This study is devoted to the analysis of capillary oscillations of a gas bubble in a liquid with an insoluble surfactant adsorbed on the surface. The influence of the Gibbs elasticity, the viscosities of the liquid and gas, as well as the shear and dilatational surface viscosities, on the damping of free oscillations is examined. Dependences of the frequency shift and the damping rate on the parameters of the problem are determined. In the limit of small viscosities and neglecting the surfactant surface diffusion, a simplified dispersion relation is obtained, which includes finite parameters of surface viscosities and Gibbs elasticity. From this relation, conditions are identified under which the damping of capillary oscillations can occur with a small frequency. Numerical solutions of the full dispersion relation demonstrate that a non-oscillatory regime is impossible for the considered configuration. An additional mode associated with Gibbs elasticity is discovered, characterized as a rule by low natural frequency and damping rate. Approximate relations for the complex natural frequency of bubble oscillations in a low-viscosity liquid in the presence of a surfactant are derived, including an estimate of the contribution of the gas inside the bubble to viscous dissipation. An original Lagrangian–Eulerian method is proposed and used to perform direct numerical simulations based on the full nonlinear Navier–Stokes equations and natural boundary conditions at the interface, accounting for shear and dilatational viscosities. The numerical data on the damping process confirm the results of the linear theory.

Turbulent Rayleigh–Bénard convection in an extended layer of square cross-section with moderate aspect ratio $L/H=8.6$ ($L$ is the length of the cell, $H$ is its height) is studied numerically for Rayleigh numbers in the range ${\textit{Ra}}= 10^6{-}10^8$. We focus on the influence of different types of boundary conditions, including asymmetrical ones, on the characteristics of Rayleigh–Bénard convection with and without an immersed freely floating body. Convection without a floating body is characterised by the formation of stable thermal superstructures with preferred location. The crucial role of the symmetry of the boundary conditions is revealed. In the case of thermal boundary conditions of different types at the upper and lower boundaries, the flow pattern in Rayleigh–Bénard convection has a regular shape. The immersed body makes random wanderings and actively mixes the fluid, preventing the formation of superstructures. The mean flow structure with an immersed body is similar for all combinations of boundary conditions except for the case of a fixed heat flux at both boundaries. The floating disk does not change the tendency of turbulent convection to form a circulation of the maximal available scale under symmetric Neumann-type conditions. The type of boundary conditions has a weak influence on the Nusselt and Reynolds number values, significantly changing the ratio of the mean and fluctuating components of the heat flux. As the Rayleigh number increases, the motions of the body become more intensive and intermittent. The increase of $Ra$ also changes the structure of the mean flow without the body but the additional mixing provided by the floating body preserves the flow structure.

We conduct three-dimensional numerical simulations on centrifugal convection (CC) in a closed annular container, incorporating gravity and no-slip top and bottom boundaries, to systematically investigate rotation-induced secondary flow. The Stewartson layer, identified by an elongated circulation in mean vertical velocity plots, emerges near the inner and outer cylinders only beyond a critical gravitational forcing. Quantitative analyses confirm that the layer thickness scales as $\delta _{\,\!\textit{st}}\sim {\textit{Ek}}^{1/3}$ due to rotational effects, consistent with results from rotating Rayleigh–Bénard convection, where $Ek$ represents the Ekman number. The internal circulation strength, however, is determined by both gravitational buoyancy and rotational effects. We propose that gravitational buoyancy drives the internal flow, which balances against viscous forces to establish a terminal velocity. Through theoretical analysis, the vertical velocity amplitude follows $W_{\,\!\textit{st}}\sim {\textit{Ek}}^{5/3}\,Ro^{-1}\,{\textit{Ra}}_g\,Pr^{-1}$, showing good agreement with simulation results across a wide parameter range. Here, $Ro^{-1}$ represents the inverse Rossby number, ${\textit{Ra}}_g$ is the gravitational Rayleigh number, and ${\textit{Pr}}$ is the Prandtl number. The theoretical predictions match simulations well, demonstrating that the Stewartson layer is gravity-induced and rotationally constrained through geostrophic balance in the CC system. These findings yield fundamental insights into turbulent flow structures and heat transfer mechanisms in the CC system, offering both theoretical advances and practical engineering applications.

In this paper, we showcase how flow obstruction by a deformable object can lead to symmetry breaking in curved domains subject to angular acceleration. Our analysis is motivated by the deflection of the cupula, a soft tissue located in the inner ear that is used to perceive rotational motion as part of the vestibular system. The cupula is understood to block the rotation-induced flow in a toroidal region with the flow-induced deformation of the cupula used by the brain to infer motion. By asymptotically solving the governing equations for this flow, we characterise regimes for which the sensory system is sensitive to either angular velocity or angular acceleration. Moreover, we show the fluid flow is not symmetric in the latter case. Finally, we extend our analysis of symmetry breaking to understand the formation of vortical flow in cavernous regions within channels. We discuss the implications of our results for the sensing of rotation by mammals.

Vertical thermal convection exhibits weak turbulence and spatio-temporally chaotic behaviour. For this configuration, we report seven new equilibria and 26 new periodic orbits. These orbits, together with four previously studied in Zheng et al. (J. Fluid Mech., 2024b, vol. 1000, p. A29) bring the number of periodic-orbit branches computed so far to 30, all solutions to the fully nonlinear three-dimensional Navier–Stokes equations. These new and unstable invariant solutions capture intricate spatio-temporal flow patterns including straight, oblique, wavy, skewed and distorted convection rolls, as well as bursts and defects. These interesting and important fluid mechanical processes in a small flow unit are shown to also appear locally and instantaneously in a chaotic simulation in a large domain. Most of the solution branches show rich spatial and/or spatio-temporal symmetries. The bifurcation-theoretic organisation of these solutions is discussed; the bifurcation scenarios include Hopf, pitchfork, saddle-node, period-doubling, period-halving, global homoclinic and heteroclinic bifurcations, as well as isolas. Furthermore, these orbits are shown to be able to reconstruct statistically the core part of the attractor, so that these results may contribute to a quantitative description of transitional fluid turbulence using periodic orbit theory.

In this paper, we study experimentally the dispersion of colloids in a two-dimensional, time-independent, Rayleigh–Bénard flow in the presence of salt gradients. Due to the additional scalar, the colloids do not follow exactly the Eulerian flow field, but have a (small) extra velocity $\boldsymbol{v}_{{dp}} = D_{{dp}}\, \boldsymbol{\nabla }\log C_s$, where $D_{{dp}}$ is the phoretic constant, and $C_s$ is the salt concentration. Such a configuration is motivated by the theoretical work by Volk et al. (2022, J. Fluid Mech., vol. 948, A42), which predicted enhanced transport or blockage in a stationary cellular flow depending on the value of a blockage coefficient. By means of high dynamical range light-induced fluorescence, we study the evolution of the colloids concentration field at large Péclet number. We find good agreement with the theoretical work, although a number of hypotheses are not satisfied, as the experiment is non-homogeneous in space, and intrinsically transient. In particular, we observe enhanced transport when salt and colloids are injected at both ends of the Rayleigh–Bénard chamber, and blockage when colloids and salt are injected together and phoretic effects are strong enough.

We present experiments of settling and dissolving sugar grains continuously sieved above a water tank with varying grain size and mass flux. Through drag and dissolution, grains force a downward flow whose dynamics are analysed in a laser sheet through particle image velocimetry and the use of home-made fluorescent sugar to track the negatively buoyant sugary water. We reveal different regimes, mostly controlled by the grain size, from a particle-constrained laminar flow at large grain size, to a turbulent plume with an effectively fluid-like behaviour when grains are small. The transitions between regimes are predicted from dimensionless numbers quantifying fluid–particle coupling, collective effects between grains and the possible onset of a Rayleigh–Taylor instability at the source. When a quasi-steady regime is reached, all grains dissolve above a finite depth, below which the flow is exclusively driven by dissolved sugar. We derive simple idealised models based on the source properties that predict the depth of this dissolution layer as well as the characteristic flow velocity.