Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform large-eddy simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, 2020, p. A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on both the array density and turbine layout. An analytical model derived from the two-scale momentum theory predicts the impact of array density very well for all 50 farms investigated and can therefore be used as an upper limit to farm performance. We also propose a new method to quantify turbine-scale losses (due to turbine–wake interactions) and farm-scale losses (due to the reduction of farm-average wind speed). They both depend on the strength of atmospheric response to the farm, and our results suggest that, for large offshore wind farms, the farm-scale losses are typically more than twice as large as the turbine-scale losses. This is found to be due to a two-scale interaction between turbine wake and farm induction effects, explaining why the impact of turbine layout on farm power varies with the strength of atmospheric response.

Forcing dense suspensions of non-cohesive particles through constrictions might result in a continuous flow, an intermittent one, or indefinite interruption of flow, i.e. a clog. While one of the most important (and obvious) controlling parameters in such a system is the neck-to-particle size ratio, the role of the liquid driving method is not so straightforward. On the one hand, widespread volume-controlled systems such as syringe pumps result in pressure and local liquid velocity increases upon eventual clogs. On the other hand, pressure-controlled systems result in a decrease of the flow through the constriction when a clog is formed. The root of the question therefore lies in the role of interparticle liquid flow and hydrodynamic forces on both the formation and stability of an arch blocking the particle transport through a constriction. In this work, we study experimentally a suspension of non-cohesive particles flowing through a constricted channel (with neck-to-particle size ratio $3.03\leq D/d\leq 5.26$) in an intermittent fashion, in which they are most sensitive to parametric changes. Due to the stochastic nature of the intermittency, we make use of statistical distributions of arrest times and of discharged particles, and surprisingly, we find that the transport of non-cohesive suspensions through constrictions actually follows a ‘slower is faster’ principle under pressure-controlled driving: low imposed pressures yield intermittent non-persistent clogs, while high imposed pressures result in longer-lasting clogs, eventually becoming everlasting, and thus reducing the net particle transport rate.

In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for $1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$ and $0.01\le {\textit {St}} \le 10$, where the Rayleigh number ${\textit {Ra}}$ and Stokes number ${\textit {St}}$ measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with ${\textit {Ra}}$ and show minor dependences on ${\textit {St}}$. The volume-averaged temperature and convective flux exhibit non-monotonic variations as ${\textit {St}}$ increases and reach their minimums at intermediate ${\textit {St}}$. The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on ${\textit {St}}$ as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model. Localised travelling wave solutions to both the fully nonlinear problem (Euler equations), and the three-layer Miyata–Choi–Camassa equations are found numerically and compared. Mode-2 solitary waves with speeds slower than the linear mode-1 long-wave speed are typically generalised solitary waves with infinite tails consisting of a resonant mode-1 periodic wave train. Herein, we evidence the existence of mode-2 embedded solitary waves, that is, we show that for specific values of the parameters, the amplitude of the oscillations in the tail are zero. For sufficiently thick middle layers, we also find branches of mode-2 solitary waves with speeds that extend beyond the mode-1 linear waves and are no longer embedded. In addition, we show how large amplitude embedded solitary waves are intimately linked to the conjugate states of the problem.

In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin–Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12 %–15 % and net mixing by a factor of 2.