Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh–Taylor instability, here only phenomenological theories are currently available. The present review provides an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh–Taylor turbulence together with numerical and experimental evidence for their support. Although the focus is mainly on the classical Boussinesq Rayleigh–Taylor turbulence of miscible fluids, the review extends to other fluid systems with viscoelastic behavior, affected by rotation of the reference frame, and, finally, in the presence of reactions.

In this perspective article, we discuss how soft matter can spearhead efforts to harness confinement as a tool to steer self-organisation across different scales and disciplines.

Pushing two fluids with different density one against the other causes the development of the Rayleigh-Taylor instability at their interface, which further evolves in a complex mixing layer. In porous media, this process is influenced by the viscous resistance experienced while flowing through the pores, which is described by the Darcy's law. Here, we investigate the mixing properties of the Darcy-Rayleigh-Taylor system in the limit of large Péclet number by means of direct numerical simulations in three and two dimensions. In the mixing zone, the balance between gravity and viscous forces results in a non-self-similar growth of elongated plumes, whose length increases linearly in time while their width follows a diffusive growth. The mass-transfer Nusselt number is found to increase linearly with the Darcy-Rayleigh number supporting a universal scaling in porous convection at high Ra numbers. Finally, we find that the mixing process displays important quantitative differences between two and three dimensions.

The behaviour of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov 4/5-law into a relation predicting the linear (in time) scaling for the second-order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterisation of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for 3d turbulence, and for 2d turbulence in the inverse cascade regime. Such parameterisation supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small- and large timescales. When large-time saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterisation allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalised root mean squared acceleration as a function of the Reynolds number, without fitting parameters.

We study the clustering properties of inertial particles in a turbulent viscoelastic fluid. The investigation is carried out by means of direct numerical simulations of turbulence in the Oldroyd-B model. The effects of polymers on the small-scale properties of homogeneous turbulence are considered in relation with their consequences on clustering of particles, both lighter and heavier than the carrying fluid. We show that, depending on particle and flow parameters, polymers can either increase or decrease clustering.

We study the effects of dimensional confinement on the evolution of incompressible Rayleigh–Taylor mixing both in a bulk flow and in porous media by means of numerical simulations of the transport equations. In both cases, the confinement to two-dimensional flow accelerates the mixing process and increases the speed of the mixing layer. Dimensional confinement also produces stronger correlations between the density and the velocity fields affecting the efficiency of the mass transfer, quantified by the dependence of the Nusselt number on the Rayleigh number. This article is part of the theme issue ‘Scaling the turbulence edifice (part 2)’.