Motivated by contradicting or insufficient information regarding the large-scale flow dynamics around surface-mounted finite-height square prisms of small aspect ratio, the present study investigates the dominant vortex shedding and low-frequency dynamics around a surface-mounted cube. These flow modes were obtained from the spectral proper orthogonal decomposition of large-eddy simulation results, at a Reynolds number of $\textit {Re}=1\times 10^4$ and two different types of boundary layer: a thin and laminar boundary layer with thickness $\delta /D=0.2$ and a thick and turbulent boundary layer with $\delta /D=0.8$. The main antisymmetric mode pair revealed a new flow pattern with the alternate shedding of streamwise flow structures, indicating a transition from the half-loops of taller prisms to only streamwise strands (i.e. no vertical core) for smaller aspect ratio. The formation process of the streamwise structures is due to a reorientation of the vorticity of the arch vortex in the streamwise direction characteristic of the shed structures. The low-frequency drift mode affected the length of the recirculation region, the strength of vortex shedding, and the near-wall flow field and pressure distribution on the cube's faces, leading to low-frequency variations in the fluctuating drag and normal force coefficients. These large-scale flow dynamics were similar for both boundary layers, but minor differences were identified, related mostly to the occurrence of flow attachment and the formation of a headband vortex for the thicker boundary layer.

Motivated by the recent numerical results of Khalid et al. (Phys. Rev. Lett., vol. 127, 2021, 134502), we consider the large-Weissenberg-number ($W$) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The instability is of the critical layer type in the distinguished ultra-dilute limit where $W(1-\beta )=O(1)$ as $W \rightarrow \infty$ ($\beta$ is the ratio of solvent-to-total viscosity). In contrast to centre modes in the Orr–Sommerfeld equation, $1-c=O(1)$ as $W \rightarrow \infty$, where $c$ is the phase speed normalised by the centreline speed as a central ‘outer’ region is always needed to adjust the non-zero cross-stream velocity at the critical layer down to zero at the centreline. The critical layer acts as a pair of intense ‘bellows’ which blows the flow streamlines apart locally and then sucks them back together again. This compression/rarefaction amplifies the streamwise-normal polymer stress which in turn drives the streamwise flow through local polymer stresses at the critical layer. The streamwise flow energises the cross-stream flow via continuity which in turn intensifies the critical layer to close the cycle. We also treat the large-Reynolds-number ($Re$) asymptotic structure of the upper (where $1-c=O(Re^{-2/3})$) and lower branches of the $Re$–$W$ neutral curve, confirming the inferred scalings from previous numerical computations. Finally, we remark that the viscoelastic centre-mode instability was actually first observed in viscoelastic Kolmogorov flow by Boffetta et al. (J. Fluid Mech., vol. 523, 2005, pp. 161–170).

The linear stability of plane Couette–Poiseuille flow (CPF) is studied with the physical effects of stratification, rotation and viscosity all included for the first time together. With no stratification, two instability mechanisms are present due to the shear and rotation which, for the most part, do not interact as they favour different forms of two-dimensionality. However, there are some small parts of parameter space where new three-dimensional instability appears indicating that Rayleigh's criterion is also violated in parameter space beyond where shear instability is expected. No fully localised centrifugal instabilities can be found for CPF, but they are shown to exist if the base flow shear has a maximum in the domain (the base flow needs to be at least cubic in the cross-stream variable rather than just quadratic as in CPF). With stable stratification present, new instabilities are found due to the combined effects of stratification and rotation, but only some appear to be of the resonance-type associated with the strato-rotational instability. The other unstable branches are more accurately interpreted as a stratification-modified centrifugal instability. Three-dimensional versions of this violate Rayleigh's criterion even when this is extended to include stratification. When stratification is stronger than rotation, the resonance-type instabilities are only dominant for cyclonic flows.

The unsteady mechanism of unstart flow for an inlet with rectangular-to-elliptical shape transition (REST) under the off-design condition at a Mach of 4 is investigated using the delay detached eddy simulation method. With the help of numerical simulations, the unsteady dynamics, especially the low-frequency characteristics of the REST inlet unstart flow, as well as the self-sustaining mechanism, is investigated. The instantaneous flow illustrates the unsteady phenomena of the REST unstart flow, including the interaction between the cowl-closure leading edge (CLE) shock and the shear layer, breathing of the separation bubble, flapping of the separation shock, instability of the shear layer and vortex shedding along the shear layer. The spectral analysis reveals that the lower frequency dynamics is associated with the breathing of the separation bubble and the flapping motion of the separation shock wave, while the higher frequency is related to the instability of the shear layer affected by cowl-closure leading edge shock and the formation of shedding vortices. Further, coherence analysis shows that the contribution of these flow structures dominating the low-frequency dynamics couple with each other. Based on the dynamic mode decomposition results, the characteristics that contribute to the unsteady behaviour of unstart flow are summarized. The streamwise vortices downstream of the separation and the shedding vortices are believed to be the main driving force of the global low-frequency unsteadiness of the REST inlet unstart flow under the off-design condition. Moreover, the CLE shock plays an important role in the process during the dominant flow structure conversion from the backflow within the separation bubble into elongated streamwise structures.

We employ the methods of statistical mechanics to obtain closures for the balance equations of momentum and fluctuation kinetic energy that govern the ballistic motion of grains rebounding at a rigid, bumpy bed that are driven by turbulent or non-turbulent shearing fluids, in the absence of mid-trajectory collisions and fluid velocity fluctuations. We obtain semi-analytical solutions for steady and fully developed saltation over horizontal beds for the vertical profiles of particle concentration and stresses and fluid and particle velocities. These compare favourably with measurements in discrete-element numerical simulations in the wide range of conditions of Earth and other planetary environments. The predictions of the particle horizontal mass flux and its scaling with the amount of particles in the system, the properties of the carrier fluid and the intensity of the shearing also agree with numerical simulations and wind-tunnel experiments.

A distinguishing feature of the bi-stable wake is that the wake persists in either of two preferred states for a sufficiently long time. Aiming to understand the persistence mechanism, this paper numerically investigates the airwake characteristics of the Chalmers ship model (CSM) using large eddy simulation with a wall-adapting local-eddy viscosity model and is complemented by experimental testings for validations. There are two cases of interest: (i) the baseline CSM with a sharp-edged superstructure front that induces massive boundary layer separation; (ii) the front-rounded (FR) CSM with suppressed flow separation. During a characteristic time ($t^*$) of 1142 (26.5 s), the baseline case has a frequently switching wake, whereas the FR wake maintains a stable asymmetric structure with only one switch attempt. To understand the different wake behaviours, the study starts by analysing wake flow structures, vortex cores and the wake dynamics, followed by investigating the instantaneous flow physics. Results suggest that the baseline wake has a weak bi-stable pattern, whereas the FR wake behaves similarly to a reflectional symmetry breaking state of a potential bi-stable wake. The wake switching is found to be driven by the tilting of (vertical-oriented) $z$-vorticity sheets from either side of the base toward the centre. This tilting behaviour is subjected to the high-magnitude vorticity that sheds from the upstream flow separation at the front sharp edges. With the sharp edges rounded in the FR case, the upstream vorticity is mitigated and the tilting effect is significantly reduced, leading to a more stable wake structure. The reasoning provided in the paper potentially explains the persistence mechanism of the bi-stable wake.

We optimize jet mixing using large eddy simulations (LES) at a Reynolds number of $3000$. Key methodological enablers consist of Bayesian optimization, a surrogate model enhanced by deep learning and persistent data topology for physical interpretation. The mixing performance is characterized by an equivalent jet radius ($R_{eq}$) derived from the streamwise velocity in a plane located $8$ diameters downstream. The optimization is performed in a 22-dimensional actuation space that comprises most known excitations. This search space parameterizes the distributed actuation imposed on the bulk flow and at the periphery of the nozzle in the streamwise and radial directions. The momentum flux measures the energy input of the actuation. The optimization quadruples the jet radius $R_{eq}$ with a $7$-armed blooming jet after around $570$ evaluations. The control input requires $2\,\%$ momentum flux of the main flow, which is one order of magnitude lower than an ad hoc dual-mode excitation. Intriguingly, a pronounced suboptimum in the search space is associated with a double-helix jet, a new flow pattern. This jet pattern results in a mixing improvement comparable to the blooming jet. A state-of-the-art Bayesian optimization converges towards this double-helix solution. The learning is accelerated and converges to another better optimum by including a deep-learning-enhanced surrogate model trained along the optimization. Persistent data topology extracts the global and many local minima in the actuation space. These minima can be identified with flow patterns beneficial to the mixing.

The flow resistance, i.e. friction factor times Reynolds number ($\,f\,{Re}$), of longitudinal-fin heat sinks with or without clearance between a shroud and the tips of the fins is an important parameter in thermal design. This is because it dictates the caloric resistance of the heat sink, i.e. change in bulk temperature of the fluid flowing through it. When there is no clearance and the common and oft-valid assumption of negligible fin thickness is invoked, $f\,{Re}$ corresponds to simply that of a rectangular duct. However, with clearance, only numerical results are available as per the well-known study by Sparrow, Baliga and Patankar (ASME J. Heat Transfer, vol. 100, 1978). We develop analytical formulae for $f\,{Re}$ for fully developed flow with clearance. The exact solution is provided by an integral formula derived via conformal mappings. Additionally, simple formulae are derived via asymptotic expansions in three cases: (1) the fin spacing is small compared to the fin height and clearance; (2) the clearance is small compared to the fin spacing, which is small compared to the fin height; (3) the same as case (2) but valid for larger clearances. The different asymptotic formulae are compared to the exact formula, and together cover almost the entire relevant parameter range (for fin spacing and clearance) with errors of less than 15 %. A formula for the limiting case of no clearance is shown to be more accurate, for any fin spacing, than a widely used correlation from the literature.