This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$ , cylinder length over diameter) and Reynolds numbers ( $Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$ , one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short- ${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

This work reports the application of a model-free deep reinforcement learning (DRL) based flow control strategy to suppress perturbations evolving in the one-dimensional linearised Kuramoto–Sivashinsky (KS) equation and two-dimensional boundary layer flows. The former is commonly used to model the disturbance developing in flat-plate boundary layer flows. These flow systems are convectively unstable, being able to amplify the upstream disturbance, and are thus difficult to control. The control action is implemented through a volumetric force at a fixed position, and the control performance is evaluated by the reduction of perturbation amplitude downstream. We first demonstrate the effectiveness of the DRL-based control in the KS system subjected to a random upstream noise. The amplitude of perturbation monitored downstream is reduced significantly, and the learnt policy is shown to be robust to both measurement and external noise. One of our focuses is to place sensors optimally in the DRL control using the gradient-free particle swarm optimisation algorithm. After the optimisation process for different numbers of sensors, a specific eight-sensor placement is found to yield the best control performance. The optimised sensor placement in the KS equation is applied directly to control two-dimensional Blasius boundary layer flows, and can efficiently reduce the downstream perturbation energy. Via flow analyses, the control mechanism found by DRL is the opposition control. Besides, it is found that when the flow instability information is embedded in the reward function of DRL to penalise the instability, the control performance can be further improved in this convectively unstable flow.

It is recently found that viscoelastic pipe flows can be linearly unstable, leading to the possibility of a supercritical transition route, in contrast to Newtonian pipe flows. Such an instability is referred to as the centre mode, which was studied numerically by Chaudhary et al. (J. Fluid Mech., vol. 908, 2021, p. A11) based on an Oldroyd-B model. In this paper, we are interested in expanding the parameter space investigated and exploring the asymptotic scalings related to this centre instability in the Oldroyd-B viscoelastic pipe flow. It is found from the asymptotic analysis that the centre mode exhibits a three-layered asymptotic structure in the radial direction, a wall layer, a main layer and a central layer, which are driven by pure viscosity, axial and/or radial pressure gradient, and a combined effect of viscosity and elasticity, respectively. Depending on the relations of the control parameters, two regimes, the long-wavelength and short-wavelength centre instabilities, emerge, for which the central-layer thicknesses are of different orders of magnitude. Our large-Reynolds-number asymptotic predictions are compared to the numerical solutions of the original eigenvalue system, and favourable agreement is achieved, especially when the parameters approach their individual limits. In addition to revealing the dominant factors and their balances, the asymptotic analysis describes the instability system by reducing the number of control parameters, and furthermore explaining the collapse of the numerical results for different re-scalings.

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