Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$, where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ($\varepsilon =0.2$), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ($\varepsilon \geqslant 0.4$) to control the 3-D modes and wake dynamics.

Buoyancy-driven bubbly flows play pivotal roles in various scenarios, such as the oxygenation and mixing in the upper ocean and the reaction kinetics in chemical and bio-reactors. This work focuses on the convective flow induced by the localised release of large air bubbles ($D_b=3.7$ mm, ${Re}_b=950$) in a water tank, exploring the resulting flow and the transition from laminar to disturbed states as a function of the Rayleigh number ranging from $3\times 10^3$ to $2\times 10^5$. At low ${Ra}$ the flow is smooth and laminar with weak temporal oscillations, while a highly disturbed state appears above a critical value ${Ra}_c$. A theoretical analysis is presented that links the mean flow circulation to the Rayleigh number. Through an experimental investigation, utilising three-dimensional particle tracking velocimetry and flow visualisation, we confirm the theory presented, and characterise the laminar to disturbed transition in the system. These findings not only enhance our fundamental understanding of buoyancy-driven convective flows but also hold significant implications for practical applications, particularly in the optimisation of bio-reactor design and other industrial processes reliant on controlled convective dynamics.

Predicting the magnitude of the slip velocity of non-tracer particles with respect to the surrounding fluid is crucial to address both fundamental and practical questions involving dispersed turbulent flows. Here we derive an analytical model to predict the slip velocity of spherical particles in homogeneous isotropic turbulence. We modulate the particle equation of motion according to the inertial filtering framework, and obtain closed-form expressions for the mean slip velocity magnitude as a function of the governing parameters. These are compared against laboratory measurements and direct numerical simulations, demonstrating close agreement for both light and heavy particles, both smaller and larger than the Kolmogorov scales. The predictive value of the model and its implications are discussed, as well as the range of validity of the underlying assumptions.