New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time $t$ ; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

We present an investigation on the onset of Darcy–Bénard instability in a two-dimensional porous medium saturated with a non-Newtonian fluid and heated from below in the presence of a uniform horizontal pressure gradient. The fluid is taken to be of power-law nature with constant rheological index and temperature-dependent consistency index . A two-dimensional linear stability analysis in the vertical plane yields the critical wavenumber and the generalised critical Rayleigh number as functions of dimensionless problem parameters, with a non-monotonic dependence from and with maxima/minima at given values of , a parameter representing the effects of consistency index variations due to temperature. A series of experiments are conducted in a Hele-Shaw cell of aspect ratio to provide a verification of the theory. Xanthan Gum mixtures (nominal concentration from 0.10 % to 0.20 %) are employed as working fluids with a parameter range and . The experimental critical wavenumber corresponding to incipient instability of the convective cells is derived via image analysis for different values of the imposed horizontal velocity. Theoretical results for critical wavenumber favourably compare with experiments, systematically underestimating their experimental counterparts by 10 % at most. The discrepancy between experiments and theory is more relevant for the critical Rayleigh number, with theory overestimating the experiments by a maximum factor less than two. Discrepancies are attributable to a combination of factors: nonlinear phenomena, possible subcritical bifurcations, and unaccounted-for disturbing effects such as approximations in the rheological model, wall slip, ageing and degradation of the fluid properties.

We study non-Newtonian effects associated with power-law rheology of behaviour index is modest. The theoretical formulation is validated through experiments conducted during both pre- and post-closure phases and aimed at measuring the front position and the profile of the current. Experimental results are in fairly good agreement with theory and allow quantitative determination of the time interval of validity of the intermediate asymptotics regime, when self-similarity is achieved and when it is lost.

Our experimental study focuses on the density and velocity field in two layers of fluid separated by a sharp density interface. Turbulence is generated by a non-invasive stirrer, a Taylor–Couette tank, and the interface is stabilized with a source of saline fluid and a source of fresh water at the bottom and top of the tank, respectively. The same volume fluxes are withdrawn by two sinks to maintain a constant volume of fluid in the tank. Our results confirm past experiments and show that a strong vertical exchange of fluid occurs close to the inner cylinder and across the interface, where the vertical turbulent length scales appear to be suppressed. For low values of kinetic energy supplied to the system, the interface may act as a rigid boundary for the turbulent eddies, with a reduction of the vertical length scales although it seems not to affect the horizontal length scales. The vertical buoyancy flux extracted at the top of the tank is fairly well reproduced by the measured correlation $\overline{\unicode[STIX]{x1D70C}^{\prime }w^{\prime }}$ between density and vertical velocity fluctuations across the interface. Quadrant analysis of the correlation terms reveals that the greatest contribution to salt flux is given by eddies that carry the lighter fluid from top to bottom across the interface. The mixing process is accompanied by a single wake-like disturbance, with a radial front advancing in the azimuthal direction across the interface, acting as a blade, and with a period that decreases with rotation rate. The wake favours the smoothing of the density step and, in a simplified model, we assume that the turbulent diffusion is active during a fraction of the cycle in the wake-mixing region, with diffusivity proportional to the transverse length scale and the speed of the wake. The mixing region is the domain between the nose of the wave-like perturbation and the section where the interface becomes ‘darker’ again after being mixed by the vortexes. The results of this model are in a fair agreement with the experiments. The potential energy of the interfacial perturbations is only a small part of the missing turbulent kinetic energy, defined as the difference in the turbulent kinetic energy between a well-mixed fluid and a two-layer fluid. Further analysis is needed to explain the mechanism of generating these perturbations and the factors that control their periodicity.

We present a combined theoretical-experimental investigation of particle-driven gravity currents advancing in circular cross section channels in the high-Reynolds number Boussinesq regime; the ambient fluid is either homogeneous or linearly stratified. The predictions of the theoretical model are compared with experiments performed in lock–release configuration; experiments were performed with conditions of both full-depth and partial-depth locks. Two different particles were used for the turbidity current, and the full range $0\le S\le 1$ of the stratification parameter was explored (S = 0 corresponds to the homogeneous case and S = 1 when the density of the ambient fluid and of the current are equal at the bottom). In addition, a few saline gravity currents were tested for comparison. The results show good agreement for the full-depth configuration, with the initial depth of the current in the lock being equal to the depth of the ambient fluid. The agreement is less good for the partial-depth cases and is improved by the introduction of a simple adjustment coefficient for the Froude number at the front of the current and accounting for dissipation. The general parameter dependencies and behaviour of the current, although influenced by many factors (e.g., mixing and internal waves), are well predicted by the relatively simple model.