Data from direct numerical simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. We developed a new method, based on an extension of the barycentric map approach, that allows us to quantify and visualize the anisotropy and componentiality of the flow at any scale. Using this we found that the bubbles significantly enhance anisotropy in the flow at all scales compared with the unladen case, and that for some bubble cases, very strong anisotropy persists down to the smallest scales of the flow. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the energy transfer among the scales of the flow, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the behaviour of the energy transfer is significantly modified by the bubbles, suggesting that the bubbles play a strong role in altering the activity of the nonlinear term in the flow. The skewness of the velocity increments also reveals a strong effect of the bubbles on the flow, changing both its sign and magnitude compared with the single-phase case. We also consider the normalized forms of the fourth-order structure functions, and the results reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation-scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.

The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor–Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which – by construction – rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to $8192^3$ (defined based on the $2{\rm \pi}$-periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative $L^2$-error of $0.27\,\%$ for the temporal evolution of the kinetic energy and $3.52\,\%$ for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.

Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on the effects of the thermal boundary condition on thermal convection, in terms of instability onset, fully developed transport properties and flow structure. We impose a Robin boundary condition, enforcing linear coupling between the temperature anomaly and its radial derivative, with the Biot number ${{\textit {Bi}}}$ as a proportionality factor in non-dimensional form. Varying ${{\textit {Bi}}}$ allows us to transition from fixed temperature for ${{\textit {Bi}}}=+\infty$, to imposed heat flux for ${{\textit {Bi}}}=0$. We find that the onset of convection is only affected by ${{\textit {Bi}}}$ in the non-rotating case. Far from onset, considering an effective Rayleigh number and a generalized Nusselt number, we show that the Nusselt and Péclet numbers follow standard universal scaling laws, independent of ${{\textit {Bi}}}$ in all cases considered. However, for the non-rotating limit, the large-scale flow structure keeps the signature of the boundary condition with more vigorous large scales for smaller ${{\textit {Bi}}}$, even though the global heat transfer and kinetic energy are the same. For all practical purposes, the Robin condition can be safely replaced by a fixed flux when ${{\textit {Bi}}} \lesssim 0.03$ and by a fixed temperature for ${{\textit {Bi}}}\gtrsim 30$. For turbulent rapidly rotating convection, the thermal boundary condition does not seem to have any impact, once the effective numbers are considered and a reference temperature profile has been chosen.

Artificial microswimmers, or ‘microbots’, have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their environment. Traditionally, self-phoretic particles are point like, but slender phoretic rods have become an increasingly prevalent design. While there has been substantial interest in creating efficient asymptotic theories for slender phoretic rods, hitherto such theories have been restricted to straight rods with axisymmetric patterning. However, modern manufacturing methods will soon allow fabrication of slender phoretic filaments with complex three-dimensional shapes. In this paper, we develop a slender body theory for the solute of self-diffusiophoretic filaments of arbitrary three-dimensional shape and patterning. We demonstrate analytically that, unlike other slender body theories, first-order azimuthal variations arising from curvature and confinement can make a leading-order contribution to the swimming kinematics.

Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity $\unicode[STIX]{x1D6FA}_{i}$ and the outer cylinder stationary. With $R_{i},R_{o}$ the inner and outer radii respectively, the radius ratio is $\unicode[STIX]{x1D702}=0.909$. The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range $Re_{i}=10^{5}{-}10^{6}$ where $Re_{i}=\unicode[STIX]{x1D6FA}_{i}R_{i}d/\unicode[STIX]{x1D708}$ and $d=R_{o}-R_{i}$ is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number $Nu$ (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number $Ta$ and $\unicode[STIX]{x1D702}$. These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of $Re_{i}/Ta$, and where $Nu\sim Ta^{1/2}$.

Upon interaction with underwater shock waves, bubbles can collapse and produce high-speed liquid jets in the direction of the wave propagation. This work experimentally investigates the impact of laser-induced underwater impulsive shock waves, i.e. shock waves with a short, finite width, of variable peak pressure on bubbles of radii in the range 10–500 $\mathrm {\mu }$m. The high-speed visualisations provide new benchmarking of remarkable quality for the validation of numerical simulations and the derivation of scaling laws. The experimental results support scaling laws describing the collapse time and the jet speed of bubbles driven by impulsive shock waves as a function of the impulse provided by the wave. In particular, the collapse time and the jet speed are found to be, respectively, inversely and directly proportional to the time integral of the pressure waveform for bubbles with a collapse time longer than the duration of shock interaction and for shock amplitudes sufficient to trigger a nonlinear bubble collapse. These results provide a criterion for the shock parameters that delimits the jetting and non-jetting behaviour for bubbles having a shock width-to-bubble size ratio smaller than one. Jetting is, however, never observed below a peak pressure value of 14 MPa. This limit, where the pressure becomes insufficient to yield a nonlinear bubble collapse, is likely the result of the time scale of the shock wave passage over the bubble becoming very short with respect to the bubble collapse time scale, resulting in the bubble effectively feeling the shock wave as a spatially uniform change in pressure, and in an (almost) spherical bubble collapse.

Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number $Re$ in which the effective Reynolds number governing the streak and roll dynamics is $\mathit {O}(1)$. Consequently, these viscous ECS are not suitable candidates for quasi-coherent structures away from the wall that necessarily are inviscid in the mean. Specifically, viscous ECS cannot account for the singular nature of the inertial domain, where the flow self-organizes into uniform momentum zones (UMZs) separated by internal shear layers and the instantaneous streamwise velocity develops a staircase-like profile. In this investigation, a large-$Re$ asymptotic analysis is performed to explore the potential for a three-dimensional, short streamwise- and spanwise-wavelength instability of the embedded shear layers to sustain a spatially distributed array of much larger-scale, effectively inviscid streamwise roll motions. In contrast to other self-sustaining process theories, the rolls are sufficiently strong to differentially homogenize the background shear flow, thereby providing a mechanistic explanation for the formation and maintenance of UMZs and interlaced shear layers that respects the leading-order balance structure of the mean dynamics.

This study explores the control of mesoscale variability by topographic features with lateral scales that are less than the scale of the eddies generated by baroclinic instability. These dynamics are described using a combination of numerical simulations and an asymptotic multiscale model. The multiscale method makes it possible to express the system dynamics by a closed set of equations written entirely in terms of mesoscale variables, thereby providing a physical basis for the development of submesoscale parameterization schemes. The submesoscale topography is shown to influence such fundamental properties of mesoscale variability as the meridional eddy-induced transport and eddy kinetic energy. It is argued that the adverse influence of submesoscale topography on baroclinic instability is ultimately caused by the homogenization tendency of potential vorticity in the bottom density layer. The multiscale model formally assumes a substantial separation between the scales of interacting flow components. However, the comparison of asymptotic solutions with their submesoscale-resolving numerical counterparts indicates that the multiscale method is remarkably accurate even when scale separation is virtually non-existent.

This study numerically investigates the flow characteristics past a solid and smooth sphere translating steadily along the axis of a cylindrical tube filled with wormlike micellar solutions in the creeping flow regime. The two-species Vasquez–Cook–McKinley and single-species Giesekus constitutive models are used to characterize the rheological behaviour of the micellar solutions. Once the Weissenberg number exceeds a critical value, an unsteady motion downstream of the sphere is observed in the case of the two-species model. We provide evidence that this unsteady motion downstream of the sphere is caused by the sudden rupture of long and stretched micelles in this region, resulting from an increase in the extensional flow strength. The corresponding single-species Giesekus model for the wormlike micellar solution, with no breakage and reformation, predicts a steady flow field under otherwise identical conditions. Therefore, it further provides evidence presented herein for the onset of this unsteady motion. Furthermore, we find that the onset of this unsteady motion downstream of the sphere is delayed as the ratio of sphere to tube diameter decreases. A similar kind of unsteady motion has also been observed in several earlier experiments for the problem of a sphere sedimenting in a tube filled with wormlike micellar solutions. We find a remarkable qualitative similarity in the flow characteristics between the present numerical results for a steadily translating sphere and prior experimental results for a falling sphere.