Direct numerical simulations (DNS) of turbulent stratified flow in an open channel with an internal heat source following the Beer–Lambert law from the surface are used to investigate the transition from neutral to strongly stable flow. Our buoyancy bulk parameter is defined through the ratio of the domain height ${\it\delta}$ to $\mathscr{L}$ , a bulk Obukhov length scale for the flow. We cover the range ${\it\lambda}={\it\delta}/\mathscr{L}=0{-}2.0$ , from neutral conditions to the onset of the stable regime, with the Reynolds number range $Re_{{\it\tau}}=200{-}800$ , at a Prandtl number of 0.71. The result is a boundary layer flow where the effects of stratification are weak in the wall region but progressively stronger in the outer layer up to the free surface. At ${\it\lambda}\simeq 1$ the turbulent kinetic energy (TKE) budget is in local equilibrium over a region extending from the near-wall region to a free-surface affected region a distance $l_{{\it\nu}}$ from the surface, with $l_{{\it\nu}}/{\it\delta}\sim Re^{-1/2}$ . In this equilibrium region the flow can be characterised by the flux Richardson number $R_{f}$ and the local Obukhov length scale ${\it\Lambda}$ . At higher ${\it\lambda}$ local mixing limit conditions are observed over an extended region. At ${\it\lambda}=2$ the flux Richardson number approaches critical limit values of $R_{f,c}\simeq 0.18$ and gradient Richardson number $Ri_{c}\simeq 0.2$ . At high ${\it\lambda}$ , we obtain a flow field where buoyancy interacts with the smallest scales of motion and the turbulent shear stress and buoyancy flux are suppressed to molecular levels. We find that this regime can be identified in terms of the parameter $Re_{\mathscr{L},c}=\mathscr{L}u_{{\it\tau}}/{\it\nu}\lesssim 200{-}400$ (where $u_{{\it\tau}}$ is the friction velocity and ${\it\nu}$ the kinematic viscosity), which is related to the $L_{\ast }$ parameter of Flores and Riley (Boundary-Layer Meteorol., vol. 139 (2), 2011, pp. 241–259) and buoyancy Reynolds number $\mathscr{R}$ . With energetic equilibrium attained, the local buoyancy Reynolds number, $Re_{{\it\Lambda}}={\it\Lambda}\langle u^{\prime }w^{\prime }\rangle ^{1/2}/{\it\nu}$ , is directly related to the separation of the Ozmidov ( $l_{O}$ ) and Kolmogorov ( ${\it\eta}$ ) length scales in the outer boundary layer by $Re_{{\it\Lambda}}\simeq \mathscr{R}\equiv (l_{O}/{\it\eta})^{4/3}$ . The inner wall region has the behaviour $\mathscr{R}\sim Re_{\mathscr{L}}Re_{{\it\tau}}$ , in contrast to stratified boundary layer flows where the buoyancy flux is non-zero at the wall and $\mathscr{R}\sim Re_{\mathscr{L}}$ .

In order to understand the flow profiles of complex fluids, a crucial issue concerns the emergence of spatial correlations among plastic rearrangements exhibiting cooperativity flow behaviour at the macroscopic level. In this paper, the rate of plastic events in a Poiseuille flow is experimentally measured on a confined foam in a Hele-Shaw geometry. The correlation with independently measured velocity profiles is quantified by looking at the relationship between the localisation length of the velocity profiles and the localisation length of the spatial distribution of plastic events. To complement the cooperativity mechanisms studied in foam with those of other soft glassy systems, we compare the experiments with simulations of dense emulsions based on the lattice Boltzmann method, which are performed both with and without wall friction. Finally, unprecedented results on the distribution of the orientation of plastic events show that there is a non-trivial correlation with the underlying local shear strain. These features, not previously reported for a confined foam, lend further support to the idea that cooperativity mechanisms, originally invoked for concentrated emulsions (Goyon et al., Nature, vol. 454, 2008, pp. 84–87), have parallels in the behaviour of other soft glassy materials.

The instability of the steady axisymmetric flow in a sealed elongated cylinder, driven by a rotating end disk, is studied with the help of numerical simulations. It is argued that this instability is of the shear-layer type, being caused by the presence of an inflection point in the radial distribution of axial velocity of the base circulatory flow. The disturbance kinetic energy is localized in both the radial and axial directions, reaching its peak near the rotating disk, where the magnitude of base-flow axial velocity is close to its maximum. The critical Reynolds number, $\mathit{Re}_{cr}$ , is found to be nearly $h$ -independent for $h>5$ ; $h$ is the cylinder length-to-radius ratio. It is shown that the sidewall co-rotation suppresses the instability. As the co-rotation increases, the centrifugal instability becomes the most dangerous, i.e. determines $\mathit{Re}_{cr}$ . Physical explanations are given for the stabilizing effect of the co-rotation, which is stronger (weaker) for the shear-layer (centrifugal) instability.

It is hypothesized that the relative stability of leading-edge vortices (LEVs) on flapping profiles can be improved by moderating LEV growth through spanwise vorticity convection and vortex stretching. Moreover, it is hypothesized that the reduced frequency $k$ and profile sweep ${\it\Lambda}$ are critical in predicting relative LEV stability as determined by the aforementioned effects. These hypotheses are then confirmed experimentally with phase-averaged particle image velocimetry (PIV) and three-dimensional particle tracking velocimetry. In particular, more stable LEVs are observed at higher reduced frequencies, which is argued to represent the ratio between the limiting vortex size and the rate of vorticity feeding. The introduction of profile sweep increased both relative LEV stability and spanwise vorticity transport. It is thought that spanwise vorticity transport improved LEV stability by acting as a sink for vorticity generated in the leading-edge shear layer.

We present a theoretical and experimental study of viscous gravity currents lubricated by another viscous fluid from below. We use lubrication theory to model both layers as Newtonian fluids spreading under their own weight in two-dimensional and axisymmetric settings over a smooth rigid horizontal surface and consider the limit in which vertical shear provides the dominant resistance to the flow in both layers. There are contributions from Poiseuille-like flow driven by buoyancy and Couette-like flow driven by viscous coupling between the layers. The flow is self-similar if both fluids are released simultaneously, and exhibits initial transient behaviour when there is a delay between the initiation of flow in the two layers. We solve for both situations and show that the latter converges towards self-similarity at late times. The flow depends on three key dimensionless parameters relating the relative dynamic viscosities, input fluxes and density differences between the two layers. Provided the density difference between the two layers is bounded away from zero, we find an asymptotic solution in which the front of the lubricant is driven by its own gravitational spreading. There is a singular limit of equal densities in which the lubricant no longer spreads under its own weight in the vicinity of its nose and ends abruptly with a non-zero thickness there. We explore various regimes, from thin lubricating layers underneath a more viscous current to thin surface films coating an underlying more viscous current and find that although a thin film does not greatly influence the more viscous current if it forms a surface coating, it begins to cause interesting dynamics if it lubricates the more viscous current from below. We find experimentally that a lubricated gravity current is prone to a fingering instability.

We present a depth-integrated equation for the mechanics of generation, propagation and dissipation of low-frequency hydro-acoustic waves due to sudden bottom displacement in a weakly compressible ocean overlying a weakly compressible viscous sediment layer. The model is validated against a full 3D computational model. Physical properties of these waves are studied and compared with those for waves over a rigid sea bed, revealing changes in the frequency spectrum and modal peaks. The resulting model equation can be used for numerical prediction in large-scale domains, overcoming the computational difficulties of 3D models while taking into account the role of bottom dissipation on hydro-acoustic wave generation and propagation.

The translational and rotational dynamics of oblate spheroidal particles suspended in a directly simulated turbulent channel flow have been examined. Inertial disk-like particles exhibited a significant preferential orientation in the plane of the mean shear. The rotational inertia about the symmetry axis of the disk-like particles hampered the spin-up of the flattest particles to match the mean flow vorticity. The influence of the particle shape on the orientation and rotation diminished as the translational inertia increased from Stokes number 1 to 30. An isotropization of both orientation and rotation could be observed in the core region of the channel. The translational motion of the oblate spheroids had a weak dependence on the aspect ratio. We therefore concluded that inertial particles sample nearly the same flow field irrespective of shape. Nevertheless, the orientation and rotation of disk-like particles turned out to be qualitatively different from the dynamics of fibre-like particles.