This review provides a comprehensive coverage of changes of the Hadley Cell extent and their impacts on the weather, climate, and society. The theories predicting the Hadley Cell width are introduced as a background for the understanding of the circulation changes and the metrics used for detection. A variety of metrics derived from various data sources have been used to quantify the Hadley Cell width. These metrics can be classified as dynamical, hydrological, thermal, and chemical metrics, based on the properties of the variables used. The dynamical metrics have faster trends than those based on thermal or hydrological metrics, with the values exceeding 1 degree per decade. The hydrological metric edge poleward trends were found a slightly faster expansion in the Northern Hemisphere than its southern counterpart. The chemical metrics show a poleward trend of more than 1 degree per decade in both hemispheres. We also suggest a few reasons for the discrepancy among trends in Hadley Cell expansion found in previous studies. Multiple forcings have been found responsible for the expansion, which seems to be more attributed to the natural variability than anthropogenic forcing. Validation of the scaling theories by the trends in Hadley Cell width suggests that theories considering the extratropical factor would be better models for predicting the Hadley Cell width changes. The Hadley Cell has an impact on different atmospheric processes on varying spatio-temporal scales, ranging from weather to climate, and finally on society. The remaining questions regarding Hadley Cell climate are briefly summarized at the end.

In this paper, we present an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) to simulate the interactions of viscous flow with deformable elastic structures, namely, two-dimensional (2D) and three-dimensional (3D) capsules formed by elastic membranes. The IB-LBFS is based on a finite-volume formulation and makes use of hydrodynamic conservation equations with fluxes computed by a kinetic approach; thus, it is more flexible and efficient than the standard immersed boundary-lattice Boltzmann methods. The membrane of the 2D capsule is represented by a set of discrete Lagrangian points, with in-plane and bending forces acting on the membrane obtained by a finite difference method. In contrast, the membrane of a 3D capsule is discretized into flat triangular elements with membrane forces calculated by an energy-based finite-element method. The IB-LBFS is first validated by studying the deformation of a circular capsule in a linear Newtonian and a power-law shear flow. Next, the deformation dynamics of a spherical, an oblate spheroidal, and a biconcave capsule in a simple shear flow are simulated. For an initially spherical capsule, the tank-treading motion of its membrane is reproduced at the steady state; while for oblate spheroidal and biconcave capsules, the swinging and tumbling motions are observed. Furthermore, under certain parameter settings, the transient mode from tumbling to swinging motions is also found, showing a rich and complex dynamic behavior of non-spherical capsules. These results indicate that the IB-LBFS can be employed in future studies concerning the dynamics of a capsule suspension in more realistic flows.

This study uses a coupled lattice Boltzmann and discrete element method to perform interface-resolved simulations of turbulent channel flow laden with finite-size cylindrical particles. The aim is to investigate interactions between wall-bounded turbulence and non-spherical particles with sharp edges. The particle-to-fluid density ratio is unity and gravity is neglected. Comparative analyses are conducted among long (length-to-diameter aspect ratio 2), unit (1) and short ( $ 1/2 $ ) cylinders, along with spheres and literature data for spheroids. Results reveal both shared and distinct dynamic behaviours of cylinders and their effects on turbulence modulation. Notably, disk-like short cylinders can remain trapped near the wall due to their flat faces aligning closely with it – a behaviour unique to particles with sharp edges. Long and unit cylinders, as well as spheres, preferentially accumulate in high-speed streaks, while short cylinders cluster in low-speed streaks, demonstrating a strong aspect-ratio effect. Near the wall, long cylinders align their axis with the streamwise direction, while short cylinders orient perpendicular to the wall. Rotationally, long cylinders primarily spin, whereas short ones predominantly tumble. These trends arise from orientation preferences and differences in axial and spanwise moments of inertia. Cylindrical particles increase wall drag compared with the single-phase case, with short cylinders causing the greatest enhancement due to strong near-wall accumulation. Overall, the influence of aspect ratio on particle dynamics and turbulence modulation is more pronounced for cylindrical particles than for spheroidal ones.