We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with increasing concentration of the dissolved solute, and we model this using the Oberbeck–Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier–Stokes equations with the advection–diffusion equation and a Stefan condition for the evolving solute–fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $\varOmega \in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt {t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency – from smaller to larger, relative to the inverse of the buoyancy-induced time scale – and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $\varOmega$. The symmetry breaking of the interface is best described in terms of $Ra/\varOmega ^2$.

This paper investigates the aerodynamic and flow characteristics of a circular cylinder near the leading-edge separated flow of an elongated rectangular cylinder. The study varies the gap-to-diameter ratio (G/D) of 0 ≤ G/D ≤ 0.4 and distance-to-diameter ratio (L / D) of 0.6 ≤ L / D ≤ 5.8 in the subcritical Reynolds-number region. Here, D, G and L are the diameter of the circular cylinder, the gap between the two isomeric cylinders and the distance between the leading edge of the rectangular cylinder and the centre of the circular cylinder, respectively. Based on smoke-wire flow visualisations, particle image velocimetry test results, lift power spectral densities and pressure distributions, flow around the circular cylinder can be classified into three regimes, i.e. broadened body, body reattachment and co-shedding. In the broadened-body regime, gap flow is negligible, and the circular cylinder behaves as an extension of the rectangular cylinder. In the body-reattachment regime, the free shear layer separated from the rectangular cylinder’s leading edge reattaches to the circular cylinder forebody, significantly modifying its incoming flow. In the co-shedding regime, the free shear layer substantially alters the vortex shedding from the circular cylinder’s lower side, resulting in a distorted alternating vortex shedding from the circular cylinder. Both the drag and lift of the circular cylinder display distinct behaviours in the three flow regimes. Two primary flow modes are recognised through proper orthogonal decomposition analysis: an alternating vortex shedding mode and a one-sided shear flow mode, which result in two Strouhal numbers of 0.205 and 0.255, respectively.

Roll patterns on floating ice shelves have been suggested to arise from viscous buckling under compressive stresses. A model of this process is explored, allowing for a power-law fluid rheology for ice. Linear stability theory of uniformly compressing base flows confirms that buckling modes can be unstable over a range of intermediate wavelengths when gravity does not play a dominant role. The rate of compression of the base flow, however, ensures that linear perturbations have wavelengths that continually shorten with time. As a consequence, linear instability only ever arises over a certain window of time $t$, and its strength can be characterised by finding the net amplification factor a buckling mode acquires for $t\to \infty$, beginning from a given initial wavenumber. Bi-axial compression, in which sideways straining flow is introduced to prevent the thickening of the base flow, is found to be more unstable than purely two-dimensional (or uni-axial) compression. Shear-thinning enhances the degree of instability in both uni-axial and bi-axial flow. The implications of the theoretical results for the glaciological problem are discussed.

The compression waves/boundary layer interaction (CWsBLI) in high-speed inlets poses significant challenges for predicting flow separation, rendering traditional shock wave/boundary layer interaction (SWBLI) scaling laws inadequate due to unaccounted effects of the coverage range of compression waves. This study aims to establish a unified scaling framework for CWsBLIs and SWBLIs by proposing an equivalent interaction intensity. Experiments were conducted in a Mach 2.5 supersonic wind tunnel, employing schlieren imaging and pressure measurements to characterise flows induced by curved surfaces at two deflection angles ($10^{\circ }, 12^{\circ }$) and varying coverage ranges of compression waves ($d$). An equivalent transformation method was developed to convert the CWsBLI into an equivalent incident SWBLI (ISWBLI), with interaction intensity derived from pressure gradients considering the coverage range. Key results reveal a critical threshold based on the interaction length of ISWBLI ($L_{\textit{single}}$): when $d \leq L_{\textit{single}}$, the interaction scale remains comparable to ISWBLI; when $d \gt L_{\textit{single}}$, the weakened adverse pressure gradient leads to a reduction in the length scale. The proposed scaling framework unifies the CWsBLIs and SWBLIs, achieving better data collapse compared to the existing methods. This work advances our understanding of complex waves/boundary layer interactions, and provides a prediction method for the length scales of CWsBLIs.

Using linear stability analysis, we study the onset and formation mechanism of wall modes in confined magnetoconvection cells with the degree of confinement characterised by the cell aspect ratio $\varGamma$. We first outline the phase diagram of the dominating factors that determine the critical Rayleigh number $Ra_c$ for the onset of convection in the $\varGamma -Ha$ phase space, with $\textit{Ha}$ being the Hartmann number. Our study shows that $Ra_c$ is primarily determined by geometrical confinement, and bulk convection onset occurs with $Ra_c = 1090 \varGamma ^{-4.0}$ for $\varGamma \lt \varGamma _{c_1} = 1.21 \textit{Ha}^{-0.48}$. No wall modes form and $Ra_c$ depends on the strength of both the confinement and magnetic field for $\varGamma _{c_1} \leqslant \varGamma \lt \varGamma _{c_2} = 4.07 \textit{Ha}^{-0.53}$. For $\varGamma _{c_2}\leqslant \varGamma \lt \varGamma _{c_3}=0.99 \textit{Ha}^{-0.10}$, wall modes emerge and $Ra_c$ drops below the bulk onset Rayleigh number for magnetoconvection. When $\varGamma \geqslant \varGamma _{c_3}$, wall modes become fully developed with an onset Rayleigh number for wall modes $Ra_{c,w} \approx 65 \textit{Ha}^{1.5}$. In this fully developed regime, the radial velocity profile and $Ra_{c,w}$ become independent of $\varGamma$. Through analysing the length scales of wall modes and their interaction with spatial confinement, we show dynamically how wall modes emerge in confined cells: while the first layer with a characteristic length scale $\ell _1 = 1.04 \textit{Ha}^{-0.56}$ forms when $\varGamma \geqslant 5.39 \textit{Ha}^{-0.58}$, the second layer with a characteristic length scale $\ell _2 = 4.94 \textit{Ha}^{-0.56}$ emerges when $\varGamma \geqslant 9.07 \textit{Ha}^{-0.53}$. These scaling relations provide practical guidelines for experimental and numerical studies of the wall-mode dynamics.