The presence of large-scale coherent structures can significantly impact the dynamics of a turbulent flow field and the behaviour of a flame stabilized in that flow. The goal of this study is to analyse how increasing free-stream turbulence can change the response of the flow to longitudinal acoustic excitation of varying amplitudes. We study the flow in the wake of a cylindrical bluff body at both non-reacting and reacting conditions, as the presence of a flame can significantly alter the global stability of the flow. The frequency of longitudinal acoustic excitation is set to match the natural frequency of anti-symmetric vortex shedding for this configuration and we vary the free-stream turbulence using perforated plates upstream of the bluff body. The results show that varying the level of free-stream turbulence can influence not only the amplitude of the coherent flow response, but also the symmetry of vortex shedding in the presence of longitudinal acoustic excitation. Increasing the turbulence intensity can fundamentally change the structure of the time-averaged flow and can directly impact the coherent flow response in two ways. First, increasing turbulence intensity can enhance the amplitude of the natural anti-symmetric vortex shedding mode in the wake. Second, increasing turbulence intensity weakens the symmetric response of the flow to the longitudinal acoustic excitation. In the non-reacting and reacting conditions, both symmetric and anti-symmetric modes are present and are characterized using a spectral proper orthogonal decomposition. We see evidence of interaction between the symmetric and anti-symmetric modes, which leads to an interference pattern in the coherent vorticity response in the shear layers. We conclude by presenting a conceptual model for the influence that turbulence has on these flows.

The particle trajectories in irrotational, incompressible and inviscid deep-water surface gravity waves are open, leading to a net drift in the direction of wave propagation commonly referred to as the Stokes drift, which is responsible for catalysing surface wave-induced mixing in the ocean and transporting marine debris. A balance between phase-averaged momentum density, kinetic energy density and vorticity for irrotational, monochromatic and spatially periodic two-dimensional water waves is derived by working directly within the Lagrangian reference frame, which tracks particle trajectories as a function of their labels and time. This balance should be expected as all three of these quantities are conserved following particles in this system. Vorticity in particular is always conserved along particles in two-dimensional inviscid flow, and as such even in its absence it is the value of the vorticity that fundamentally sets the drift, which in the Lagrangian frame is identified as the phase-averaged momentum density of the system. A relationship between the drift and the geometric mean water level of particles is found at the surface, which highlights connections between the geometry and dynamics. Finally, an example of an initially quiescent fluid driven by a wavelike pressure disturbance is considered, showing how the net momentum and energy from the surface pressure disturbance transfer to the wave field, and recognizing the source of the mean Lagrangian drift as the net momentum required to generate an irrotational surface wave by any conservative force.

We investigate the retraction of a circular thin film coated with insoluble surfactants, which is punctured at its centre. We assume that the surface pressure of the liquid–gas interface is related to the number density of surfactants through a linear equation of state, which is characterized by a single parameter: the Gibbs dilation modulus. To solve the governing equations and track the deformation of the domain, we use the finite element method with an arbitrary Lagrangian–Eulerian approach where the film surface is sharp. Our simulations show that the surface elasticity introduced by the surfactants slows down the retraction and introduces oscillations at early times. In agreement with previous experiments and theoretical analysis, we find that the presence of surfactants introduces perturbations of the film thickness over progressively larger distances as the surface elasticity increases. The surface perturbations travel faster than the retracting edge of the film at a speed proportional to the Gibbs modulus. For large values of the Gibbs modulus, the interface behaviour approaches that of an incompressible two-dimensional solid. Our analysis sheds light on the effect of insoluble surfactants on the opening of a circular hole in a thin film and can be extended to investigate the onset of surface cracks and fractures.

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$, respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$, where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

A novel selective mode decomposition, proper orthogonal decomposition and dynamic mode decomposition methods are used to analyse large-eddy simulation data of the flow field about a NACA0012 airfoil at low Reynolds numbers of $5\times 10^4$ and $9\times 10^4$, and at near-stall conditions. The objective of the analysis is to investigate the structure of the laminar separation bubble (LSB) and its associated low-frequency flow oscillation (LFO). It is shown that the flow field can be decomposed into three dominant flow modes: two low-frequency modes (LFO-Mode-1 and LFO-Mode-2) that govern an interplay of a triad of vortices and sustain the LFO phenomenon, and a high-frequency oscillating (HFO) mode featuring travelling Kelvin–Helmholtz waves along the wake of the airfoil. The structure and dynamics of the LSB depend on the energy content of these three dominant flow modes. At angles of attack lower than the stall angle of attack and above the angle of a full stall, the flow is dominated by the HFO mode. At angles of attack above the stall angle of attack the LFO-Mode-2 overtakes the HFO mode, triggers instability in the LSB and initiates the LFO phenomenon. Previous studies peg the structure, stability and bursting conditions of the separation bubble to local flow parameters. However, the amplitude of these local flow parameters is dependent on the energy content of the three dominant flow modes. Thus, the present work proposes a more robust bursting criterion that is based on global eigenmodes.

The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees–Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas specific volume instead of the gas fraction.