Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction, and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the nonstratified, homogeneous mixture case, while a U-shaped flame surface, whose leading edge propagates upstream at the channel centerline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling, and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to the Karlovitz number, and it is shown that a nominal channel-flow Karlovitz number, ${\text{Ka}}_{\text{in}}^{\text{ch}}$, based on the wall-normal variation of canonical turbulence ($t_{\eta }={(\nu /\epsilon )}^{1/2}$) and chemistry ($t_l={\delta }_l/S_l$) timescales in fully developed channel flow, compares well with an effective Karlovitz number, ${\text{Ka}}_{\text{fl}}^{\text{ch}}$, extracted from the present DNS datasets using conditionally sampled values of $t_{\eta }$ and $t_l$ in the immediate vicinity of the flame ($0.1<C<0.3$).

Shear thickening is the increase of viscosity as shear rate or stress increases. For concentrated or dense suspensions of solid particles, this phenomenon may take the extreme form known as discontinuous shear thickening (DST). In DST, the relative viscosity ${\eta }_r$ exhibits a discontinuous variation when presented as a function of the shear rate $\dot{\gamma }$, typically with a large jump in viscosity at the discontinuity; ${\eta }_r\left(\varphi \right)=\eta \left(\varphi \right)/{\eta }_0$, with ${\eta }_0$ the suspending fluid viscosity and $\varphi$ the solid volume fraction. Rate dependence implies that ${\eta }_r$ is a function not only of $\varphi$ but also of $\dot{\gamma }$ or the shear stress $\sigma$. A scenario in which the close interactions between particles undergo a stress-driven lubricated-to-frictional (LF) transition provides a coherent mechanistic basis for the shear thickening seen in dense suspensions. Prior study of shear thickening leading to the proposal of the LF transition is briefly reviewed. The LF scenario and its predictions are presented, along with a perspective on unresolved issues on widely different scales, from contact interactions to system-spanning force networks.

Gas turbines and rocket engines sometimes suffer from violent oscillations caused by feedback between acoustic waves and flames in the combustion chamber. These are known as thermoacoustic oscillations and they often occur late in the design process. Their elimination usually requires expensive tests and redesign. Full scale tests and laboratory scale experiments show that these oscillations can usually be stabilized by making small changes to the system. The complication is that, while there is often just one unstable natural oscillation (eigenmode), there are many possible changes to the system. The challenge is to identify the optimal change systematically, cheaply, and accurately. This paper shows how to evaluate the sensitivities of a thermoacoustic eigenmode to all possible system changes with a single calculation by applying adjoint methods to a thermoacoustic Helmholtz solver. These sensitivities are calculated here with finite-difference and finite-element methods, in the weak form and the strong form, with the discrete adjoint and the continuous adjoint, and with a Newton method applied to a nonlinear eigenvalue problem and an iterative method applied to a linear eigenvalue problem. This is a detailed comparison of adjoint methods applied to thermoacoustic Helmholtz solvers. matlab codes are provided for all methods and all figures so that the techniques can be easily applied and tested. This paper explains why the finite difference of the strong form equations with replacement boundary conditions should be avoided and why all of the other methods work well. Of the other methods, the discrete adjoint of the weak form equations is the easiest method to implement; it can use any discretization and the boundary conditions are straightforward. The continuous adjoint is relatively easy to implement but requires careful attention to boundary conditions. The summation by parts finite difference of the strong form equations with a simultaneous approximation term for the boundary conditions is more challenging to implement, particularly at high order or on nonuniform grids. Physical interpretation of these results shows that the well-known Rayleigh criterion should be revised for a linear analysis. This criterion states that thermoacoustic oscillations will grow if heat release rate oscillations are sufficiently in phase with pressure oscillations. In fact, the criterion should contain the adjoint pressure rather than the pressure. In self-adjoint systems the two are equivalent. In non-self-adjoint systems, such as all but a special case of thermoacoustic systems, the two are different. Finally, the sensitivities of the growth rate of oscillations to placement of a hot or cold mesh are calculated, simply by multiplying the feedback sensitivities by a number. These sensitivities are compared successfully with experimental results. With the same technique, the influence of the viscous and thermal acoustic boundary layers is found to be negligible, while the influence of a Helmholtz resonator is found, as expected, to be considerable.

Steady-state thermal counterflow of superfluid ${}^4\mathrm{He}$ (He II) is experimentally investigated in a channel of square cross section, with a planar heater placed at its bottom. We focus on the flow region close to the heat source, which has received little attention to date. Relatively small particles of solid deuterium hydride, having a density comparable to that of He II, are suspended in the liquid and their flow-induced dynamics is studied by using the particle tracking velocimetry technique. The comparison with results obtained in similar conditions with solid deuterium particles, which are about 1.4 times denser than He II, confirms that, in the heater proximity, the mean distance between quantized vortices, representing the characteristic length scale of the flow, appears to be about one order of magnitude smaller than that expected in the bulk, at the same temperature and applied heat flux. Additionally, we find that the lighter particles seem to experience a slightly denser vortex tangle, supporting therefore the view that heavy particles tend to stay trapped on quantized vortices for longer times than light ones. In the range of investigated parameters, the heavier particles consequently appear to be more suitable to probe the occurrence of vortex reconnections, deemed to be crucial in explaining energy dissipation mechanisms in quantum flows.

Rotationally symmetric systems can exhibit acoustic fluctuations in the azimuthal direction. In experimental works the nature (standing or spinning) of these fluctuations is often described by a set of indicators. These indicators either depend on the chosen frame of reference or are not state space variables for the acoustic field. Conversely, in theoretical works the field is projected on two orthogonal modes, and the system is characterized in terms of two amplitudes and one phase difference. Also in these works the nature of the field is not a state space variable but a derived quantity. Moreover the phase difference between the two modes is undetermined when one of the amplitudes of the two modes is zero, making the phase space ill-posed. We present a solution to these limitations, and we show how the acoustic field can be embedded in quaternion algebra, by calculating a suitable analytic signal of the complex-valued embedding of the acoustic field. This allows us to map the state of the system to a point that moves as function of time on a two-dimensional sphere in three-dimensional (3D) space, the Poincaré-Bloch sphere. To each state of the system corresponds just one point in this 3D space, which is then a well-posed phase space. We term the spherical coordinates of the point the amplitude of oscillation, the nature angle, and the orientation angle. The amplitude of oscillation of the system is the radius of the sphere. The nature angle is the latitude angle and positions the point closer to the equator (pure standing mode states) or closer to the poles (pure spinning mode states). The orientation angle is the longitude angle and describes the position of the pressure antinodes of the part of the acoustic field that is standing. These coordinates have a straightforward physical interpretation, can be easily calculated from experimental data, and are at the same time state space variables of a simple and elegant ansatz that can be used in low-order models. We also present an example of characterization of an experimental azimuthal thermoacoustic instability.

We study the stability of dilute suspensions of spheroids in Taylor Couette flow. We focus on axisymmetric perturbations and on the limiting cases of thin disks and long rods. It is found that in the non-Brownian limit, the rods have a negligible effect on the stability, while the disks are destabilizing. The instability is driven by a tilting of the disks, which draws energy from the base flow into azimuthal velocity fluctuations. The resulting instability mode has a wavelength which is smaller than the unstable Newtonian mode. These findings may serve to understand experiments using clay suspensions in the literature.

We present a design and experimental study of microfluidic converging nozzles which creates a stable liquid sheet jet. The sheet jets formed by the nozzles can be varied between order 10 μm to submicron thicknesses (a measured minimum thickness of 560 nm). A parametric study of the jet structure was performed including 51-fold variation of Reynolds number, 20-fold variation of Weber number, 89-fold variation of capillary number, and 12-fold variation of nozzle exit aspect ratio. These studies benefited from variation of working liquids, nozzle geometry, 10-fold variation of flow rate, and 7.1-fold variation of key length scales. Navier-Stokes simulations of internal fluid flow were also performed to identify key physical phenomena. These studies were used to propose and test physical scaling theories for jet thickness, length, and width of the primary sheet. The scaling theories are also informed by classic studies of colliding jets with similar flow structures. For sheet thickness, we present two scaling approaches: one relying on internal fluid flow calculations and the other based solely on nozzle geometry. For sheet length and width, scaling theories are presented based on the nozzle geometry and essential dimensionless flow parameters. The scalings do not require numerical simulation of external flow and exhibit efficient collapse across the parameter space. Together, the fabrication method and scaling theories provide a clear path to the rapid and efficient design of liquid sheet jets.

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section, if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the force coupling method was used to numerically investigate the inertia-induced particle alignment, using square-channel geometry. The method was first shown to be suitable to capture the quasisteady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise interparticle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square-channel flow [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. The new result highlighted by our numerical simulations is that the interparticle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is $\approx 1$ and the particle-to-channel height size ratio is $\approx 0.1$, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. It is argued that when several particles are hydrodynamically connected moving as a unique structure (the train) with a steady streamwise velocity, large-scale hydrodynamic perturbations induced at the train scale prohibit small-scale vortex connection between the leading and second particles, forcing the leading particle to leave the train.

The reconstruction of the Reynolds stress from data provided by a large-eddy simulation (LES) is commonly based on the assumption that the statistical average of the filtered LES quantities is the same as that of the unfiltered ones. As such, the Reynolds stress is given by the sum of the resolved stress associated with the large-eddy simulation and the mean subfilter scale and subgrid scale stresses. In this paper LES is considered from a purely mathematical point of view corresponding to a convolution operation applied to the Navier-Stokes equations, thus solely with subfilter scale stresses. In this context we derive and test an exact relation between the Reynolds stress and the resolved stress in order to quantify exactly the possible effect of the interference between the mean and the subfilter scale. A resolution criterion that should reinforce the independence of the scales is proposed and it is shown that the interference effect could have some relevance if the resolution is inadequate.

Recent work has explored linear internal wave transmission and reflection across a density staircase. Here, weakly nonlinear theory is used to extend previous linear internal wave solutions to include nonlinear effects at density interfaces within the staircase. Near-resonant forcing of freely propagating modes of the staircase by weakly nonlinear incident internal waves is shown to occur for some wavelength-frequency combinations. In some cases, this results in the staircase radiating double-frequency, double-wave-number harmonic waves. In others, incident waves excite one or more interfacial waves which propagate along the density interfaces within the staircase. This nonlinear effect is expected to be significant for internal waves of realistic amplitude incident on oceanic thermohaline staircases.

A laboratory investigation using three-dimensional particle tracking velocimetry is performed to uncover the distinctive Lagrangian dynamics of turbulent Rayleigh-Bénard convection at aspect ratios $\mathrm{\Gamma }=1.2$ and 2, where emphasis is placed on the Lagrangian statistics of thermal plumes. A laterally extended investigation volume allowed us to capture the dynamics of the relatively high vertical motion. Approximately $3.5\times {10}^7$ events were analyzed at Rayleigh numbers of $\text{Ra}\approx 1.1\times {10}^{10}$ for $\mathrm{\Gamma }=1.2$ and $\text{Ra}\approx 2.8\times {10}^9$ for $\mathrm{\Gamma }=2$. The probability density functions (PDFs) of the vertical Lagrangian acceleration exhibited heavier tails compared with the lateral counterpart away from the near-wall boundary layer, which evidenced higher Lagrangian intermittency in the vertical direction. The second-order, conditional acceleration PDFs with various vertical-velocity magnitude thresholds indicate that the intense vortical motion promotes stronger vertical acceleration with respect to the lateral. A comparison with previous works reveals the influence of roll dynamics induced by $\mathrm{\Gamma }$ on the distribution of the vertical acceleration. The pair dispersion is explored and showed $t^2$ behavior under the local Kolmogorov timescale (${\tau }_{\eta }$) for both aspect ratios, with some departure at scales sufficiently lower than ${\tau }_{\eta }$.

This experimental in vitro work investigates material transport properties in a model left ventricle in the case of aortic regurgitation, a valvular disease characterized by a leaking aortic valve and consequently double-jet filling within the elastic left ventricular geometry. This study suggests that material transport phenomena are strongly determined by the motion of the counterrotating vortices driven by the regurgitant aortic and mitral jets. The overall particle residence time appears to be significantly longer with moderate aortic regurgitation, attributed to the dynamics resulting from the timing between the onset of the two jets. Increasing regurgitation severity is shown to be associated with higher frequencies in the time-frequency spectra of the velocity signals at various points in the flow, suggesting nonlaminar mixing past moderate regurgitation. Additionally, a large part of the regurgitant inflow is retained for at least one cardiac cycle. Such an increase in particle residence time accompanied by the occurrence and persistence of a number of attracting Lagrangian coherent structures presents favorable conditions and locations for activated platelets to agglomerate within the left ventricle, potentially posing an additional risk factor for patients with aortic regurgitation.

We simulate the isothermal, incompressible, time-dependent flow of Boger fluids, using the FENE-CR constitutive model, in the optimized shape cross-slot extensional rheometer [Haward et al., Phys. Rev. Lett. 109, 128301 (2012)]. We uncover a family of predominantly elastic instabilities resulting from the interaction of stationary asymmetric and time-dependent flow transitions. The superposition of these instabilities, with varying degrees of relative amplitude, produces five distinct flow regimes which are classified by their elasticity, suggesting that the dynamic system is situated in the vicinity of a triple point in the inertia-elasticity-viscosity parameter space. A detailed characterization of the various associated modes of instability is provided. Spectral analysis of the first component of the velocity vector suggests that the flow regimes featuring loss of birefringence strand integrity become chaotic and locally turbulent near the center of the cross-slot, above a certain flow rate threshold.

Longitudinal velocity-derivative skewness $S_0$ is directly proportional to the rate of enstrophy generation and hence is a key parameter for characterizing small-scale turbulence. Obtaining $S_0$ requires accurate measurements of the finest scales in the dissipation subrange. In this paper we define a derivative skewness of the inertial range scales that is readily accessible experimentally, and we derive its value analytically. The results depend on the filtering procedure of small scales. Analytically derived inertial range skewness is compared with those computed by high-resolution numerical simulations and obtained in laboratory and field experiments. An alternative definition of the derivative skewness in the full and the inertial range scales is examined to identify the effects of intermittency.

We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr $=0.7$, a Rayleigh number Ra $={10}^5$, and an aspect ratio $\mathrm{\Gamma }=16$ is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem et al. [Phys. Rev. E 93, 063107 (2016)], builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent $k$-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times ${\tau }^L$ and lengths ${\lambda }_U^L$ of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, $\tau$ and ${\lambda }_U$, respectively. This trajectory-based clustering is found to work for times $t\lesssim \tau \approx {\tau }^L$. Longer time periods $t\gtrsim {\tau }^L$ require a change of the analysis method to a density-based trajectory clustering by means of time-averaged Lagrangian pseudotrajectories, which is applied in this context for the first time. A small coherent subset of the pseudotrajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.

Lock-exchange suspension gravity current in a tilted narrow pipe is studied experimentally at very low Reynolds numbers. We investigate the interpenetration of a heavy particle-laden fluid on top of a light pure fluid by considering the effects of the initial volume fraction of particles ${\varphi }_0$ and inclination angle of the pipe from vertical $\beta$. Density mismatch between heavy and light phases is maintained low (Boussinesq limit) to allow a stable quasiparallel viscous flow. Pertaining to whether particles stay mixed in the suspension or sediment, three distinct mixing, transitionary, and sedimentary regimes are identified. Results of the classification over a wide range of particle concentration ${\varphi }_0\in \left[0.05,0.50\right]$ and inclination angle $\beta \in \left[0^{\circ },{88}^{\circ }\right]$ are proposed in dimensionless phase diagrams suitable for industrial calculations. Mixing behavior emerges at sharp inclinations as flow continues steadily along the pipe. Sedimentary behavior is attributed to the decelerating flows that involve dilute or packed suspensions over nearly horizontal angles. To quantify the interpenetration rate, a scaling analysis is performed to approximate the velocity of the particle-laden front for different values of ${\varphi }_0$ and $\beta$. Furthermore, the impacts of the fluid's viscosity and particle size are investigated in detail. Reducing the particle size generally weakens the sedimentary behavior of the flow. Increasing the liquid's viscosity has almost no effect on regime transition, yet it results in slower advancing speed across all tilt angles.

We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave background. Such a coexistence is expected by the integrable turbulence theory for the nonlinear Schrödinger equation (NLSE), and we report the first experimental observation in the context of hydrodynamic waves. We characterize the formation, the properties, and the dynamics of these nonlinear coherent structures (solitons and extreme events) within the incoherent wave background. The extreme events result from the strong steepening of wave train fronts, and their emergence occurs after roughly one nonlinear length scale of propagation (estimated from the NLSE). Solitons arise when nonlinearity and dispersion are weak, and of the same order of magnitude as expected from the NLSE. We characterize the statistical properties of this state. The number of solitons and extreme events is found to increase all along the propagation, the wave-field distribution has a heavy tail, and the surface elevation spectrum is found to scale as a frequency power law with an exponent $-4.5\pm 0.5$. Most of these observations are compatible with the integrable turbulence theory for the NLSE although some deviations (e.g., power-law spectrum, asymmetrical extreme events) result from effects proper to hydrodynamic waves.

We present complementary numerical and asymptotic studies of the flow over a heated, semi-infinite flat plate for a fluid with temperature-dependent viscosity. Liquid-type viscosities are found to entrain both the velocity and temperature profiles closer to the plate with increasing temperature sensitivity; gas-type viscosities are found to exhibit the reverse effect. A linear stability analysis is presented and we find that increasing the temperature dependence of the fluid (from gas- to liquid-type behavior) results in an increased critical Reynolds number to a point of maximum stability. Using an energy-balance approach, we determine that this behavior is primarily driven by the inviscid instability of the modified steady flow, rather than being a result of modified viscous instability effects. Application and extension of the results are considered in the context of chemical vapor deposition.

We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles ($\beta =-{15}^{\circ }$, $-{30}^{\circ }$, and $-{45}^{\circ }$, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of $\text{Ka}=13.1$ and 330), and flow Reynolds numbers covering the range $\text{Re}=0.6–193$. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about $40\mathrm{mm}$ symmetrically on either side the centerline of the film span ($80\mathrm{mm}$ in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number $\text{Ka}(=13.1)$ flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid $\text{Ka}(=330)$ flows, rivulets were observed typically above $\text{Re}\approx 30,$ depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with increasing Re, reaching a maximum that shifted to higher Re at larger inclinations. Furthermore, in flows that displayed pronounced rivulet formation [i.e., large (negative) $\beta$ and higher Re], the local film-height standard deviation in regions corresponding to the rivulet crests and troughs was reduced compared to the film-height standard deviation calculated over the entire examined film region. The mean rivulet wavelength also increased at larger inclinations, peaking at 26 mm when $\text{Ka}=330$. Based on our experimental results and theoretical arguments, we hypothesize that the formation of rivulets can be attributed, at small $\beta$, to a secondary Rayleigh-Taylor instability mechanism that destabilizes the suspended two-dimensional wavefronts, and at larger $\beta$, to the primary Rayleigh-Taylor instability mechanism of a flat film coating the underside of the inclined plate.

Single-point turbulence statistics are compared in the roughness sublayer (RSL) of turbulent open-channel flows over smooth wall and wall roughness with different textures using direct numerical simulations (DNS). The goal is to identify how the range of scales contained in a roughness topography affects the drag generation, momentum transfer, and energy balance. The presence of large surface wavelengths is shown to reduce the overall surface slope, leading to a sparser distribution of roughness-wake regions. This may provide a physical explanation why a wider scale surface tends to produce lower friction coefficient and higher Reynolds stress anisotropy as observed previously. In addition, despite recent observations of negligible form-induced turbulent kinetic energy (TKE) productions over narrow-scale surface such as sand grains and gravel bed, it is shown that these productions can be significant over a multiscale surface. We also identify several factors crucial for these productions; they include the roughness drag coefficient, the roughness geometry function, and both micro- and macroscopic surface scales.