Direct numerical simulation of the incompressible Navier–Stokes equations is used to study flows where laminar boundary-layer separation is followed by turbulent reattachment forming a closed region known as a laminar separation bubble. In the simulations a laminar boundary layer is forced to separate by the action of a suction profile applied as the upper boundary condition. The separated shear layer undergoes transition via oblique modes and Λ-vortex-induced breakdown and reattaches as turbulent flow, slowly recovering to an equilibrium turbulent boundary layer. Compared with classical experiments the computed bubbles may be classified as ‘short’, as the external potential flow is only affected in the immediate vicinity of the bubble. Near reattachment budgets of turbulence kinetic energy are dominated by turbulence events away from the wall. Characteristics of near-wall turbulence only develop several bubble lengths downstream of reattachment. Comparisons are made with two-dimensional simulations which fail to capture many of the detailed features of the full three-dimensional simulations. Stability characteristics of mean flow profiles are computed in the separated flow region for a family of velocity profiles generated using simulation data. Absolute instability is shown to require reverse flows of the order of 15–20%. The three-dimensional bubbles with turbulent reattachment have maximum reverse flows of less than 8% and it is concluded that for these bubbles the basic instability is convective in nature.

We investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream. The very near wake (up to three diameters) is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio. We perform systematic spectral direct (DNS) and large-eddy simulations (LES) at Reynolds number (Re) between 500 and 5000 with resolution ranging from 200 000 to 100 000 000 degrees of freedom. In this paper, we analyse in detail results at Re = 3900 and compare them to several sets of experiments. Two converged states emerge that correspond to a U-shape and a V-shape mean velocity profile at about one diameter behind the cylinder. This finding is consistent with the experimental data and other published LES. Farther downstream, the flow is dominated by the vortex shedding dynamics and is not as sensitive to the aforementioned factors. We also examine the development of a turbulent state and the inertial subrange of the corresponding energy spectrum in the near wake. We find that an inertial range exists that spans more than half a decade of wavenumber, in agreement with the experimental results. In contrast, very low-resolution spectral simulation as well as other dissipative LES do not describe accurately the inertial range although they predict low-order statistics relatively accurately. This finding is analysed in the context of coherent structures using a phase averaging technique and a procedure to extract the most energetic (on the average) eigenmodes of the flow. The results suggest that a dynamical model would require of the order of twenty modes to describe the vortex shedding dynamics with reasonable accuracy.

Numerical simulations with a non-hydrostatic anelastic model are carried out to reproduce hydraulic tank experiments on stratified flow past a two-dimensional mountain ridge, for a Froude number of 0.6 and a Reynolds number of 200. The gravity wave thus generated steepens, overturns and breaks. Numerical simulations and experiments are directly compared showing close agreement. Ground friction is found to have a major influence. It induces a boundary-layer separation on the lee slope of the mountain and a low-level trapped lee wave inhibiting the downstream propagation of the breaking region above. Consequently, the three-dimensional vortices generated within the unstable two-dimensional overturning wave have a toroidal shape in agreement with experimental observations. Sensitivity to the shape of the initial three-dimensional perturbation is studied. In the case of harmonic disturbances, spectral analysis reveals that during the growth phase of the instability, harmonics are coherently produced by the nonlinear transverse advection term. During the later phase of quasi-steady turbulence, the vortices have a morphology that does not depend on the type of the initial perturbation.

Pulsed-wire measurements of the streamwise mean velocity and Reynolds stress, mean and fluctuating surface shear stress, and other statistics have been made in a sharp- edged turbulent separation bubble formed behind a normal flat plate mounted on the front of a long splitter plate, covering nearly a decade range of low Reynolds number. The streamwise Reynolds stress increases appreciably with Reynolds number, from a level comparable with that in an isolated plane mixing layer to more than twice that level, while the change in the mean flow is at most slight. It is inferred using previous measurements that the other stresses do not change as much, thereby leaving the mean flow relatively unaffected. The mean wall shear stress and the r.m.s. of the (streamwise) fluctuations decrease in fixed proportion with increasing Reynolds number. Normalized p.d.f. distributions of velocity and wall shear stress do not change, except in the vicinity of the secondary separation bubble. At low Reynolds number the development length of the overlying mixing layer is an appreciable proportion of the bubble length, the development length being a function of the momentum thickness at separation. It is argued that the observed changes with Reynolds number in the bulk of the flow arise primarily as a result of a change in response of this layer to the fluctuating rates of strain imposed by the recirculating flow; at a low Reynolds number the response of the shear layer structures to the fluctuating rates of strain is less than it is at a high Reynolds number. As a consequence of the sensitivity to fluctuating strain rates the structure of the layer differs fundamentally from that of an isolated mixing layer.

The measurements help to reconcile previous measurements in this flow geometry which otherwise appear to be inconsistent. Moreover, in most of the previous measurements the flow width was not sufficient for end effects to have been negligible, most noticeably in the near-wall flow, where such effects are largest.

We develop a Lagrangian model of both one-particleIn this paper ‘particle’ and ‘fluid element’ are synonymous. and two-particle turbulent diffusion in high Reynolds number and low Froude number stably stratified non- decaying turbulence. This model is a kinematic simulation (KS) that obeys both the linearized Boussinesq equations and incompressibility. Hence, turbulent diffusion is anisotropic and is studied in all three directions concurrently with incompressibility satisfied at the level of each and every trajectory.

Horizontal one-particle and two-particle diffusions are found to be independent of the buoyancy (Brünt–Väissälä) frequency N. For one-particle diffusion we find that

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and

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where i = 1,2 and u′ and L are a r.m.s. velocity and a length-scale of the energy-containing motions respectively, and

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This capping of one-particle vertical diffusion requires the consideration of the entire three-dimensional flow, and we show that each and every trajectory is vertically bounded for all times if the Lagrangian vertical pressure acceleration a3 is bounded for all times. Such an upper bound for a3 can be derived from the linearized Boussinesq equations as a consequence of the coupling between vertical pressure acceleration and the horizontal and vertical velocities.

Two-particle vertical diffusion exhibits two plateaux. The first plateau's scaling is different according to whether the initial separation Δ0 between the two particles is larger or smaller than η, the smallest length-scale of the turbulence:

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The second plateau is reached when the two particles become statistically independent, and therefore

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The transition between the two plateaux coincides with the time when the two particles start moving significantly apart in the horizontal plane.

Three-dimensional dilational and sinuous wave propagation on infinite or semi- infinite thin planar sheets flowing into a gas of negligible density is investigated. The assumption of thin sheets allows the reduction of the problem dimensionality by integration across the sheet thickness. For finite-amplitude disturbances, the strongest nonlinear effects occur when the cross-sectional wavenumber (l) is close to the streamwise wavenumber (k). First, dilational wave propagation is considered. When l is close to k for infinite sheets, higher harmonics are generated in the streamwise direction, and the standing wave with finite amplitude in the cross-sectional plane becomes at. As time passes, the waves return to the initial wave shape. This process is repeated in a cycle. A similar phenomenon is found in semi-infinite sheets with low Weber number. When l is close to k for semi-infinite sheets and Weber number is high, fluid accumulates into fluid lumps interspaced by one wavelength in the cross- sectional direction as well as in the streamwise direction. This leads to the formation of initially non-spherical ligaments or large droplets from the liquid sheet. Secondly, sinuous wave propagation is considered. When l is close to k for semi-infinite sheets and Weber number is high, fluid agglomerates in the edge of the sheet interspaced by half a wavelength in the cross-sectional direction as well as in the streamwise direction. A three-dimensional visualization of the computational results shows that the disturbance at the nozzle exit induces fluid to agglomerate into half-spherical lumps, which indicate the formation of ligaments or large droplets from the liquid sheet. A similar phenomenon is found in the case of infinite sheets.

Thread injection is a promising method for different minimally invasive medical applications. This paper documents an experimental study dealing with an axially moving thread in annular pipe flow. Mass flow and axial force on the thread are measured for a 0.46 mm diameter thread in pipes with diameters between 0.55 and 1.35 mm. The experiments with thread velocities of up to 1.5 ms−1 confirm the findings of theoretical studies that for clinical requirements the radius ratio between thread and pipe is crucial for the adjustments of mass ow and force on the thread.

In both regimes, laminar and turbulent flow, the thread shows a characteristic oscillatory behaviour without touching the pipe wall. Resonance-like oscillations indicate circular thread motions around the pipe centre. The oscillating eccentricities may arise from longitudinal inhomogeneities of the thread shape and flow disturbances which cause non-stationary lateral momenta. According to established findings on annular flow with eccentric cylinders we assume that the mass flow, which is high compared to the concentric model, is caused by the temporary thread eccentricities. These findings should be considered in clinical applications to avoid possible thread blockage due to resonance-like vibrations.

Results are reported of thermocapillary flow experiments performed aboard the Spacelab. Oscillatory thermocapillary flows were investigated in open cylindrical containers filled with 2 cS kinematic viscosity (Prandtl number = 27 at 25 °C) silicone oil. The fluid was heated by a cylindrical cartridge heater placed at the symmetry axis of the container while the container sidewall was maintained at a lower temperature. Test containers with three different diameters of 1.2, 2.0 and 3.0 cm were used. The ratio of heater to test container diameter was fixed at 0.1. The liquid free-surface shape was either flat or concave. The flow and temperature fields were investigated for steady and oscillatory flows. Free-surface deformation was observed during oscillations. The conditions for the onset of oscillatory flow were determined. It is shown that the Marangoni number alone does not correlate the onset conditions. A new parameter, which represents free surface deformation, is derived for flat free surfaces and is shown to correlate the onset conditions well. Infrared images of free surface and oscillation frequencies are also presented.

We present numerical solutions of a two-dimensional inviscid Burgers equation which provides an asymptotic description of the Mach reflection of weak shocks. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley for steady weak-shock reflection. A theoretical analysis indicates that there is an expansion fan at the triple point, in addition to the three shocks. The supersonic patch is extremely small, and this work is the first time it has been resolved.

Processing the data from a large variety of zero-pressure-gradient boundary layer flows shows that the Reynolds-number-dependent scaling law, which the present authors obtained earlier for pipes, gives an accurate description of the velocity distribution in a self-similar intermediate region adjacent to the viscous sublayer next to the wall. The appropriate length scale that enters the definition of the boundary layer Reynolds number is found for all the flows under investigation.

Another intermediate self-similar region between the free stream and the first intermediate region is found under conditions of weak free-stream turbulence. The effects of turbulence in the free stream and of wall roughness are assessed, and conclusions are drawn.

Two-dimensional thermal convection in the presence of a strong oblique magnetic field is studied using an asymptotic expansion in inverse powers of the Chandrasekhar number. The linear stability problem reveals the existence of two distinct scales in the vertical structure of the critical eigenfunctions: a small length-scale whose vertical wavenumber kz is comparable with the large horizontal wavenumber k⊥ selected at onset, and a large-scale modulation which forms an envelope on the order of the layer depth d. The small-scale structure in the vertical results from magnetic alignment that forces fluid motions to be (nearly) parallel to the field lines. For convective transport in the vertical this constraint must be relaxed. This is achieved by molecular dissipation which allows weak upward (downward) motions of hot (cold) fluid elements across the field lines and results in a large-scale vertical modulation of the magnetic columns. Using the scaling suggested by the linear theory, strongly nonlinear steady and overstable solutions are constructed. These are characterized by large departures of the mean temperature profile from the conduction profile. For overstable rolls two modes of convection are uncovered. The first ‘vertical field’ mode is characterized by thin thermal boundary layers and a Nusselt number that increases rapidly with the applied Rayleigh number; this mode is typical of steady convection as well. The second or ‘horizontal field’ mode is present in overstable convection only and has broad thermal boundary layers and a Nusselt number that remains small and approximately independent of the Rayleigh number. At large Rayleigh numbers this regime is characterized by a piecewise linear temperature profile with a small isothermal core. The ‘horizontal field’ mode is favoured for substantial inclinations of the field and sufficiently small ohmic diffusivity. The transition between the two regimes is typically hysteretic and for fixed inclination and diffusivity may occur with increasing Rayleigh number. Similar but highly asymmetric states are obtained for depth-dependent ζ, where ζ is the ratio of ohmic to thermal diffusivity. These results are obtained from a nonlinear eigenvalue problem for the Nusselt number and mean temperature profile, and suggest a possible explanation for the sharp boundary between the umbra and penumbra in sunspots.

Motivated by our interest in unsteady aerodynamics of insect flight, we devise a computational tool to solve the Navier–Stokes equation around a two-dimensional moving wing, which mimics biological locomotion. The focus of the present work is frequency selection in forward flapping flight. We investigate the time scales associated with the shedding of the trailing- and leading-edge vortices, as well as the corresponding time-dependent forces. We present a generic mechanism of the frequency selection as a result of unsteady aerodynamics.

High-resolution DPIV and LDV measurements were made in a turbulent mixed- boundary corner, i.e. a turbulent boundary layer generated by horizontal flow of water along a vertical wall in the vicinity of a horizontal free surface. This work is an extension of an earlier numerical/experimental study which established the existence of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak, slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. The objective of the current investigation, then, was to understand the combined effects of a horizontal, shear-free, free surface and a vertical, rigid, no-slip boundary on turbulent kinetic energy transport. The context of this work is providing physical insights and quantitative data for advancing the state of the art in free-surface turbulence modelling. Experiments were conducted in a large free-surface water tunnel at momentum-thickness Reynolds numbers, Reθ, of 670 for the DPIV studies, and 1150 for the LDV measurements. A high-resolution, two-correlation DPIV program was used to generate ensembles of vector fields in planes parallel to the free surface. These data were further processed to obtain profiles of turbulent kinetic energy transport terms, such as production and dissipation. In addition, profiles of streamwise and surface-normal velocity were made (as functions of distance from the wall) using two-component LDV. Key findings of this study include the fact that both turbulent kinetic energy production and dissipation are dramatically reduced close to the free surface. Far from the wall, this results in an increase in surface-parallel uctuations very close to the free surface. The degree of this anisotropy and the spatial scales over which it exists are critical data for improved free-surface turbulence models.

Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film.