This paper investigates the amplification and propagation of swirl fluctuations in turbulent swirling flows using resolvent analysis. Swirl fluctuations have been repeatedly observed in acoustically excited swirl flows and play a significant role in triggering thermoacoustic instabilities in swirl-stabilized flames. While recent research on simplified rotating laminar base flows suggests that the linear inertial-wave mechanism is a key driver of swirl fluctuations, it remains unclear whether this applies to the fully turbulent regime and whether a linear method is sufficient for modelling. To address this issue, a turbulent swirling pipe flow is considered using large-eddy simulations and phase-locked particle image velocimetry, which are combined with mean-field resolvent analysis. A sound agreement between the empirical and physics-based modes is found in terms of shape and propagation velocity. The latter is particularly important for thermoacoustic time-lag models. The comparison with a generic rotating pipe flow shows that the observed swirl fluctuations are indeed driven by a linear inertial wave mechanism. The resolvent framework is, then, exploited to further investigate the coupling and amplification mechanisms in detail. It is discovered that the combined effects of inertia and strong shear lead to very high amplification rates of the swirl fluctuations, explaining the high potential of these structures to trigger combustion instabilities. The study further demonstrates the capability of the resolvent to reveal the driving mechanisms of flow response structures in highly complex turbulent flows, and it opens the path for efficient physics-based optimization to prevent combustion instabilities.

This paper presents a numerical study on the flow around two tandem circular cylinders beneath a free surface at a Reynolds number of $180$. The free-surface effects on the wake dynamics and hydrodynamic forces are investigated through a parametric study, covering a parameter space of gap ratios from $0.20$ to $2.00$, spacing ratios from $1.50$ to $4.00$ and Froude numbers from $0.2$ to $0.8$. A jet-like flow accompanied by a shear layer of positive vorticity separating from the free surface is formed in the wake at small gap ratios, which significantly alters the wake pattern through its dynamic behaviours. At shallow submergence depths, the three-dimensional wake transitions from mode B to mode A as the distance between the cylinders increases. As submergence depth increases, the wavy deformation of the primary vortex cores disappears in the wake, and the flow transitions to a two-dimensional state. Higher Froude numbers can extend the effect of the free surface to deeper submergence depths. The critical spacing ratio tends to be larger at higher Froude numbers. Furthermore, the free-surface deformation is examined. The free-surface profile typically comprises a hydraulic jump immediately ahead of the upstream cylinder, trapped waves in the vicinity of the two tandem cylinders and well-defined travelling waves on the downstream side. The frequencies of the waves cluster around the vortex shedding frequency, indicating a close association between the generation of waves and the vortex shedding process.

Not all the information in a turbulent field is relevant for understanding particular regions or variables in the flow. Here, we present a method for decomposing a source field into its informative $\boldsymbol {\varPhi }_{I}(\boldsymbol {x},t)$ and residual $\boldsymbol {\varPhi }_{R}(\boldsymbol {x},t)$ components relative to another target field. The method is referred to as informative and non-informative decomposition (IND). All the necessary information for physical understanding, reduced-order modelling and control of the target variable is contained in $\boldsymbol {\varPhi }_{I}(\boldsymbol {x},t)$, whereas $\boldsymbol {\varPhi }_{R}(\boldsymbol {x},t)$ offers no substantial utility in these contexts. The decomposition is formulated as an optimisation problem that seeks to maximise the time-lagged mutual information of the informative component with the target variable while minimising the mutual information with the residual component. The method is applied to extract the informative and residual components of the velocity field in a turbulent channel flow, using the wall shear stress as the target variable. We demonstrate the utility of IND in three scenarios: (i) physical insight into the effect of the velocity fluctuations on the wall shear stress; (ii) prediction of the wall shear stress using velocities far from the wall; and (iii) development of control strategies for drag reduction in a turbulent channel flow using opposition control. In case (i), IND reveals that the informative velocity related to wall shear stress consists of wall-attached high- and low-velocity streaks, collocated with regions of vertical motions and weak spanwise velocity. This informative structure is embedded within a larger-scale streak–roll structure of residual velocity, which bears no information about the wall shear stress. In case (ii), the best-performing model for predicting wall shear stress is a convolutional neural network that uses the informative component of the velocity as input, while the residual velocity component provides no predictive capabilities. Finally, in case (iii), we demonstrate that the informative component of the wall-normal velocity is closely linked to the observability of the target variable and holds the essential information needed to develop successful control strategies.

We analyse the motion of a flagellated bacterium in a two-fluid medium using slender body theory. The two-fluid model is useful for describing a body moving through a complex fluid with a microstructure whose length scale is comparable to the characteristic scale of the body. This is true for bacterial motion in biological fluids (entangled polymer solutions), where the entanglement results in a porous microstructure with typical pore diameters comparable to or larger than the flagellar bundle diameter, but smaller than the diameter of the bacterial head. Thus, the polymer and solvent satisfy different boundary conditions on the flagellar bundle and move with different velocities close to it. This gives rise to a screening length $L_B$ within which the fluids exchange momentum and the relative velocity between the two fluids decays. In this work, both the solvent and polymer of the two-fluid medium are modelled as Newtonian fluids with different viscosities $\mu _s$ and $\mu _p$ (viscosity ratio $\lambda = \mu _p/\mu _s$), thereby capturing the effects solely introduced by the microstructure of the complex fluid. From our calculations, we observe an increased drag anisotropy for a rigid, slender flagellar bundle moving through this two-fluid medium, resulting in an enhanced swimming velocity of the organism. The results are sensitive to the interaction between the bundle and the polymer, and we discuss two physical scenarios corresponding to two types of interaction. Our model provides an explanation for the experimentally observed enhancement of swimming velocity of bacteria in entangled polymer solutions and motivates further experimental investigations.