We study the dispersion of bubble swarms rising in initially quiescent water using three-dimensional Lagrangian tracking of deformable bubbles and tracer particles in an octagonal bubble column. Two different bubble sizes (3.5 mm and 4.4 mm) and moderate gas volume fractions ($0.52\,\%{-}1.20\,\%$) are considered. First, we compare the dispersion inside bubble swarms with that for single-bubble cases, and find that the horizontal mean squared displacement (MSD) in the swarm cases exhibits oscillations around the asymptotic scaling predicted for a diffusive regime. This occurs due to wake-induced bubble motion; however, the oscillatory behaviour is heavily damped compared to the single-bubble cases due to the presence of bubble-induced turbulence (BIT) and bubble–bubble interactions in the swarm. The vertical MSD in bubble swarms is nearly an order of magnitude faster than in the single-bubble cases, due to the much higher vertical fluctuating bubble velocities in the swarms. We also investigate tracer dispersion in BIT, and find that concerning the time to transition away from the ballistic regime, larger bubbles with a higher gas void fraction transition earlier than tracers, consistent with Mathai et al. (2018, Phys. Rev. Lett., vol. 121, 054501). However, for bubble swarms with smaller bubbles and a lower gas void fraction, they transition at the same time. This differing behaviour is due to the turbulence being more well-mixed for the larger bubble case, whereas for the smaller bubble case, the tracer dispersion is highly dependent on the wake fluctuations generated by the oscillating motion of nearby bubbles.

Experiments are carried out in a smooth-wall turbulent boundary layer (TBL) ($\textit{Re}_\tau \geq 3500$) subjected to different pressure gradient (PG) histories. Oil-film interferometry is used to measure the skin friction evolution over the entire history while wide-field particle image velocimetry captures the mean flow field. This data are used to demonstrate the influence of PG history on skin friction as well as other integral quantities such as displacement ($\delta ^*$) and momentum thickness ($\theta$). Based on observations from the data, a new set of ordinary differential equations are proposed to model the streamwise evolution of a TBL subjected to different PG histories. The model is calibrated using a limited number of experimental cases and its utility is demonstrated on other cases. Moreover, the model is applied to data from large-eddy simulations of flows in adverse PG conditions (Bobke et al. 2017, J. Fluid Mech. 820, 667–692). The model is subsequently used to identify the impact of PG history length on the boundary layer. This can also be interpreted as determining the spatial frequency response of the boundary layer to PG disturbances. Results suggest that short spatial variations in PGs primarily affect a small portion of the TBL evolution, whereas longer-lasting ones have a more extensive impact.

We consider two-dimensional (2-D) free surface gravity waves in prismatic channels, including bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow-water equations) we derive a one-dimensional transverse averaged model describing dispersive effects related solely to variations of the channel topography. These effects have been demonstrated in Chassagne et al. 2019 J. Fluid Mech. 870, 595–616 to be predominant in the propagation of bores with Froude numbers below a critical value of approximately 1.15. The model proposed is fully nonlinear, Galilean invariant, and admits a variational formulation under natural assumptions about the channel geometry. It is endowed with an exact energy conservation law, and admits exact travelling-wave solutions. Our model generalises and improves the linear equations proposed by Chassagne et al. 2019 J. Fluid Mech. 870, 595–616, as well as in Quezada de Luna and Ketcheson, 2021 J. Fluid Mech. 917, A45. The system is recast in two useful forms appropriate for its numerical approximations, whose properties are discussed. Numerical results allow the verification of the implementation of these formulations against analytical solutions, and validation of our model against fully 2-D nonlinear shallow-water simulations, as well as the famous experiments by Treske 1994 J. Hyd. Res. 32, 355–370.