The paper investigates the phenomena occurring in a Taylor–Couette flow system subject to a steady axial pressure gradient in a small envelope of the Taylor–Reynolds state space under transitional regimes. A remarkable net power reduction necessary to simultaneously drive the two flows compared to that required to drive the Taylor–Couette flow alone is documented under non-trivial conditions. The energy transfer process characterizing the large-scale coherent structures is investigated by processing a set of statistically independent realizations obtained from direct numerical simulation. The analysis is conducted with an incompressible three-dimensional Navier–Stokes flow solver employing a spectral representation of the unknowns.

Nonlinear interactions between sea waves and the sea bottom are a major mechanism for energy transfer between the different wave frequencies in the near-shore region. Nevertheless, it is difficult to account for this phenomenon in stochastic wave forecasting models due to its mathematical complexity, which mostly consists of computing either the bispectral evolution or non-local shoaling coefficients. In this work, quasi-two-dimensional stochastic energy evolution equations are derived for dispersive water waves up to quadratic nonlinearity. The bispectral evolution equations are formulated using stochastic closure. They are solved analytically and substituted into the energy evolution equations to construct a stochastic model with non-local shoaling coefficients, which includes nonlinear dissipative effects and slow time evolution. The nonlinear shoaling mechanism is investigated and shown to present two different behaviour types. The first consists of a rapidly oscillating behaviour transferring energy back and forth between wave harmonics in deep water. Owing to the contribution of bottom components for closing the class III Bragg resonance conditions, this behaviour includes mean energy transfer when waves reach intermediate water depths. The second behaviour relates to one-dimensional shoaling effects in shallow water depths. In contrast to the behaviour in intermediate water depths, it is shown that the nonlinear shoaling coefficients refrain from their oscillatory nature while presenting an exponential energy transfer. This is explained through the one-dimensional satisfaction of the Bragg resonance conditions by wave triads due to the non-dispersive propagation in this region even without depth changes. The energy evolution model is localized using a matching approach to account for both these behaviour types. The model is evaluated with respect to deterministic ensembles, field measurements and laboratory experiments while performing well in modelling monochromatic superharmonic self-interactions and infra-gravity wave generation from bichromatic waves and a realistic wave spectrum evolution. This lays physical and mathematical grounds for the validity of unexplained simplifications in former works and the capability to construct a formulation that consistently accounts for nonlinear energy transfers from deep to shallow water.

High-speed schlieren cinéphotography of the firing of a high-energy plasma-jet igniter reveal turbulent structures similar in appearance to laboratory models of thermals or turbulent puffs. Measurements of the growth rates of these features together with those of their impulse and thermal energy confirm this similarity. A simple model based on the entrainment assumption gives a good description of the motion of the element and also of the decay of the internal temperature.

We extend the vorticity-based modelling approach of Borden & Meiburg (Phys. Fluids, vol. 25 (10), 2013, 101301) to non-Boussinesq gravity currents and derive an analytical expression for the Froude number without the need for an energy closure or any assumptions about the pressure. The Froude-number expression we obtain reduces to the correct form in the Boussinesq limit and agrees closely with simulation data. Via detailed comparisons with simulation results, we furthermore assess the validity of three key assumptions underlying both our as well as earlier models: (i) steady-state flow in the moving reference frame; (ii) inviscid flow; and (iii) horizontal flow sufficiently far in front of and behind the current. The current approach does not require an assumption of zero velocity in the current.

An extension to the classical shallow-water equation (SWE) is derived that exactly satisfies the bed condition and can be regarded as an approximation to wave scattering at the next order in the small parameter $(h/\unicode[STIX]{x1D706})^{2}$ (depth to wavelength ratio squared). In the frequency domain, the extended SWE shares the same simple structure as the standard SWE with coefficients modified by terms relating to the bed variation. In three dimensions the governing equation demonstrates that variable topography gives rise to anisotropic effects on wave scattering not present in the standard SWE, with consequences for the design of water wave metamaterials. Numerical examples illustrate that approximations to wave scattering using the extended SWE are significantly improved in comparison with the standard SWE.

We derive new analytical results for the hydrodynamic force exerted on a sinusoidally oscillating porous shell and a sphere of uniform density in the Stokes limit. The coupling between the spherical particle and the solvent is done using the Debye–Bueche–Brinkman (DBB) model, i.e. by a frictional force proportional to the local velocity difference between the permeable particle and the solvent. We compare our analytical results and existing dynamic theories to lattice–Boltzmann simulations of the full Navier–Stokes equations for the oscillating porous particle. We find our analytical results to agree with simulations over a broad range of porosities and frequencies.

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

The application of local periodic heating for control of a spatially developing shear layer downstream of a finite-thickness splitter plate is examined by numerically solving the two-dimensional Navier–Stokes equations. At the trailing edge of the plate, an oscillatory heat flux boundary condition is prescribed as the thermal forcing input to the shear layer. The thermal forcing introduces a low level of oscillatory surface vorticity flux and baroclinic vorticity at the actuation frequency in the vicinity of the trailing edge. The vortical perturbations produced can independently excite the fundamental instability that accounts for shear layer roll-up as well as the subharmonic instability that encourages the vortex pairing process farther downstream. We demonstrate that the nonlinear dynamics of a spatially developing shear layer can be modified by local oscillatory heat flux as a control input. We believe that this study provides a basic foundation for flow control using thermal-energy-deposition-based actuators such as thermophones and plasma actuators.

We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.

A combined experimental and numerical study of transitional pulsatile flow through a planar constriction is presented. The parametric space that we adopt is similar to the one reported in a variety of past experiments relevant to the flow through stenosed arteries. In general, the flow just downstream of the constriction is dominated by the dynamic of the accelerating/decelerating jet that forms during each pulsatile cycle. We found a switch in the shedding frequency and roll-up dynamics, just after the flow rate approaches its maximum value in the cycle. The flow in the reattached area further downstream is also affected by the jet dynamics. A ‘synthetic’ turbulent-like wall-layer develops, an is constantly supported by streamwise vortices that originate from the spanwise instabilities of the large coherent structures generated by the jet. The relation of these structures to the phase-averaged turbulent statistics and the turbulent kinetic energy budgets is discussed.

We provide experimental measurements for the effective scaling of the Taylor–Reynolds number within the bulk $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number $\mathit{Ta}$), in the ultimate regime of Taylor–Couette flow. We define $Re_{\unicode[STIX]{x1D706},bulk}=(\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}}))^{2}(15/(\unicode[STIX]{x1D708}\unicode[STIX]{x1D716}_{bulk}))^{1/2}$, where $\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}})$ is the bulk-averaged standard deviation of the azimuthal velocity, $\unicode[STIX]{x1D716}_{bulk}$ is the bulk-averaged local dissipation rate and $\unicode[STIX]{x1D708}$ is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate $\unicode[STIX]{x1D716}(r)$ using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range – without invoking Taylor’s hypothesis. We find an effective scaling of $\unicode[STIX]{x1D716}_{\mathit{bulk}}/(\unicode[STIX]{x1D708}^{3}d^{-4})\sim \mathit{Ta}^{1.40}$, (corresponding to $\mathit{Nu}_{\unicode[STIX]{x1D714},\mathit{bulk}}\sim \mathit{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.40}$) and direct numerical simulations ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\unicode[STIX]{x1D702}_{\mathit{bulk}}/d\sim \mathit{Ta}^{-0.35}$ and the turbulence intensity as $I_{\unicode[STIX]{x1D703},\mathit{bulk}}\sim \mathit{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor–Reynolds number effectively scales as $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}\sim \mathit{Ta}^{0.18}$ in the present parameter regime of $4.0\times 10^{8}<\mathit{Ta}<9.0\times 10^{10}$.

Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien–Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

The fundamental solution to steady ship waves accounting for viscous effects (the viscous-ship-wave Green function) is investigated within the framework of the weakly damped free-surface flow theory. An explicit expression of the viscous-ship-wave Green function is firstly derived, and an accurate and efficient technique is described to evaluate the Green function via decomposing the free-surface term into the local-flow component and wave component. To delve into the physical features of the viscous-ship-wave Green function, the asymptotic approximations in the far field due to Kelvin, Havelock and Peters are presented for the flow-field point located inside, at and outside the Kelvin wedge. In addition, uniform approximations to the wave component based on the Chester–Friedman–Ursell (CFU) approximation and the Kelvin–Havelock–Peters (KHP) approximation are carried out. Both numerical evaluation and asymptotic approximations show that the singular behaviour is eliminated and the divergent waves associated with large wavenumbers leading to rapid oscillations are severely damped when viscous effects are accounted for. In addition, viscous effects also alter the apparent wake angle associated with the wave pattern created by a high-speed translating source, and the apparent wake angle is dependent on both $\mathscr{U}^{-1}$ and $\mathscr{U}^{-2}$, where $\mathscr{U}$ is the translating speed of the source.

This paper investigates the noise radiation produced by a rotor inside a duct, which is convected by a swirling-translating mean flow. The study is based on an extension of Gennaretti's and Morino's boundary element method to the frequency domain for scattering problems in conjunction with a spinning rotor source model in the presence of a swirl flow. The proposed formulation is validated against exact solutions and is further used to investigate the effects of the translating flow Mach number and swirling flow angular velocity on noise radiation to the far field. The scattered sound is highly affected by the convecting mean flow. The modal content of the scattered field increases when increasing the translating flow Mach number, while a swirling flow leads to a reduction of the mode propagation, if co-rotating with respect to the azimuthal order of the spinning source, or an increase of the modal content, if counter-rotating with respect to the source. In general, the mean translating flow moves the main lobes of the directivity patterns downstream, while in some cases the mean swirling flow neglects this effect and the downstream lobe is completely shifted.