The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F0 at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F0, for all t satisfying the inequalities vt Lt; r2 and F0t2 [Lt ] 4πρr4. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λm, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v½/2λmt½, where λm = λm(F0) decreases as F0 increases. The larger F0 is the faster the steady state is established.

We have experimentally examined the effects of a common soluble surfactant on gas bubbles in liquid flows in inclined tubes. Air bubbles of known size (λ = 0.8, 1.0, 1.5) are held stationary under minimum flow conditions in tubes inclined at fixed angles (ω = 25°, 45°, 65°, 90°). Sodium dodecyl sulphate (SDS) is infused into the bulk flow at two bulk concentrations (C = 10% or 100% critical micelle concentration (CMC)). In addition to recording pressure and flow waveforms, we capture video images of bubbles before and during exposure to the surfactant. Modification of the interfacial properties by the surfactant results in extremely dynamic bubble behaviour including interfacial deformation, deformation plus axial translation, and bubble detachment from the wall plus translation. We measure the corresponding time-dependent pressure gradient within the tube. The surfactant mediated responses observed are dependent upon the interrelated effects of C, λ and ω. A high bulk concentration of surfactant may produce more rapid modification of bubble shape and influence wetting, thus increasing the potential for bubble detachment. The likelihood that detachment will occur increases further as bubble volume in increased. In both vertical tubes in which contact forces are absent and in non-vertical tubes, the infusion of surfactant may result in axial translation either in the direction of, or opposite to, the direction of the bulk flow. Critical to the translation and/or detachment of the bubble is the surfactant-mediated modification of contact line mechanics. Contact line velocities corresponding to rates of shrinkage of dewetted surface area are extracted from experimental data. We also explore the potential effects of surfactants on interfacial remobilization. This investigation demonstrates the potential use of surfactants to be used for dislodging dewetted gas bubbles by the intentional manipulation of interfacial properties.

When two species A and B are introduced through different parts of the bounding surface into a region of turbulent flow, molecules of A and B are brought together by the combined actions of the turbulent velocity field and molecular diffusion. A random flight model is developed to simulate the relative motion of pairs of fluid elements and random motions of the molecules, based on the models of Durbin (1980) and Sawford & Hunt (1986). The model is used to estimate the cross-correlation between fluctuating concentrations of A and B, $\overline{c_Ac_B}$, at a point, in non-premixed homogeneous turbulence with a moderately fast or slow second-order chemical reaction. The correlation indicates the effects of turbulent and molecular mixing on the mean chemical reaction rate, and it is commonly expressed as the ‘segregation’ or ‘unmixedness’ parameter $\alpha(=\overline{c_Ac_B}/\overline{C}_A\overline{C}_B) $ when normalized by the mean concentrations $\overline{C}_A$ and $\overline{C}_B$. It is found that α increases from near −1 to zero with the time (or distance) from the moment (or location) of release of two species in high-Reynolds-number flow. Also, the model (and experiments) agrees with the exact results of Danckwerts (1952) that $\overline{c_Ac_B}/(\overline{c^2_A}\overline{c^2_B})^{\frac{1}{2}} = -1$ for mixing without reaction. The model is then extended to account for the effects on the segregation parameter α of chemical reactions between A and B. This leads to α eventually decreasing, depending on the relative timescales for turbulent mixing and for chemical reaction (i.e. the Damköhler number). The model also indicates how a number of other parameters such as the turbulent scales, the Schmidt number, the ratio of initial concentrations of two reactants and the mean shear affect the segregation parameter α.

The model explains the measurements of α in previously published studies by ourselves and other authors, for mixing with and without reactions, provided that the reaction rate is not very fast. Also the model is only strictly applicable for a limited mixing time t, such that t [lsim ] TL where TL is the Lagrangian timescale, because the model requires that the interface between A and B is effectively continuous and thin, even if highly convoluted. Flow visualization results are presented, which are consistent with the physical idea underlying the two-particle model.

Streaks in pre-transitional boundary layers are analysed and their properties are extracted from direct numerical simulation data. Streaks that induce breakdown to turbulence via secondary instability are shown to differ from the remainder of the population in various attributes. Conditionally averaged flow fields establish that they are situated farther away from the wall, and have a larger cross-sectional area and higher peak amplitude. The analysis also shows that the momentum thickness acts as a similarity parameter for the properties of the streaks. Probability density functions of the streak amplitude, area, and shear along the streaks, collapse among the various pressure gradients when plotted as a function of the momentum thickness. A prediction scheme for laminar–turbulent transition based on artificial neural networks is presented, which can identify the streaks that will eventually induce the formation of turbulent spots. In comparison to linear stability theory, the approach achieves a higher prediction accuracy at considerably lower computational cost.

A tethered cylinder may be considered an extension of the widely studied problem of a hydro-elastically mounted cylinder. Here we numerically investigate the flow past a positively buoyant tethered cylinder for a range of mass ratios and tether length ratios at a Reynolds number Re = 200. The results are found to be qualitatively similar to related experimental work performed at significantly higher Reynolds numbers. Two important findings are related in this paper. First, we find that the action of the tethered cylinder oscillating at an angle to the flow induces a mean lift coefficient. Second, a critical mass ratio (m*crit) is found below which large-amplitude oscillations are noted, similar to that previously reported for the case of a hydro-elastically mounted cylinder. For short tether lengths, (m*crit) is significantly greater than that found for a hydro-elastically mounted cylinder. As the tether length increases, the (m*crit) decreases and asymptotes to that of a hydro-elastically mounted cylinder as the tether length approaches infinity.

Two-dimensional incompressible and heterogeneous free jets are studied numerically. They are characterized by two linearly unstable modes: the sinuous mode and the varicose mode. When the density is constant, the sinuous mode dominates, in a sense that it has a maximum growth rate nearly three times greater than that of the varicose mode, both in the temporal and spatial stability frameworks. This suggests that jet evolution at the linear and nonlinear regimes, at least at early stage, would be sinuous with the frequency and wavenumber of the most unstable mode. This is confirmed in the present work. When the jet density is decreased, it is found that the varicose mode growth rate is enhanced and its maximum value can exceed that of the sinuous mode. Furthermore, in the spatial case, only the varicose mode is subject to a convective/absolute instability transition. It is shown, however, that the maximum varicose growth rate exceeds that of the sinuous mode before the transition occurs. Therefore, a natural question is: does the convective/absolute transition dictate its frequency to the nonlinear evolution of the jet, leading to a global oscillating varicose mode, or is it, simply, the frequency of the maximum varicose growth rate that does? The main part of this paper is devoted to answering this question by direct numerical simulation for a wide range of jet-exit to ambient density ratios.

Steady two-dimensional flows past a parabolic obstacle lying on the free surface in water of finite depth are considered. The fluid is treated as inviscid and incompressible and the flow is assumed to be irrotational. Gravity is included in the free-surface condition. The problem is solved numerically by using boundary integral equation techniques. It is shown that there are solutions for which the flow is supercritical both upstream and downstream and others for which the flow is subcritical both upstream and downstream. These flows have continuous tangents at both ends of the obstacle at which separation occurs. For supercritical flows, there are up to three solutions corresponding to the same value of the Froude number when the obstacle is concave and up to two solutions when the obstacle is convex. For subcritical flows, there are solutions with waves behind the obstacle. As the Froude number decreases, these waves become steeper and the numerical calculations suggest that they, ultimately, reach limiting configurations with a sharp crest forming a 120° angle.

A normalized formulation of the problem of isothermal bubble growth, dominated by viscosity and diffusion, reveals that in its full generality the problem involves eight dimensionless parameters. Limiting cases for extreme values of each of these parameters are investigated.

The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet (J. Fluid Mech., vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing.

In this paper we develop an integral model for an unsteady turbulent jet that incorporates longitudinal dispersion of two distinct types. The model accounts for the difference in the rate at which momentum and energy are advected (type I dispersion) and for the local deformation of velocity profiles that occurs in the vicinity of a sudden change in the momentum flux (type II dispersion). We adapt the description of dispersion in pipe flow by Taylor (Proc. R. Soc. Lond. A, vol. 219, 1953, pp. 186–203) to develop a dispersion closure for the longitudinal transportation of energy in unsteady jets. We compare our model’s predictions to results from direct numerical simulation and find a good agreement. The model described in this paper is robust and can be solved numerically using a simple central differencing scheme. Using the assumption that the longitudinal velocity profile in a jet has an approximately Gaussian form, we show that unsteady jets remain approximately straight-sided when their source area is fixed. Straight-sidedness provides an algebraic means of reducing the order of the governing equations and leads to a simple advection–dispersion relation. The physical process responsible for straight-sidedness is type I dispersion, which, in addition to determining the local response of the area of the jet, determines the growth rate of source perturbations. In this regard the Gaussian profile has the special feature of ensuring straight-sidedness and being insensitive to source perturbations. Profiles that are more peaked than the Gaussian profile attenuate perturbations and, following an increase (decrease) in the source momentum flux, lead to a local decrease (increase) in the area of the jet. Conversely, profiles that are flatter than the Gaussian amplify perturbations and lead to a local increase (decrease) in the area of the jet.