We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ($k_p$ being the peak wavenumber in the shallow area of depth $h_2$), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role.

The natural frequencies for sloshing without coupling with lateral tank motions differ from the natural sloshing frequencies with coupling. A consequence is that the nonlinear multimodal sloshing theory for prescribed tank motion should be revised when studying the liquid sloshing dynamics in connection with marine structures in ocean waves. The needed revisions are done for a rectangular rigid tank with finite liquid depth. Steady-state resonant solutions of the constructed nonlinear modal equations are derived to analytically describe the coupled resonant sloshing and sway of a floating rigid body in regular incident deep water waves with two-dimensional flow conditions at the lowest coupled sloshing–sway natural frequency. The steady-state theoretical results are validated by comparing them with the model tests by Rognebakke & Faltinsen (J. Ship Res., vol. 47, issue 3, 2003, pp. 208–221). The occurrence of an instability frequency range is theoretically justified.

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, using only $10\,\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\,\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is only of about $20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.

The large-scale pulsations of shock-induced separation with length scale that significantly exceeds the incoming boundary layer thickness are investigated. The shock–boundary layer interaction (SBLI) unit is generated by an inward-turning axisymmetric compression ramp at an inflow Mach number of 2.5. A substantial region surrounding the centre azimuth exhibited mean and dynamic flow features that are consistent with two-dimensional separation. Two-dimensional highly resolved maps of surface pressure field are obtained using fast-response pressure-sensitive paint fluorescence imaging at 40 kHz repetition rate. The measurement domain covered significant regions of the incoming boundary layer through the relaxing boundary layer downstream of the reattachment as well as over 25 boundary layer thicknesses in the azimuthal direction. These measurements provide new insights into the spanwise coupling of the SBLI unit in addition to its inherent dynamics. The power spectral density (PSD) of the centreline pressure exhibits very good agreement with theoretical models and complementary measurements using fast-response pressure transducers, which served to validate the pressure field measurements. Detailed examination of the PSD reveals strong agreement with the literature, which includes the peak Strouhal number of the separation and reattachment shock motions as well as the downward frequency shift along the separation bubble. Furthermore, the pressure fluctuation maps reveal streamwise-elongated structures just downstream of the ramp leading edge that persist well downstream of the reattachment. A time sequence of conditional average pressure fluctuation maps is constructed surrounding isolated pressure excursions in the intermittent region. This sequence, along with two-point cross correlation analysis, provides critical information about the flow processes that drive the separation bubble pulsations in the SBLI units with large separation scales. Overall, the imbalance in the mass within the separation bubble appears to be the critical mechanism that drives the separation bubble pulsations. Furthermore, the pressure perturbations originating at azimuthally offset locations are also observed to influence the separation bubble dynamics.

The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$, where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$, the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$-dependence, $Nu-1\propto \widetilde {Ra}^{3}$.

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ($Re$) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

We derive an analytical solution for the acoustic streaming inside a rigid tube resulting from a pseudo-standing wave field, generated by two counterpropagating travelling waves. We solve the second-order axisymmetric problem that follows from the perturbation expansion of the governing equations. In the process, we impose no restriction on the diameter of the tube with respect to the thickness of the viscous boundary layer and acoustic wavelength. The derived solution is then used to study the evolution of streaming patterns inside the tube when geometrical and material parameters are varied. We show how the Schlichting streaming torus at the wall bounds the Rayleigh streaming near the axis of the tube. Decreasing the ratio ($\varXi$) of the tube radius to the viscous boundary layer thickness gradually expands the Schlichting streaming, suppressing the Rayleigh streaming. Considering the average mass transport velocity, the Rayleigh streaming vanishes at the critical ratio $\varXi _{{S}}^{{M}}=6.2$. The critical ratio is independent of fluid properties in the limit of large acoustic wavelength relative to the radius of the tube ($\varLambda$). When $\varLambda$ decreases towards unity, large-scale Eckart-like streaming develops near the axis, superseding the Rayleigh streaming, while the Schlichting streaming remains at the wall. In addition, we demonstrate the relevance of the compressibility of the streaming flow and of the full inclusion of the spatial variation of the Reynolds stress that acts as the streaming source. The study is especially relevant for microfluidic systems, wherein the viscous boundary layer can reach significant thicknesses.

Understanding the development and breakup of interfacial waves in a two-phase mixing layer between the gas and liquid streams is paramount to atomization. Due to the velocity difference between the two streams, the shear on the interface triggers a longitudinal instability, which develops to interfacial waves that propagate downstream. As the interfacial waves grow spatially, transverse modulations arise, turning the interfacial waves from quasi-two-dimensional to fully three-dimensional. The inlet gas turbulence intensity has a strong impact on the interfacial instability. Therefore, parametric direct numerical simulations are performed in the present study to systematically investigate the effect of the inlet gas turbulence on the formation, development and breakup of the interfacial waves. The open-source multiphase flow solver, PARIS, is used for the simulations and the mass–momentum consistent volume-of-fluid method is used to capture the sharp gas–liquid interfaces. Two computational domain widths are considered and the wide domain will allow a detailed study of the transverse development of the interfacial waves. The dominant frequency and spatial growth rate of the longitudinal instability are found to increase with the inlet gas turbulence intensity. The dominant transverse wavenumber, determined by the Rayleigh–Taylor instability, scales with the longitudinal frequency, so it also increases with the inlet gas turbulence intensity. The holes formed in the liquid sheet are important to the disintegration of the interfacial waves. The hole formation is influenced by the inlet gas turbulence. As a result, the sheet breakup dynamics and the statistics of the droplets formed also change accordingly.

A fundamental study has been conducted to understand the mean and turbulence characteristics and their role in mixing processes of starting turbulent plumes initiated by a heated area source and released into a neutral atmosphere. Large eddy simulation has been performed in a domain of size 7 km (vertical) and $4~\text {km} \times 4~\text {km}$ (horizontal) for five different cases with surface heat flux varying from 0.5–2.5 km s$^{-1}$. With increasing buoyancy flux, the plume Reynolds number $Re$ (based on the maximum centreline velocity) increases from $6 \times 10^{7}\text {--}10^{8}$; however, the Froude number $Fr$ does not increase monotonically with increasing $B_o$, it varies from 1.091–1.149. Key physics that contributes to mixing and entrainment of ambient fluid into the plume has been investigated. The buoyancy- and shear-production of turbulence kinetic energy contributes to the mixing processes within the plume. The characteristic features of a starting plume are: the presence of a spiralling columnar neck region surrounding the central core that extends to $5D$ ($D$ is the source diameter), and which is capped with an unsteady head region that actively entrains fluid due to instabilities at the plume interface. Formation of vortex rings and instability mechanisms are linked to the entrainment process. Unsteady entrainment has been calculated using first principles, and the results revealed that entrainment, though negligible initially, initiates with the growth of the instabilities in the head region of the plume, and it correlates with the local Reynolds number in the head region.

Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform large-eddy simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, 2020, p. A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on both the array density and turbine layout. An analytical model derived from the two-scale momentum theory predicts the impact of array density very well for all 50 farms investigated and can therefore be used as an upper limit to farm performance. We also propose a new method to quantify turbine-scale losses (due to turbine–wake interactions) and farm-scale losses (due to the reduction of farm-average wind speed). They both depend on the strength of atmospheric response to the farm, and our results suggest that, for large offshore wind farms, the farm-scale losses are typically more than twice as large as the turbine-scale losses. This is found to be due to a two-scale interaction between turbine wake and farm induction effects, explaining why the impact of turbine layout on farm power varies with the strength of atmospheric response.

Large-scale intermittency is a widely observed phenomenon in convective surface layer turbulence that induces non-Gaussian temperature statistics, while such a signature is not observed for velocity signals. Although approaches based on probability density functions have been used so far, those are not able to explain to what extent the signals’ temporal structure impacts the statistical characteristics of the velocity and temperature fluctuations. To tackle this issue, a visibility network analysis is carried out on a field-experimental dataset from a convective atmospheric surface layer flow. Through surrogate data and network-based measures, we demonstrate that the temperature intermittency is related to strong nonlinear dependencies in the temperature signals. Conversely, a competition between linear and nonlinear effects tends to inhibit the temperature-like intermittency behaviour in streamwise and vertical velocities. Based on present findings, new research avenues are likely to be opened up in studying large-scale intermittency in convective turbulence.

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$, in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$, a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.