We present an experimental investigation aimed at understanding the effects of surface roughness on the time-mean drag coefficient ($\bar {C}_{D}$) of finite-span cylinders ($\text {span/diameter} = \text {aspect ratio}$, $0.51 \le AR \le 6.02$) freely rolling without slip on an inclined plane. While lubrication theory predicts an infinite drag force for ideally smooth cylinders in contact with a smooth surface, experiments yield finite drag coefficients. We propose that surface roughness introduces an effective gap ($G_{eff}$) resulting in a finite drag force while allowing physical contact between the cylinder and the plane. This study combines measurements of surface roughness for both the cylinder and the plane panel to determine a total relative roughness ($\xi$) that can effectively describe $G_{eff}$ at the point of contact. It is observed that the measured $\bar {C}_{D}$ increases as $\xi$ decreases, aligning with predictions of lubrication theory. Furthermore, the measured $\bar {C}_{D}$ approximately matches combined analytical and numerical predictions for a smooth cylinder and plane when the imposed gap is approximately equal to the mean peak roughness ($R_p$) for rough cylinders, and one standard deviation peak roughness ($R_{p, 1\sigma }$) for relatively smooth cylinders. As the time-mean Reynolds number ($\overline {Re}$) increases, the influence of surface roughness on $\bar {C}_{D}$ decreases, indicating that wake drag becomes dominant at higher $\overline {Re}$. The cylinder aspect ratio ($AR$) is found to have only a minor effect on $\bar {C}_{D}$. Flow visualisations are also conducted to identify critical flow transitions and these are compared with visualisations previously obtained numerically. Variations in $\xi$ have little effect on the cylinder wake. Instead, $AR$ was observed to have a more pronounced effect on the flow structures observed. The Strouhal number ($St$) associated with the cylinder wake shedding was observed to increase with $\overline {Re}$, while demonstrating little dependence on $AR$.

We investigate effect of porous insert located upstream of the separation edge of a backward-facing step (BFS) in early transitional regime as a function of Reynolds number. This is an example of hydrodynamic system that is a combination of separated shear flow with large amplification potential and porous materials known for efficient flow destabilisation. Spectral analysis reveals that dynamics of BFS is dominated by spectral modes that remain globally coherent along the streamwise direction. We detect two branches of characteristic frequencies in the flow and with Hilbert transform we characterise their spatial support. For low Reynolds numbers, the dynamics of the flow is dominated by lower frequency, whereas for sufficiently large Reynolds numbers cross-over to higher frequencies is observed. Increasing permeability of the porous insert results in decrease in Reynolds number value, at which frequency cross-over occurs. By comparing normalised frequencies on each branch with local stability analysis, we attribute Kelvin–Helmholtz and Tollmien–Schlichting instabilities to upper and lower frequency branches, respectively. Finally, our results show that porous inserts enhance Kelvin–Helmholtz instability and promote transition to oscillator-type dynamics. Specifically, the amplitude of vortical (BFS) structures associated with higher-frequency branch follows Landau model prediction for all investigated porous inserts.

Regular reflection (RR) to Mach reflection (MR) transitions (${\rm RR}\leftrightarrow {\rm MR}$) on long wedges in steady supersonic flows have been well studied and documented. However, in a short wedge where the wedge length is small, the transition prediction becomes really challenging owing to the interaction of the expansion fan emanating from the trailing edge of the wedge with the incident shock and the triple/reflection point. The extent of this interaction depends on the distance between the wedge trailing edge and the symmetry line (Ht). This distance is a geometric combination of the distance of the wedge leading edge from the symmetry line $(H)$, the wedge angle ($\theta$) and the wedge length $(w)$. In the present study, we used the method of characteristics to model the complete wave interactions which accurately predicted shock curvatures and the reflection configurations for all ranges of the incoming flow Mach number. In the case of short wedges, the transition criterion strongly depends on the wedge length, which can be so adjusted even to eliminate the ${\rm RR}\rightarrow {\rm MR}$ transitions till the wedge angle reaches the no-reflection domain. Transition lines for both the detachment criterion and von Neumann criterion are also drawn to investigate the dual solution domain, and the reflection configurations were verified experimentally for the first time on short wedges. By using proper input configuration parameter ($w/H$), various types of shifts in the dual solution domain for short wedges are studied and categorised into three types, namely Type I, Type II and Type III.

In this paper, we investigate a sink-driven three-layer flow in a radial Hele-Shaw cell. The three fluids are of different viscosities, with one fluid occupying an annulus-like domain, forming two interfaces with the other two fluids. Using a boundary integral method and a semi-implicit time stepping scheme, we alleviate the numerical stiffness in updating the interfaces and achieve spectral accuracy in space. The interaction between the two interfaces introduces novel dynamics leading to rich pattern formation phenomena, manifested by two typical events: either one of the two interfaces reaches the sink faster than the other (forming cusp-like morphology), or they come very close to each other (suggesting a possibility of interface merging). In particular, the inner interface can be wrapped by the other to have both scenarios. We find that multiple parameters contribute to the dynamics, including the width of the annular region, the location of the sink, and the mobilities of the fluids.

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani & Park, Phys. Rev. Fluids, 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

We examine the fluid flow forced by precession of a rotating cylindrical container using numerical simulations and experimental flow measurements with ultrasonic Doppler velocimetry. The analysis is based on the decomposition of the flow field into contributions with distinct azimuthal symmetry or analytically known inertial modes and the corresponding calculation of their amplitudes. We show that the predominant fraction of the kinetic energy of the precession-driven fluid flow is contained only within a few large-scale modes. The most striking observation shown by simulations and experiments is the transition from a flow dominated by large-scale structures to a more turbulent behaviour with the small-scale fluctuations becoming increasingly important. At a fixed rotation frequency (parametrized by the Reynolds number, $Re$) this transition occurs when a critical precession ratio is exceeded and consists of a two-stage collapse of the directly driven flow going along with a massive modification of the azimuthal circulation (the zonal flow) and the appearance of an axisymmetric double-roll mode limited to a narrow range of precession ratios. A similar behaviour is found in experiments which make it possible to follow the transition up to Reynolds numbers of $Re\approx 2\times 10^6$. We find that the critical precession ratio decreases with rotation, initially showing a particular scaling ${\propto }Re^{-({1}/{5})}$ but developing an asymptotic behaviour for $Re\gtrsim 10^5$ which might be explained by the onset of turbulence in boundary layers.