In this study, mean velocity and temperature profiles for turbulent vertical convection (VC) confined in an infinite channel are investigated theoretically. The analysis starts from the governing equations of the thermal flow, with Reynolds shear stress and turbulent heat flux closed by the mixing length theory. Employing a three-sublayer description of the mean fields, the mean velocity and temperature profiles are found to be linear laws near the channel wall (viscosity-dominated sublayer), and they follow power laws close to the channel centre (turbulence-dominated sublayer). The characteristic scales of velocity, temperature and length in the present profiles arise naturally from the system normalisation, rather than from scaling analyses, thus ensuring a sound mathematical description. The derived profiles are verified fully via various literature data available in the classical regime; further, they are compared with the reported profiles, and the results indicate that the present profiles are the only ones with the ability to interpret data accurately from different sources, demonstrating much better versatility. Meanwhile, we provide analytical arguments showing that in the ultimate regime, the mean profiles in VC may remain in power laws, rather than the log laws inferred by analogy with Rayleigh–Bénard convection (RBC) systems. The power profiles recognised in this study are induced by the effect of buoyancy, which is in parallel with the mean flow in VC and contributes to the streamwise momentum transport, whereas in RBC systems, buoyancy is perpendicular to the mean flow, and does not influence the streamwise momentum transport, resulting in log profiles, being similar to the case of wall shear flows.

Barchan dunes migrate in swarms, with rich but not fully revealed self-stabilization mechanisms. The interaction between dunes is considered as one of the key reasons for these mechanisms. Contact-type interactions, known as collisions, have been widely studied, while non-contact-type interactions have received less attention. In this paper, a water tunnel experiment was performed to study the non-contact dune chasing. With the aid of numerical simulations, a general model was proposed to interpret the convergence of distance between two dunes chasing each other. The model consists of three factors: inter-dune repulsive vortex, embracing vortex downstream, and difference in dune mass. Then, we reported a scaling law, expressed as the relation between the normalized dune spacing and time, to describe the convergence of dune spacing, and develop a governing equation in the form of area summation to explain the violation of convergence by combining the above-mentioned three factors, both of which were verified experimentally. Our findings could help advance the understanding of the self-stabilization characteristics of dune swarms in nature.

Collision among barchan dunes is a main cause for the dune swarm to achieve size and speed selection, and it can be divided into two patterns: coalescence and ejection. Here, a three-dimensional (3D) cellular automaton model is applied to collectively study the effects of inter-dune space and relative dune size on these collision patterns. A parameter space is established that includes a transition surface distinguishing coalescence and ejection. Confirmed by field observations and subaquatic experiments, a comprehensive depiction of transition between coalescence and ejection is provided, which may bring new constraints on the morphodynamics of barchan dune fields.