A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. (J. Fluid Mech., vol. 930, 2022, A30). These explorations hinted that a small number of interacting mechanics can drive long-time behaviours in this model, cast in the context of the well-studied alga Chlamydomonas and its rheotactic behaviours in such flows. Here, we explore this model analytically via a multiple-scale asymptotic analysis, seeking to formally identify the causal factors that shape the behaviour of these swimmers in Poiseuille flow. By capturing the evolution of a Hamiltonian-like quantity, we reveal the origins of the long-term drift in a single swimmer-dependent constant, whose sign determines the eventual behaviour of the swimmer. This constant captures the nonlinear interaction between the oscillatory speed and effective hydrodynamic shape of deforming swimmers, driving drift either towards or away from rheotaxis.

The effects of surfactants on a mechanically generated plunging breaker are studied experimentally in a laboratory wave tank. Waves are generated using a dispersively focused wave packet with a characteristic wavelength of $\lambda _0 = 1.18$ m. Experiments are performed with two sets of surfactant solutions. In the first set, increasing amounts of the soluble surfactant Triton X-100 are mixed into the tank water, while in the second set filtered tap water is left undisturbed in the tank for wait times ranging from 15 min to 21 h. Increasing Triton X-100 concentrations and longer wait times lead to surfactant-induced changes in the dynamic properties of the free surface in the tank. It is found that low surface concentrations of surfactants can dramatically change the wave breaking process by changing the shape of the jet and breaking up the entrained air cavity at the time of jet impact. Direct numerical simulations (DNS) of plunging breakers with constant surface tension are used to show that there is significant compression of the free surface near the plunging jet tip and dilatation elsewhere. To explore the effect of this compression/dilatation, the surface tension isotherm is measured in all experimental cases. The effects of surfactants on the plunging jet are shown to be primarily controlled by the surface tension gradient ($\Delta \mathcal {E}$) while the ambient surface tension of the undisturbed wave tank ($\sigma _0$) plays a secondary role.

We demonstrate how to accelerate the computationally taxing process of deep reinforcement learning (DRL) in numerical simulations for active control of bluff body flows at high Reynolds number ($Re$) using transfer learning. We consider the canonical flow past a circular cylinder whose wake is controlled by two small rotating cylinders. We first pre-train the DRL agent using data from inexpensive simulations at low $Re$, and subsequently we train the agent with small data from the simulation at high $Re$ (up to $Re=1.4\times 10^5$). We apply transfer learning (TL) to three different tasks, the results of which show that TL can greatly reduce the training episodes, while the control method selected by TL is more stable compared with training DRL from scratch. We analyse for the first time the wake flow at $Re=1.4\times 10^5$ in detail and discover that the hydrodynamic forces on the two rotating control cylinders are not symmetric.

We study passive scalar fluctuations convected by statistically stationary homogeneous isotropic turbulence under a uniform mean scalar gradient. In order to elucidate the parameter dependence of small-scale statistics of scalar fluctuations, we conduct direct numerical simulations of passive scalar turbulence with 59 different combinations of Reynolds number and Schmidt number. For all the cases, we compute time-average statistics of various quantities, which include the scalar derivative skewness and flatness, the ratio of parallel-to-perpendicular scalar-gradient variances, and the anisotropy parameter recently proposed (Hill, Phys. Rev. Fluids, vol. 2, 2017, 094601). Notably, the degree of small-scale anisotropy of passive scalar fluctuation is characterised by a universal function of the Péclet number $Pe_{\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}}=u^{\prime }\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}/\unicode[STIX]{x1D705}$, where $u^{\prime }$ is the root mean square velocity, $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$ the Taylor microscale of scalar fluctuation, $\unicode[STIX]{x1D705}$ the mass diffusivity. In the definition of the Péclet number, the use of $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$, rather than the Taylor microscale of velocity fluctuation, is key to collapsing the data of different Reynolds and Schmidt numbers. When the Péclet number is low, large-scale anisotropic scalar structures emerge irrespective of the Reynolds number. These structures are elongated along the direction of the uniform mean scalar gradient, and their size is significantly larger than the integral length scale of velocity fluctuation.

Asymptotic homogenization is employed to formulate upscaled effective boundary conditions at a smooth virtual surface for a natural-convection flow over a periodically roughened vertical wall, to bypass the expensive numerical resolution of flow and temperature fields near and within wall corrugations. Microscale problems are found by expanding near-wall variables in terms of a small parameter $\epsilon$, the ratio between the microscopic and the macroscopic length scales. The expressions of the upscaled velocity and temperature boundary conditions are provided up to second-order accuracy in $\epsilon$. The case of transverse square ribs is considered as a representative example. The classical Navier-slip condition for the streamwise and the spanwise velocity components is modified at second order by the gradient of the normal stress and the time derivative of the shear stress. The streamwise slip velocity is additionally corrected by a buoyancy term at first order and a temperature-gradient term at second order. The normal velocity at the virtual surface appears only as a second-order transpiration condition. A Robin-like condition for the temperature is found, where the wall temperature is corrected with a temperature-gradient term representing thermal slip. The accuracy levels and the applicability range of the effective conditions to mimic the macroscopic flow behaviour are investigated under laminar flow conditions, in comparison with results of full feature-resolving simulations. A formal validity limit for the approximation is sought in terms of a single accuracy criterion ($C$), which combines the effects of the Grashof number and the ribs’ density. The introduced model is further tested on different rib geometries.

The shock wave–turbulent boundary layer interaction over a compression corner is studied using global stability analysis (GSA) and resolvent analysis based on a separation of scales between the low-frequency, large-scale motions and the turbulent fluctuations. The GSA identifies a leading stationary mode, which becomes globally unstable as the ramp angle is beyond a critical value. For globally stable flows, the resolvent analysis captures two-dimensional and three-dimensional local maxima in optimal gain, both of which are due to modal resonance between the forcing and the leading global mode. Notably, the frequency-premultiplied optimal gain associated with two-dimensional disturbances peaks at a low frequency. For different interaction strengths, the peak frequencies collapse onto a universal value of 0.015 when non-dimensionalized using the length of the separation region and the free-stream velocity. A numerical simulation perturbed with the corresponding optimal forcing reveals that the response is in the form of a back-and-forth shock motion.

Direct numerical simulations (DNS) are used to examine a spatially developing non-equilibrium three-dimensional turbulent boundary layer (3DTBL) over a flat plate. The present flow is a ‘shear-driven’ 3DTBL owing to a sudden imposition of a surface spanwise velocity ${W_S}$. Particular attention is given to the effects of cross-flow and Reynolds number. In the DNS, three values of the inlet momentum thickness Reynolds number, $R{e_{{\theta _0}}} = 300$, 600 and 900, are used with several values of ${W_S}$. The present largest ${W_S}$ is twice the free-stream velocity ${U_0}$, comparable to the maximum value of the spinning cylinder experiment by Lohmann (Trans. ASME I: J. Fluids Engng, vol. 98, 1976, pp. 354–363). After imposing ${W_S}$, the mean streamwise vorticity ${\overline \varOmega _x}$ increasingly propagates away from the wall where there is close relationship between a deficit of mean streamwise velocity and inviscid skewing (i.e. three-dimensionality). At a downstream station of a 3DTBL, near-plateaus appear in the skin friction coefficients where the magnitudes depend intrinsically on ${W_S}$. The approach to the collateral state is, however, slow for mean streamwise velocity $\overline U$ where the Reynolds shear stress $\overline {uv}$ extracts energy from the mean flow inefficiently. As the Reynolds number increases, the mean velocity magnitude ${Q_r}$ tends to show the log law but with a larger von Kármán constant than in a two-dimensional turbulent boundary layer. Instantaneously, toppling u structures dominate owing to cross-flow and become more prominent with increasing Re. Statistically, the latter spanwise length scale increases linearly with respect to y below y/δ99 = 0.2, which indicates that cross-flow yields a self-similar behaviour.

In this study, we connect concepts that have been recently developed in thermoacoustics, specifically (i) high-order spectral perturbation theory, (ii) symmetry-induced degenerate thermoacoustic modes, (iii) intrinsic thermoacoustic modes and (iv) exceptional points. Their connection helps gain physical insight into the behaviour of the thermoacoustic spectrum when parameters of the system are varied. First, we extend high-order adjoint-based perturbation theory of thermoacoustic modes to the degenerate case. We provide explicit formulae for the calculation of the eigenvalue corrections to any order. These formulae are valid for self-adjoint, non-self-adjoint or even non-normal systems; therefore, they can be applied to a large range of problems, including fluid dynamics. Second, by analysing the expansion coefficients of the eigenvalue corrections as a function of a parameter of interest, we accurately estimate the radius of convergence of the power series. Third, we connect the existence of a finite radius of convergence to the existence of singularities in parameter space. We identify these singularities as exceptional points, which correspond to defective thermoacoustic eigenvalues, with infinite sensitivity to infinitesimal changes in the parameters. At an exceptional point, two eigenvalues and their associated eigenvectors coalesce. Close to an exceptional point, strong veering of the eigenvalue trajectories is observed. As demonstrated in recent work, exceptional points naturally arise in thermoacoustic systems due to the interaction between modes of acoustic and intrinsic origin. The role of exceptional points in thermoacoustic systems sheds new light on the physics and sensitivity of thermoacoustic stability, which can be leveraged for passive control by small design modifications.

A two-dimensional model of a hydraulic fracture propagating in a weakly consolidated, highly permeable reservoir rock during a waterflooding operation is described in this paper. The model recognizes the essential differences that exist between this class of fractures and conventional hydraulic fracturing treatments of oil and gas wells, namely: (i) the large-scale perturbations of pore pressure and the associated poroelastic effects caused by extended injection time; (ii) the extremely small volume of fluid stored in the fracture compared with the injected volume; and (iii) the leakage of water from both the borehole and the propagating fracture. The model consists of a set of equations encompassing linear elastic fracture mechanics, porous media flow and lubrication theory. Three asymptotic solutions applicable at different time regimes are found theoretically, and numerical results are obtained from the discretized governing equations. The solution reveals that the injection pressure does not evolve monotonically, as it increases with time in the early time radial-flow regime but decreases in the late time fracture-flow regime. Thus, the peak injection pressure does not correspond to a breakdown of the formation, as usually assumed, but rather to a transition between two regimes of porous media flow. However, this problem exhibits an extreme sensitivity of the time scales on a dimensionless injection rate $\mathcal {I}$. If $\mathcal {I} \lessapprox 1$, the time to reach the peak pressure could become so large that it cannot be observed in field operations, i.e. the fracture remains hydraulically invisible. Finally, it is found that poroelasticity significantly affects the response of the system, by increasing the injection pressure and delaying the time at which the peak pressure takes place.

A capillary surface in or around exotic cylinders cannot locate itself, since the configurations of the exotic cylinders with a variable radius permit an entire continuum of equilibrium menisci, all of which have the same potential energy. The ‘exotic’ property indicates that all the menisci have the smallest eigenvalues $\unicode[STIX]{x1D706}_{1}=0$ for the corresponding Sturm–Liouville problems without a volume constraint for stability analysis. Three types of exotic cylinders are addressed and the Sturm–Liouville problems with $\unicode[STIX]{x1D706}=0$ for stability analysis are solved numerically. Notably, the two-dimensional cases can be solved analytically. In the method of Slobozhanin & Alexander (Phys. Fluids, vol. 15, 2003, pp. 3532–3545), the stability of the meniscus is determined by comparing the boundary parameter $\unicode[STIX]{x1D712}_{1}$ and the critical value $\unicode[STIX]{x1D712}_{1}^{\ast }$, which is derived directly from the solution of the Sturm–Liouville problem with $\unicode[STIX]{x1D706}=0$. Results validate that the exotic cylinders have the boundary parameters $\unicode[STIX]{x1D712}_{1}=\unicode[STIX]{x1D712}_{1}^{\ast }$. Motivated by this observation, a new way to determine the critical value $\unicode[STIX]{x1D712}_{1}^{\ast }$ under pressure disturbances for stability analysis is proposed without solving the Sturm–Liouville problem with $\unicode[STIX]{x1D706}=0$.