities 0.12–0.32 times the friction velocity), which, at most instances, show opposing trends compared to unladen pipe flow statistics. Neutrally buoyant particles show a slightly increased overall drag and suppressed turbulent stresses, but elevated particle–fluid interaction drag and results in elongated turbulent structures compared to the unladen flow, whereas $\rho _{p}/\rho _{f}=1.05$ particles exhibit a slight overall drag reduction even with increased radial turbulent stresses, and shorter streamwise structures compared to the unladen flow. These differences are enhanced with increasing $St^+$ and $\phi _v$, and can be attributed to the small but non-negligible settling velocity of denser particles, which also leads to differing statistics in the upper and lower pipe halves.

We perform simulations of a two-fluid–structure interaction problem involving liquid–gas flow past a fully submerged stationary circular cylinder. Interactions between the liquid–gas interface with finite surface tension and flow disturbances arising from the cylinder induce a variety of interfacial phenomena and wake structures. We map different interface regimes in a parameter space defined by the Bond number $Bo \in [100, 5000]$ and the submergence depth $h/D \in [1, 2.5]$ of the cylinder while keeping the Reynolds (Re) and Weber (We) numbers fixed at 150 and 1000, respectively. The emerging interface features are classified into three distinct regimes: interfacial waves generated by Strouhal vortices, the entrainment of multi-scale gas bubbles and the reduced deformation state. In the interfacial wave regime, we demonstrate that the frequency of transverse interface fluctuations at a specific streamwise location is identical to the vortex shedding frequency. Additionally, the wavelength of interfacial waves is determined by the size of vortex pairs consisting of alternating Strouhal vortices. In the gas entrainment regime at $ Bo = 1000$, our bubble-size distributions reveal that the entrained bubbles have sizes ranging from one to two orders of magnitude smaller than the cylinder. These multi-scale bubbles are formed primarily through plunging and surfing breakers at $h/D = 2.5$. In contrast, at $h/D = 1$, smaller bubbles initially emerge from the breakup of a gas finger. Over time, some of these bubbles grow in size through coalescence cascades. The influence of $ Re \in [50, 150]$ and $ We \in [700, 1100]$ on gas entrainment is quantified in terms of mean bubble size and count. Lastly, we demonstrate how the deformability of the liquid–gas interface drives the hydrodynamic lift force acting on the cylinder. The net downward lift materializes only in the gas entrainment and reduced deformation regimes due to the broken symmetry of the front stagnation point. While our study focuses on two-dimensional simulations, we also provide insights into the three-dimensional gas entrainment mechanism for one of the extreme cases at $h/D = 1$.

This work reports high-fidelity shock-tube experiments on the convergent Richtmyer–Meshkov (RM) instability at a heavy gas layer. The convergent shock tube is designed based on shock dynamics theory, significantly mitigating interface deceleration and reflected shock. As a result, long-term observation of instability growth up to nonlinear stage, free of interface deceleration and reshock, is achieved. Various types of SF$_6$ layers surrounded by air with controllable thicknesses and shapes, created using a soap film technique, are examined. For thick layers, the evolutions of the outer and inner interfaces are nearly decoupled regardless of the layer shape. The weakly nonlinear model of Wang (Phys. Plasmas,vol. 22, 2015, p. 082702), designed for cylindrical RM instability at a single interface, provides a reasonable prediction of perturbation growth at the inner interface, while slightly underestimating instability growth at the outer interface, as it neglects the effects of rarefaction wave. For thin layers, perturbation growth is fastest at either interface when both interfaces initially possess in-phase perturbations, moderate when only one interface is initially perturbed and slowest when the two interfaces have anti-phase perturbations. This variation in growth rates is due to the fact that the evolution of a thin layer is influenced by both reverberating waves and interface coupling, with each factor being highly sensitive to the layer shape. The original vortex method is extended to address the convergent RM instability by incorporating the influences of unsteady background flow, interface coupling and reverberating waves into the transport of a vortex sheet. This extended vortex method enables accurate prediction of convergent RM instability at a gas layer, covering the full range from early linear to late nonlinear stages.

Turbulent flows over porous substrates are studied via a systematic exploration of the dependence of the flow properties on the substrate parameters, including permeability $K$, grain pitch $L$ and depth $h$. The study uses direct numerical simulations mainly for staggered-cube substrates with $L^+\approx 10$–$50$, $\sqrt {K}/L\approx 0.01$–$0.25$ and depths from $h=O(L)$ to $h\gg L$, ranging from typical impermeable rough surfaces to deep porous substrates. The results indicate that the permeability has significantly greater relevance than the grain size and microscale topology for the properties of the overlying flow, including the mean-flow slip and the shear across the interface, the drag increase relative to smooth-wall flow and the statistics and spectra of the overlying turbulence, whereas the direct effect of grain size is only noticeable near the interface as grain-coherent flow fluctuations. The substrate depth also has a significant effect, with shallower substrates suppressing the effective transpiration at the interface. Based on the direct-simulation results, we propose an empirical ‘equivalent permeability’ $K_{eq}^t$ that incorporates this effect and scales well the overlying turbulence for substrates with different depths, permeabilities, etc. This result suggests that wall normal transpiration driven by pressure fluctuations is the leading contributor to the changes in the drag and the overlying turbulence. Based on this, we propose a conceptual $h^+$–$\sqrt {K^+}$ regime diagram where, for any given substrate topology, turbulence transitions smoothly from that over impermeable rough surfaces with $h=O(L)$ to that over deep porous substrates with $h^+\gtrsim 50$, with the latter limit determined by the typical lengthscale of the overlying pressure fluctuations.