This paper extends the work of Tamano & Morinishi (J. Fluid Mech., vol. 548, 2006, pp. 361–373) by simulating supersonic turbulent channel flow with asymmetric thermal walls using a larger computational domain and a finer mesh. Direct numerical simulation is carried out for four cases with different thermal wall boundaries at the top wall at fixed $Ma=1.5$, $Re=6000$ and $Pr=0.72$, while the bottom wall is maintained at a constant temperature of $T_L$ equal to the reference temperature. These cases are referred to as the adiabatic case TAd, where the top wall is adiabatic; the pseudo-adiabatic case T32, where the top wall is isothermal with temperature $T_{w,t}=T_A$; the sub-adiabatic case T25, with $T_{w,t}=0.77T_A$; and the super-adiabatic case T40, with $T_{w,t}=1.24T_A$. Here, $T_A=3.234$ is the mean temperature at the adiabatic wall in the TAd case. The objective of this study is to compare and contrast the TAd case with its corresponding T32 case, and to investigate the effect of the wall temperature difference between the two isothermal walls. Comparisons of the basic turbulent statistics, the heat transfer between the Favre-averaged mean-flow kinetic energy, the Favre-averaged turbulent kinetic energy and the Favre-averaged mean internal energy, as well as the wall heat transfer properties, indicate that the TAd case and its corresponding T32 case are generally equivalent. The only discernible difference is in the region very close to the top wall for the temperature-fluctuation-related quantities. The analysis reveals that the asymmetry of the thermal walls causes asymmetry in the flow and thermal fields. In addition, the transfer of the heat generated by the pressure dilatation and the viscous stress is facilitated by the turbulent heat flux term and the mean molecular heat flux term.

Shock-tube experiments and theoretical studies have been performed to highlight mode-coupling in an air–SF$_6$–air fluid layer. Initially, the two interfaces of the layer are designed as single mode with different basic modes. It is found that as the two perturbed interfaces become closer, interface coupling induces a different mode from the basic mode on each interface. Then mode coupling further generates new modes. Based on the linear model (Jacobs et al., J. Fluid Mech., vol. 295, 1995, pp. 23–42), a modified model is established by considering the different accelerations of two interfaces and the waves’ effects in the layer, and provides good predictions to the linear growth rates of the basic modes and the modes generated by interface coupling. It is observed that interface coupling behaves differently to the nonlinear growth of the basic modes, which can be characterized generally by the existing or modified nonlinear model. Moreover, a new modal model is established to quantify the mode-coupling effect in the layer. The mode-coupling effect on the amplitude growth is negligible for the basic modes, but is significant for the interface-coupling modes when the initial wavenumber of one interface is twice the wavenumber of the other interface. Finally, amplitude freeze-out of the second single-mode interface is achieved theoretically and experimentally through interface coupling. These findings may be helpful for designing the target in inertial confinement fusion to suppress the hydrodynamic instabilities.

An improved version of the non-equilibrium theory of non-homogeneous turbulence of Chen & Vassilicos (J. Fluid Mech., vol. 938, 2022, A7) predicts that an intermediate range of length scales exists where the interscale turbulence transfer rate, the two-point interspace turbulence transport rate and the two-point pressure gradient velocity correlation term in the two-point small-scale turbulent energy equation are all proportional to the turbulence dissipation rate and independent of length scale. Particle image velocimetry measurements in a field of view under the turbulence-generating impellers in a baffled water tank support these predictions and show that the measured small-scale turbulence is significantly non-homogeneous. The particle image velocimetry measurements also suggest that the rate with which large scales lose energy to the small scales in the two-point large-scale turbulent energy equation also appears to be approximately proportional to the turbulence dissipation rate and independent of length scale in the same intermediate range and that this rate may not balance the interscale turbulence transfer rate in the two-point small-scale turbulent energy equation because of turbulent energy transport caused by the non-homogeneity.

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$, in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ($A = \sqrt {A_{ij}A_{ij}}$) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$. The boundedness and compactness of the $b_{ij}$-space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

The scaling universality of structure functions is studied for artificially thickened turbulent boundary-layer flows in over-tripped impacts by using hot-wire measurement datasets. The self-similarity behaviours in the inner and outer regions are examined from the viewpoint of different flow mechanisms. In the inner region, the relative ratios between structure functions for the energy-containing range of scales exhibit universality behaviour, in accordance with Townsend's attached eddy hypothesis. This universality of the energy-containing range of scales extends further away from the wall by increasing the tripping intensity. On the other hand, the impact of the external intermittency on the self-similarity of small-scale turbulence is examined through the intermittent zone in over-tripped conditions. Towards the boundary-layer edge, the structure functions exhibit a growing departure from self-similarity and analytical prediction, and it is demonstrated that the departure is primarily due to external intermittency. Moreover, based on the conditional statistics concentrated in the turbulent regimes, it is revealed that the small scales in the turbulence regime are homogenized in a self-similar behaviour, which is independent of the current tripping conditions.

Heated supersonic rectangular twin jets (SRTJ) with a total temperature ratio of 2, using nozzles of design Mach number 1.5 and aspect ratio 2, were investigated in flow regimes from overexpanded to the design condition (Mj = 1.3–1.5). This work complements our recently published work in unheated SRTJ using the same experimental facility (Samimy et al., J. Fluid Mech, vol. 959, 2023, A13). Localized arc filament plasma actuators (LAFPAs) were used to excite the natural instabilities in the jets, thereby controlling the flow and acoustics. The results show that the jets were coupled primarily out-of-phase in overexpanded cases, that the coupling had significant effects on the near-field (NF) pressure fluctuations, and that these fluctuations were considerably higher for in-phase than for out-of-phase coupled cases. The results also revealed that the far-field (FF) overall sound pressure level is significantly higher on the minor axis plane of the SRTJ and that the onset of Mach wave radiation contributes to the increased acoustic radiation at the peak noise direction. The LAFPAs successfully controlled the coupling and were able to reduce the NF pressure fluctuations by 10 dB. However, only 1 to 2 dB FF noise reduction at the peak noise radiation direction was achieved. The overall trends of the baseline results and response of the flow to excitation are qualitatively similar in unheated and heated cases, but the details are significantly different.

The oscillations of buoyant bodies in stratified fluids are deduced from the variations of their added mass. Three configurations are considered: a body displaced from its neutral level then released; a Cartesian diver set into oscillation by a modulation of the hydrostatic pressure, then released; and a body attached to a pendulum to which an impulse is applied. The first configuration is related to the dynamics of Lagrangian floats in the ocean. Two particular bodies are considered: an elliptic cylinder of horizontal axis, typical of two-dimensional bodies; and a spheroid of vertical axis, typical of three-dimensional bodies. The ultimate motion of the body consists of oscillations at the buoyancy frequency with an amplitude decaying algebraically with time. Before that, the resonant response of the system is observed, either aperiodic exponential decay when the system has no intrinsic dynamics, or exponentially damped oscillation otherwise. Comparison with available measurements demonstrates the need to include viscous dissipation in the analysis. At high Stokes number, dissipation comes from the Basset–Boussinesq memory force and is affected negligibly by the stratification; at low Stokes number, dissipation comes from Stokes resistance and exhibits a significant effect of the stratification.

Gravitational sedimentation and the collision of particles play key roles in various natural and engineering processes. In practice, particles are often non-spherical in shape with non-uniform mass distribution. In this study we investigate how the mass eccentricity influences the settling and gravitational collision of non-spherical particles in a quiescent fluid. Firstly, we theoretically analyse the effect of mass centre offset on the settling motion of a single spheroid under the low-Reynolds-number assumption. We find that the competition of fluid-inertia torque and gravitational torque determines the terminal settling mode of the spheroid. As the mass centre offset increases from zero to a critical value, the orientation of a settling spheroid undergoes a transition from the broad-side-on to narrow-side-on alignment. With an intermediate mass centre offset, the settling spheroid prefers an oblique orientation with a horizontal drift. Secondly, we investigate the gravitational collision rate of settling spheroids. With the change of particle orientation, the collision kernel exhibits a non-monotonic variation with a maximum when particles settle with an intermediate oblique orientation. Therefore, adjusting the mass centre offset to alter particle orientation can indirectly affect the collision rate of settling spheroidal particles. In summary, our findings reveal the significance of the mass eccentricity on particle dynamics in fluid flows, and suggest a potential approach for manipulating the settling motion and collision rate of non-spherical particles by adjusting their mass centre position.

Motivated by buoyancy-driven flows within geological formations, we study the evolution of a (dense) gravity current in a porous medium bisected by a thin interbed layer. The gravity current experiences distributed drainage along this low-permeability boundary. Our theoretical description of this flow takes into account dispersive mass exchange with the surrounding ambient fluid by considering the evolution of the bulk and dispersed phases of the gravity current. In turn, we model basal draining by considering two bookend limits, i.e. no mixing versus perfect mixing in the lower layer. Our formulations are assessed by comparing model predictions against the output of complementary numerical simulations run using COMSOL. Numerical output is essential both for determining the value of the entrainment coefficient used within our theory and for assessing the reasonableness of key modelling assumptions. Our results suggest that the degree of dispersion depends on the dip angle and the depth and permeability of the interbed layer. We further find that the nose position predictions made by our theoretical models are reasonably accurate up to the point where the no mixing model predicts a retraction of the gravity current front. Thereafter, the no mixing model significantly under-predicts, and the perfect mixing model moderately over-predicts, numerical data. Reasons for the failure of the no mixing model are provided, highlighting the importance of convective instabilities in the lower layer. A regime diagram is presented that defines the parametric region where our theoretical models do versus do not yield predictions in good agreement with numerical simulations.

We develop a comprehensive model for the creeping Poiseuille Bingham flow in channels equipped with a patterned wall, i.e. decorated with grooves or stripes that may represent a superhydrophobic (SH) or a chemically patterned (CP) surface, respectively, with longitudinal, transverse and oblique groove (stripe) orientations with respect to the applied pressure gradient. We rely on the Navier slip law to model the boundary condition on the slippery grooves. We develop semi-analytical, explicit-form and complementary computational fluid dynamics models, with solutions that have reasonable agreement. In contrast to its Newtonian analogue, a distinct solution for the oblique configuration, with an a priori unknown transform matrix, must be developed due to the viscoplastic nonlinear rheology. Our focus is to systematically analyse the effects of the Bingham number ($B$), slip number ($b$), groove periodicity length ($\ell$), slip area fraction ($\varphi$) and groove orientation angle ($\theta$), on the slip velocities, effective slip length ($\chi$), slip angle difference ($\theta -s$), mixing index ($I_M$), flow anisotropy and flow regimes. In particular, we demonstrate that, as $B$ increases, the maximum values of the shear component of $\chi$, $\theta -s$ and $I_M$ occur progressively at smaller values of $\theta$, compared with their Newtonian counterparts.