The Rayleigh number ($\mathit{Ra}$) scaling of the global Bolgiano length scale ${L}_{B, global} $ and the local Bolgiano length scale ${L}_{B, centre} $ in the centre region of turbulent Rayleigh–Bénard convection are investigated for Prandtl numbers $\mathit{Pr}= 0. 7$ and $4. 38$ and $3\times 1{0}^{5} \leq \mathit{Ra}\leq 3\times 1{0}^{9} $. It is found that ${L}_{B, centre} $ does not necessarily exhibit the same scaling as ${L}_{B, global} $. While ${L}_{B, global} $ is monotonically deceasing as ${L}_{B, global} \sim {\mathit{Ra}}^{- 0. 10} $ for both $\mathit{Pr}$, ${L}_{B, centre} $ shows a steep increase beyond a certain $\mathit{Ra}$ value. The complex scaling of the local Bolgiano length scale in the centre is a result of the different behaviour of the temperature-variance dissipation rate, ${\epsilon }_{T} $, and the turbulent-kinetic-energy dissipation rate, ${\epsilon }_{u} $. This shows that for sufficiently high $\mathit{Ra}$ the flow is well-mixed and hence temperature is passively advected. It is also observed that the $\mathit{Ra}$-range in which ${L}_{B, centre} $ exhibits the same scaling as the global Bolgiano length scale is increasing with increasing $\mathit{Pr}$. It is further observed that for $\mathit{Pr}= 4. 38$ and $\mathit{Ra}\leq 3\times 1{0}^{7} $ the local vertical heat flux in the centre region is balanced by the turbulent-kinetic-energy dissipation rate. For higher $\mathit{Ra}$ we find that the local heat flux is decreasing. At $\mathit{Pr}= 0. 7$ we do not observe such a balance, as the measured heat flux is between the heat fluxes estimated through the turbulent-kinetic-energy dissipation rate and the temperature-variance dissipation rate. We therefore suggest that the balance of the local heat flux might be Prandtl-number dependent. The conditional average of the local vertical heat flux $\mathop{\langle \mathit{Nu}\vert {\epsilon }_{u} , {\epsilon }_{T} \rangle }\nolimits_{\mathit{centre}} $ in the core region of the flow reveals that the highest vertical heat flux occurs for rare events with very high dissipation rates, while the joint most probable dissipation rates are associated with very low values of vertical heat flux. It is also observed that high values of ${\epsilon }_{u} $ and ${\epsilon }_{T} $ tend to occur together. It is further observed that the longitudinal velocity structure functions approach Kolmogorov K41 scaling. The temperature structure functions appear to approach Bolgiano–Obukhov BO59 scaling for $r\gt {L}_{B, centre} $, while a scaling exponent smaller than the BO59 scaling is observed for separations $r\lt {L}_{B, centre} $. The mixed velocity and temperature structure function for $\mathit{Ra}= 1\times 1{0}^{9} $ and $\mathit{Pr}= 4. 38$ shows a short $4/ 5$-scaling for $r\gt {L}_{B, centre} $. Our results suggest that BO59 scaling might be more clearly observable at higher Prandtl and moderate Rayleigh numbers.

The present article aims at enhancing the computation of the global stability modes of the internal flow of solid rocket motors (SRMs) approximated by the Taylor–Culick solution. This modal approach suffers from the consequences of the non-normality of the global linearized incompressible Navier–Stokes operator, namely the lack of robustness of the eigenvalues that can lead to the computation of pseudo-modes rather than actual eigenmodes. In this respect, the effects of non-normality associated with strongly amplified eigenfunctions are highlighted on a simplified convective–diffusive stability problem with uniformly accelerated base state, the latter property being a typical characteristic of the Taylor–Culick flow. Non-convergence zones for the eigenvalues are exhibited for large Reynolds numbers and are related to the critical sensitivity to disturbances applied to one of the boundary conditions. For this reason, and according to experimental and numerical data related to the stability of simplified SRMs, a global stability analysis is performed assuming that the hydrodynamic fluctuations emerge from a geometrical defect applied at the sidewall. This comes to fix the upstream boundary condition at the abscissa of the sidewall disturbance. The resulting eigenmodes are shown to be discrete, numerically converged, well identified by a finite number of points of undefined phase of the velocity fluctuations. They marginally depend on Reynolds number variations, but are modified by changes on the boundaries location. As in the simplified problem, the inflow boundary condition is the most critical in terms of sensitivity to numerical errors, although not dramatic. Finally, the sensitivity analysis to infinitesimal base flow changes indicates that the variations applied close to the inflow boundary condition induce the largest move of the eigenvalues. In spite of the large non-normal effects induced by the large polynomial growth of the eigenfunctions, this paper shows that discrete instabilities may emerge from a wall defect, in contrast to configurations without such a geometrical perturbation whose dynamics may be rather driven by pseudo-modes.

We consider the stability of a planar gas–liquid foam with low liquid fraction, in the absence of surfactants and stabilizing particles. We adopt a network modelling approach introduced by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543), treating the gas bubbles as polygons, the accumulation of liquid at the bubble vertices (Plateau borders) as dynamic nodes and the liquid bridges separating the bubbles as uniformly thinning free films; these films can rupture due to van der Waals intermolecular attractions. The system is initialized as a periodic array of equally pressurized bubbles, with the initial film thicknesses sampled from a normal distribution. After an initial transient, the first film rupture initiates a phase of dynamic rearrangement where the bubbles rapidly coalesce, evolving toward a new quasi-equilibrium. We present Monte Carlo simulations of this coalescence process, examining the time intervals over which large-scale rearrangement occurs as a function of the model parameters. In addition, we show that when this time interval is rescaled appropriately, the evolution of the normalized number of bubbles is approximately self-similar.

We present a theoretical and experimental study of viscous gravity currents introduced at the surface of a denser inviscid fluid layer of finite depth inside a vertical Hele-Shaw cell. Initially, the viscous fluid floats on the inviscid fluid, forming a self-similar, buoyancy-driven current resisted predominantly by the viscous stresses due to shear across the width of the cell. Once the viscous current contacts the base of the cell, the flow can be considered in two regions: a grounded region in which the current lies in full contact with the base; and a floating region. The subsequent advance of the grounding line separating these regions is shown to be controlled by the thickening of the current associated with balancing the local shear stresses. An understanding of the flow transitions is developed using asymptotic and numerical analysis of a model based on lubrication theory.

A novel method to create a discontinuous gaseous interface with a minimum-surface feature by the soap film technique is developed for three-dimensional (3D) Richtmyer–Meshkov instability (RMI) studies. The interface formed is free of supporting mesh and the initial condition can be well controlled. Five air/SF6 interfaces with different amplitude are realized in shock-tube experiments. Time-resolved schlieren and planar Mie-scattering photography are employed to capture the motion of the shocked interface. It is found that the instability at the linear stage in the symmetry plane grows much slower than the predictions of previous two-dimensional (2D) impulsive models, which is ascribed to the opposite principal curvatures of the minimum surface. The 2D impulsive model is extended to describe the general 3D RMI. A quantitative analysis reveals a good agreement between experiments and the extended linear model for all the configurations including both the 2D and 3D RMIs at their early stages. An empirical model that combines the early linear growth with the late-time nonlinear growth is also proposed for the whole evolution process of the present configuration.

We investigate the optimal morphologies for fast and efficient anguilliform swimmers at intermediate Reynolds numbers, by combining an evolution strategy with three-dimensional viscous vortex methods. We show that anguilliform swimmer shapes enable the trapping and subsequent acceleration of regions of fluid transported along the entire body by the midline travelling wave. A sensitivity analysis of the optimal morphological traits identifies that the width thickness in the anterior of the body and the height of the caudal fin are critical factors for both speed and efficiency. The fastest swimmer without a caudal fin, however, still retains 80 % of its speed, showing that the entire body is used to generate thrust. The optimal shapes share several features with naturally occurring morphologies, but their overall appearances differ. This demonstrates that engineered swimmers can outperform biomimetic swimmers for the criteria considered here.

Direct numerical simulations are used to investigate potential enstrophy in stratified turbulence with small Froude numbers, large Reynolds numbers, and buoyancy Reynolds numbers ($R{e}_{b} $) both smaller and larger than unity. We investigate the conditions under which the potential enstrophy, which is a quartic quantity in the flow variables, can be approximated by its quadratic terms, as is often done in geophysical fluid dynamics. We show that at large scales, the quadratic fraction of the potential enstrophy is determined by $R{e}_{b} $. The quadratic part dominates for small $R{e}_{b} $, i.e. in the viscously coupled regime of stratified turbulence, but not when $R{e}_{b} \gtrsim 1$. The breakdown of the quadratic approximation is consistent with the development of Kelvin–Helmholtz instabilities, which are frequently observed to grow on the layerwise structure of stratified turbulence when $R{e}_{b} $ is not too small.

Miscible thermals are formed by instantaneously releasing a finite volume of buoyant fluid into stagnant ambient. Their subsequent motion is then driven by the buoyancy convection. The gross characteristics (e.g. overall size and velocity) of a thermal have been well studied and reported to be self-similar. However, there have been few studies concerning the internal structure. Here, turbulent miscible thermals (with initial density excess of 5 % and Reynolds number around 2100) have been investigated experimentally through a large number of realizations. The vorticity and density fields were quantified separately by particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques. Ensemble-averaged data of the transient development of the miscible thermals are presented. Major outcomes include: (i) validating Turner’s assumption of constant circulation within a buoyant vortex ring; (ii) measuring the vorticity and density distributions within the miscible thermal; (iii) quantifying the effect of baroclinicity on the generation and destruction of vorticity within the thermal; and (iv) identifying the significantly slower decay rate of the peak density as compared to the mean.

We present a depth-integrated equation for the mechanics of propagation of low-frequency hydroacoustic waves due to a sudden bottom displacement associated with earthquakes. The model equation can be used for numerical prediction in large-scale domains, overcoming the computational difficulties of three-dimensional models and so creating a solid base for tsunami early warning systems.