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Two simulations of turbulent Couette flows were performed at friction Reynolds numbers of 1000 and 2000 in a large box of dimensions $L_x=16{\\rm \\pi} h$, $L_y=2h$ and $L_z=6{\\rm \\pi} h$, where h is the semi-height of the channel. The study focuses on the differences in the intensity and scaling of turbulence at these two Reynolds numbers. The 2000 case showed a lack of a clear log layer with a higher value of the Von Kármán constant $\\kappa$ than Poiseuille channels. The intensities were well-scaled in the buffer layer and below, with a second maximum of the streamwise intensity at approximately 350 wall units. Contrary to Poiseuille channels, the dissipation scales close to the wall in wall units. This fact can be attributed to the constant value of the derivative of the streamwise intensity in wall units. The intensities of the 2000 case showed remarkable differences compared with those at Reynolds number 1000 at the channel centre, likely due to the organization of large scales of the streamwise fluctuactions, $u$. These large scales were thought to be considered ‘infinite’. However, for the 2000 case, while all the structures have a width of $\\ell _z \\approx 6/8{\\rm \\pi} h$, their length varies from $\\ell _x \\approx 6{\\rm \\pi} h$ to $\\ell _x \\approx 16{\\rm \\pi} h$, which clearly contradicts the trends obtained in the past. This is a new effect that has not been reported for turbulent Couette flow and points to the uncertainty and sensitivity that is observed for certain statistical quantities.

Direct numerical simulations of the flow past an impulsively started cylinder at high Reynolds numbers (25k–100k) reveal an intriguing portrait of unsteady separation. Vorticity generation and vortex shedding entails a cascade of separation events on the cylinder surface that are reminiscent of Kelvin–Helmholtz instabilities. Primary vortices roll up along the cylinder surface as a result of instabilities of the initially attached vortex sheets, followed by vortex eruptions, creation of secondary vorticity and formation of dipole structures that are subsequently ejected from the surface of the cylinder. We analyse the vortical structures and their relationship to the forces experienced by the cylinder. This striking cascade of vortex instabilities may serve as reference for reduced-order models of flow separation and as guide for flow control of separated flows at high Reynolds numbers.

In turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surface roughness, the scaling exponent $\\unicode[STIX]{x1D6FD}$ in the relationship between the Nusselt number $Nu$ and the Rayleigh number $Ra$ , $Nu\\sim Ra^{\\unicode[STIX]{x1D6FD}}$ can be ${\\approx}1/2$ locally, provided that $Ra$ is large enough to ensure that the thermal boundary layer thickness $\\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$ is comparable to the roughness height. However, at even larger $Ra$ , $\\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$ becomes thin enough to follow the irregular surface and $\\unicode[STIX]{x1D6FD}$ saturates back to the value for smooth walls (Zhu et al., Phys. Rev. Lett., vol. 119, 2017, 154501). In this paper, we prevent this saturation by employing multiscale roughness. We perform direct numerical simulations of two-dimensional RB convection using an immersed boundary method to capture the rough plates. We find that, for rough boundaries that contain three distinct length scales, a scaling exponent of $\\unicode[STIX]{x1D6FD}=0.49\\pm 0.02$ can be sustained for at least three decades of $Ra$ . The physical reason is that the threshold $Ra$ at which the scaling exponent $\\unicode[STIX]{x1D6FD}$ saturates back to the smooth wall value is pushed to larger $Ra$ , when the smaller roughness elements fully protrude through the thermal boundary layer. The multiscale roughness employed here may better resemble the irregular surfaces that are encountered in geophysical flows and in some industrial applications.

Topology is introducing new tools for the study of fluid waves. The existence of unidirectional Yanai and Kelvin equatorial waves has been related to a topological invariant, the Chern number, that describes the winding of $f$ -plane shallow water eigenmodes around band-crossing points in parameter space. In this previous study, the topological invariant was a property of the interface between two hemispheres. Here we ask whether a topological index can be assigned to each hemisphere. We show that this can be done if the shallow water model in the $f$ -plane geometry is regularized by an additional odd-viscosity term. We then compute the spectrum of a shallow water model with a sharp equator separating two flat hemispheres, and recover the Kelvin and Yanai waves as two exponentially trapped waves along the equator, with all the other modes delocalized into the bulk. This model provides an exactly solvable example of bulk-interface correspondence in a flow with a sharp interface, and offers a topological interpretation for some of the transition modes described by Iga (J. Fluid Mech., vol. 294, 1995, pp. 367–390). It also paves the way towards a topological interpretation of coastal Kelvin waves along a boundary and, more generally, to an understanding of bulk-boundary correspondence in continuous media.

The effect of damping the longest streaks in wall-bounded turbulence is explored using numerical experiments. It is found that long streaks are not required for the self-sustenance of the bursting process, which is relatively little affected by their absence. In particular, there are turbulence states in which the fluctuations of the streamwise velocity have approximately the same length as the bursts, and are thus presumably associated with the bursts themselves, while the burst structure is essentially indistinguishable from flows in which longer velocity fluctuations are present. This suggests that the long streaks found in unmodified flows may be by-products, rather than active parts of the process.

The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral-type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profile, the optimal swimmer can be a puller, pusher or neutral. Using an asymptotic approach, we find that amongst all the modes of the shape function, only the third mode determines, to leading order, the swimming type of the optimal swimmer.

Experimental evidence is provided to demonstrate that the upstream-travelling waves in two jets screeching in the A1 and A2 modes are not free-stream acoustic waves, but rather waves with support within the jet. Proper orthogonal decomposition is used to educe the coherent fluctuations associated with jet screech from a set of randomly sampled velocity fields. A streamwise Fourier transform is then used to isolate components with positive and negative phase speeds. The component with negative phase speed is shown, by comparison with a vortex-sheet model, to resemble the upstream-travelling jet wave first studied by Tam & Hu (J. Fluid Mech., vol. 201, 1989, pp. 447–483). It is further demonstrated that screech tones are only observed over the frequency range where this upstream-travelling wave is propagative.

Fluid deformable surfaces show a solid–fluid duality which establishes a tight interplay between tangential flow and surface deformation. We derive the governing equations as a thin film limit and provide a general numerical approach for their solution. The simulation results demonstrate the rich dynamics resulting from this interplay, where, in the presence of curvature, any shape change is accompanied by a tangential flow and, vice versa, the surface deforms due to tangential flow. However, they also show that the only possible stable stationary state in the considered setting is a sphere with zero velocity.

We report non-monotonic wettability effects on displacement efficiency in heterogeneous porous structures at the post-breakthrough stage, in contrast to the monotonic ones in homogeneous porous structures. Experiments on designed microfluidic chips show that there exists a critical wettability to attain the highest efficiency of displacement in the porous matrix structure combined with a preferential flow pathway, while a stronger wettability of the displacing fluid leads to a higher displacement efficiency on the same matrix structure only. The porous structure with or without a preferential flow pathway results in totally different topological characteristics of phase distribution during displacement. Pore-scale mechanisms are identified to elucidate the formation of this non-monotonic wettability rule: cooperative pore filling under weakly water-wet conditions yields the best displacement; corner flow under strongly water-wet conditions and Haines events under strongly oil-wet conditions decrease the displacement efficiency. The pore-scale findings may provide unique insights into the joint effects of both wettability and flow heterogeneity on fluid displacement in porous media.

Abrupt depth transitions (ADTs) have recently been identified as potential causes of ‘rogue’ ocean waves. When stationary and (close-to-) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, that the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.