Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.

Metachronal rowing is a biological propulsion mechanism employed by many swimming invertebrates (e.g. copepods, ctenophores, krill and shrimp). Animals that swim using this mechanism feature rows of appendages that oscillate in a coordinated wave. In this study, we used observations of a swimming ctenophore (comb jelly) to examine the hydrodynamic performance and vortex dynamics associated with metachronal rowing. We first reconstructed the beating kinematics of ctenophore appendages based on a high-speed video of a metachronally coordinated row. Following the reconstruction, two numerical models were developed and simulated using an in-house immersed-boundary-method-based computational fluid dynamics solver. The two models included the original geometry (16 appendages in a row) and a sparse geometry (8 appendages, formed by removing every other appendage along the row). We found that appendage tip vortex interactions contribute to hydrodynamic performance via a vortex-weakening mechanism. Through this mechanism, appendage tip vortices are significantly weakened during the drag-producing recovery stroke. As a result, the swimming ctenophore produces less overall drag, and its thrust-to-power ratio is significantly improved (up to 55.0 % compared with the sparse model). Our parametric study indicated that such a propulsion enhancement mechanism is less effective at higher Reynolds numbers. Simulations were also used to investigate the effects of substrate curvature on the unsteady hydrodynamics. Our results illustrated that, compared with a flat substrate, arranging appendages on a curved substrate can boost the overall thrust generation by up to 29.5 %. These findings provide new insights into the fluid dynamic principles of propulsion enhancement underlying metachronal rowing.

We consider the dynamics of a two-dimensional incompressible perfect fluid on a Möbius strip embedded in $\mathbb {R}^{3}$. The vorticity–stream function formulation of the Euler equations is derived from an exterior-calculus form of the momentum equation. The non-orientability of the Möbius strip and the distinction between forms and pseudo-forms this introduces lead to unusual properties: a boundary condition is provided by the conservation of circulation along the single boundary of the strip, and there is no integral conservation for the vorticity density or for any odd function thereof. A finite-difference numerical implementation is used to illustrate the Möbius-strip realisation of familiar phenomena: translation of vortices along boundaries, shear instability and decaying turbulence.

Transport of solutes through channels with rough boundaries is abundant in natural and engineered settings. However, it is not known currently what the consequences of an abruptly alternating boundary are for the solute dispersion, in particular when advected by inertial fluid flow. To investigate this, we compute numerically the time-asymptotic longitudinal dispersion coefficient of a passive solute advected by fluid flow through a two-dimensional channel with square boundary roughness. We determine how the effective diffusion coefficient depends on the boundary amplitude, Péclet number and Reynolds number. For creeping flow, the effective diffusion coefficient is found to be enhanced significantly through the recirculation zones. Increasing fluid inertia reduces the effective diffusion coefficient by up to a factor of two for high Péclet numbers. We interpret this behaviour by analysing residence times computed from Lagrangian particle simulations.

This work shows how the early stages of perturbation growth in a viscosity-stratified flow are different from those in a constant-viscosity flow, and how nonlinearity is a crucial ingredient. We derive the viscosity-varying adjoint Navier–Stokes equations, where gradients in viscosity force both the adjoint momentum and the adjoint scalar. By the technique of direct-adjoint looping, we obtain the nonlinear optimal perturbation which maximises the perturbation kinetic energy of the nonlinear system. While we study three-dimensional plane Poiseuille (channel) flow with the walls at different temperatures, and a temperature-dependent viscosity, our findings are general for any flow with viscosity variations near walls. The Orr and modified lift-up mechanisms are in operation at low and high perturbation amplitudes, respectively, at our subcritical Reynolds number. The nonlinear optimal perturbation contains more energy on the hot (less-viscous) side, with a stronger initial lift-up. However, as the flow evolves, the important dynamics shifts to the cold (more-viscous) side, where wide high-speed streaks of low viscosity grow and persist, and strengthen the inflectional quality of the velocity profile. We provide a physical description of this process and show that the evolution of the linear optimal perturbation misses most of the physics. The Prandtl number does not qualitatively affect the findings at these times. The study of nonlinear optimal perturbations is still in its infancy, and viscosity variations are ubiquitous. We hope that this first work on nonlinear optimal perturbation with viscosity variations will lead to wider studies on transition to turbulence in these flows.

We performed numerical simulations of a homogeneous swarm of bubbles rising at large Reynolds number, $Re=760$, with volume fractions ranging from 1 % to 10 %. We consider a simplified model in which the interfaces are not resolved, but which allows us to simulate flows with a large number of bubbles and to emphasize the interactions between bubble wakes. The liquid phase is described by solving, on an Eulerian grid, the Navier–Stokes equations, including sources of momentum which model the effect of the bubbles. The dynamics of each bubble is determined within the Lagrangian framework by solving an equation of motion involving the hydrodynamic forces exerted by the fluid accounting for the correction of the fictitious self-interaction of a bubble with its own wake. The comparison with experiments shows that this coarse-grained simulations approach can reliably describe the dynamics of the resolved flow scales. We use conditional averaging to characterize the mean bubble wakes and obtain in particular the typical shear imposed by the rising bubbles. On the basis of the spectral decomposition of the energy budget, we observe that the flow is dominated by production at large scales and by dissipation at small scales and we rule out the presence of an intermediate range in which the production and dissipation are locally in balance. We propose that the $k^{-3}$ subrange of the energy spectra results from the mean shear rate imposed by the bubbles, which controls the rate of return to isotropy.

We derive weakly dispersive Boussinesq equations using a $\unicode[STIX]{x1D70E}$ coordinate for the vertical direction, employing a series expansion in powers of $\unicode[STIX]{x1D70E}$. We restrict attention initially to the case of constant still-water depth $h$ in order to simplify subsequent analysis, and consider equations based on expansions about the bottom elevation $\unicode[STIX]{x1D70E}=0$, and then about a reference elevation $\unicode[STIX]{x1D70E}_{\unicode[STIX]{x1D6FC}}$ in order to improve linear dispersion properties. We use a perturbation analysis, suggested recently by Madsen & Fuhrman (J. Fluid Mech., vol. 889, 2020, A38), to show that the resulting models are not subject to the trough instability studied there. A similar analysis is performed to develop a model for interfacial waves in a two-layer fluid, with comparable results. We argue, by extension, that a necessary condition for eliminating trough instabilities is that the model’s nonlinear dispersive terms should not contain still-water depth $h$ and surface displacement $\unicode[STIX]{x1D702}$ separately.

One of the most dramatic effects of vibrational and chemical non-equilibrium in hypersonic flows occurs in the bow-shock detachment process in flow over a wedge. This was shown theoretically and in reflected shock tunnel experiments by Hornung & Smith (J. Fluid Mech., vol. 93, 1979, pp. 225–239). In the present work, the effect is first demonstrated by computation of two-dimensional non-equilibrium flows. The effect of the finite transverse extent of the wedge is then studied by three-dimensional computations of non-relaxing flows. An analytical formula is obtained that gives the shock detachment distance of a finite wedge for ideal-gas and equilibrium flows. In the experiment, the finite transverse extent of the wedge competes with the non-equilibrium effects, as each introduces a new length scale. The carbon dioxide and nitrogen flows of the experiment are therefore computed in three dimensions and with two-temperature chemistry accounting for vibrational and chemical non-equilibrium. In the case of nitrogen flow, the agreement between experiment and computation is not good, the experimental detachment distance being larger. A number of possible reasons are quantitatively examined. A conclusive resolution of the discrepancy is considered to require a repeat of the experiment with more accurately characterized conditions. In the case of the carbon dioxide experiments, the computed results agree remarkably well with experiment. This is partially due to the fact that the condition is very close to equilibrium, where the sensitivity of the detachment process to relaxation effects is small. The analytical expression for the dimensionless detachment distance agrees very well with all the three-dimensional computations of non-relaxing flows.

The statistical relation between ocean wave geometry and water particle movements can be formulated in the stochastic Gauss–Lagrange model. In this paper we use Slepian models to obtain detailed information of the sea surface elevation in the neighbourhood of local maxima in a Gaussian wave model and of the movements of the top particle of the waves. We present full conditional distributions of the Gaussian vertical and horizontal movements in the Gauss–Lagrange model, and represent them as one regression component depending on the height and curvature at the wave maxima and one residual component. These conditional distributions define the explicit vertical and horizontal Slepian models. The Slepian models are used to simulate individual min–max–min waves in space, in particular their front–back asymmetry, and the velocity vector of the particle at the wave maximum. We find that there is a strong relation between the degree of front–back wave asymmetry and the direction of the particle movement. We discuss the role of second-order corrections to the Gaussian components and find only minor effects for the sea states studied. The Slepian model is shown to be an efficient tool to obtain detailed information about Gaussian and related models in the neighbourhood of critical points, without the need for time and space consuming simulations. In particular, they permit easy simulation of shape and kinematics of rare extreme waves.