Showing papers in "Journal of Fluid Mechanics in 2007"

Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

Abstract: This is a publisher’s version of an article published in Journal of Fluid Mechanics © 2007 Cambridge University Press. www.cambridge.org/

Structural sensitivity of the first instability of the cylinder wake

Abstract: The stability properties of the flow past an infinitely long circular cylinder are studied in the context of linear theory. An immersed-boundary technique is used to represent the cylinder surface on a Cartesian mesh. The characteristics of both direct and adjoint perturbation modes are studied and the regions of the flow more sensitive to momentum forcing and mass injection are identified. The analysis shows that the maximum of the perturbation envelope amplitude is reached far downstream of the separation bubble, where as the highest receptivity is attained in the near wake of the cylinder, close to the body surface. The large difference between the spatial structure of the two-dimensional direct and adjoint modes suggests that the instability mechanism cannot be identified from the study of either eigenfunctions separately. For this reason a structural stability analysis of the problem is used to analyse the process which gives rise to the self-sustained mode. In particular, the region of maximum coupling among the velocity components is localized by inspecting the spatial distribution of the product between the direct and adjoint modes. Results show that the instability mechanism is located in two lobes placed symmetrically across the separation bubble, confirming the qualitative results obtained through a locally plane-wave analysis. The relevance of this novel technique to the development of effective control strategies for vortex shedding behind bluff bodies is illustrated by comparing the theoretical predictions based on the structural perturbation analysis with the experimental data of Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 71).

Energy-minimizing kinematics in hovering insect flight

Abstract: We investigate aspects of hovering insect flight by finding the optimal wing kinematics which minimize power consumption while still providing enough lift to maintain a time-averaged constant altitude over one flapping period. In particular, we study the flight of three insects whose masses vary by approximately three orders of magnitude: fruitfly (Drosophila melanogaster), bumblebee (Bombus terrestris), and hawkmoth (Manduca sexta). Here, we model an insect wing as a rigid body with three rotational degrees of freedom. The aerodynamic forces are modelled via a quasi-steady model of a thin plate interacting with the surrounding fluid. The advantage of this model, as opposed to the more computationally costly method of direct numerical simulation via computational fluid dynamics, is that it allows us to perform optimization procedures and detailed sensitivity analyses which require many cost function evaluations. The optimal solutions are found via a hybrid optimization algorithm combining aspects of a genetic algorithm and a gradient-based optimizer. We find that the results of this optimization yield kinematics which are qualitatively and quantitatively similar to previously observed data. We also perform sensitivity analyses on parameters of the optimal kinematics to gain insight into the values of the observed optima. Additionally, we find that all of the optimal kinematics found here maintain the same leading edge throughout the stroke, as is the case for nearly all insect wing motions. We show that this type of stroke takes advantage of a passive wing rotation in which aerodynamic forces help to reverse the wing pitch, similar to the turning of a free-falling leaf.

A turbulent jet in crossflow analysed with proper orthogonal decomposition

Abstract: Detailed instantaneous velocity fields of a jet in crossflow have been measured with stereoscopic particle image velocimetry (PIV). The jet originated from a fully developed turbulent pipe flow and entered a crossflow with a turbulent boundary layer. The Reynolds number based on crossflow velocity and pipe diameter was 2400 and the jet to crossflow velocity ratios were R=3.3 and R=1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R=3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core. The analysis identifies jet shear-layer vortices and finds that these vortical structures are more local and thus less dominant. For R=1.3, on the other hand, jet shear-layer vortices are the most dominant, while the wake vortices are much less important. For both cases, the analysis finds that the shear-layer vortices are not coupled to the dynamics of the wake vortices. Finally, the hanging vortices are identified and their contribution to the counter-rotating vortex pair (CVP) and interaction with the newly created wake vortices are described.

The efficiency of a turbine in a tidal channel

Abstract: There is an upper bound to the amount of power that can be generated by turbines in tidal channels as too many turbines merely block the flow. One condition for achievement of the upper bound is that the turbines are deployed uniformly across the channel, with all the flow through them, but this may interfere with other uses of the channel. An isolated turbine is more effective in a channel than in an unbounded flow, but the current downstream is non-uniform between the wake of the turbines and the free stream. Hence some energy is lost when these streams merge, as may occur in a long channel. We show here, for ideal turbine models, that the fractional power loss increases from 1/3 to 2/3 as the fraction of the channel cross-section spanned by the turbines increases from 0 to close to 1. In another scenario, possibly appropriate for a short channel, the speed of the free stream outside the turbine wake is controlled by separation at the channel exit. In this case, the maximum power obtainable is slightly less than proportional to the fraction of the channel cross-section occupied by turbines.

Global stability of base and mean flows : a general approach and its applications to cylinder and open cavity flows

Abstract: This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Karman vortex street regime that sets in for supercritical Reynolds numbers Re > 46. Barkley (Europhys. Lett. vol.75, 2006, p. 750) has recently studied the linear properties of the associated mean flow, i.e. the flow which is obtained by a time average of this unsteady periodic flow. He observed, thanks to a global mode analysis, that the mean flow is marginally stable and that the eigenfrequencies associated with the global modes of the mean flow fit the Strouhal to Reynolds experimental function well in the range 46 < Re < 180. The aim of this article is to give a theoretical proof of this result near the bifurcation. For this, we do a global weakly nonlinear analysis valid in the vicinity of the critical Reynolds number Rec based on the small parameter e = Rec−1 − Re−1 ≪ 1. We compute numerically the complex constants λ and μ′ which appear in the Stuart-Landau amplitude equation: dA/dt = e λA − eμ′ A|A|2. Here A is the scalar complex amplitude of the critical global mode. By analysing carefully the nonlinear interactions yielding the term μ′, we show for the cylinder flow that the mean flow is approximately marginally stable and that the linear dynamics of the mean flow yields the frequency of the saturated Stuart-Landau limit cycle. We will finally show that these results are not general, by studying the case of the bifurcation of an open cavity flow. In particular, we show that the mean flow in this case remains strongly unstable and that the frequencies associated with the eigenmodes do not exactly match those of the nonlinear unsteady periodic cavity flow. It will be demonstrated that two precise conditions must hold for a linear stability analysis of a mean flow to be relevant and useful.

Large-scale features in turbulent pipe and channel flows

Abstract: In recent years there has been significant progress made towards understanding the large-scale structure of wall-bounded shear flows. Most of this work has been conducted with turbulent boundary layers, leaving scope for further work in pipes and channels. In this article the structure of fully developed turbulent pipe and channel flow has been studied using custom-made arrays of hot-wire probes. Results reveal long meandering structures of length up to 25 pipe radii or channel half-heights. These appear to be qualitatively similar to those reported in the log region of a turbulent boundary layer. However, for the channel case, large-scale coherence persists further from the wall than in boundary layers. This is expected since these large-scale features are a property of the logarithmic region of the mean velocity profile in boundary layers and it is well-known that the mean velocity in a channel remains very close to the log law much further from the wall. Further comparison of the three turbulent flows shows that the characteristic structure width in the logarithmic region of a boundary layer is at least 1.6 times smaller than that in a pipe or channel.

Active control of high-speed and high-Reynolds-number jets using plasma actuators

Abstract: Localized arc filament plasma actuators are used to control an axisymmetric Mach 1.3 ideally expanded jet of 2.54 cm exit diameter and a Reynolds number based on the nozzle exit diameter of about 1.1×106. Measurements of growth and decay of perturbations seeded in the flow by the actuators, laser-based planar flow visualizations, and particle imaging velocimetry measurements are used to evaluate the effects of control. Eight actuators distributed azimuthally inside the nozzle, approximately 1 mm upstream of the nozzle exit, are used to force various azimuthal modes over a large frequency range (StDF of 0.13 to 1.3). The jet responded to the forcing over the entire range of frequencies, but the response was optimum (in terms of the development of large coherent structures and mixing enhancement) around the jet preferred Strouhal number of 0.33 (f = 5 kHz), in good agreement with the results in the literature for low-speed and low-Reynolds-number jets. The jet (with a thin boundary layer, D/θ ∼ 250) also responded to forcing with various azimuthal modes (m = 0 to 3 and m = ±1, ±2, ±4), again in agreement with instability analysis and experimental results in the literature for low-speed and low-Reynolds-number jets. Forcing the jet with the azimuthal mode m = ±1 at the jet preferred-mode frequency provided the maximum mixing enhancement, with a significant reduction in the jet potential core length and a significant increase in the jet centreline velocity decay rate beyond the end of the potential core.

Scaling analysis and simulation of strongly stratified turbulent flows

Abstract: Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re >> 1 and horizontal Froude number F-h > 1, viscous forces are unimportant and l(v) scales as l ...

Flapping dynamics of a flag in a uniform stream

Abstract: We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρ s h /(ρ f L); the Reynolds number, Re=VL/ν; and the non-dimensional bending rigidity, K B = EI / (ρfV 2 L 3 ). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid-structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier-Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (K B = to-4) and relatively high Reynolds number (Re=10 3 ). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regime of chaotic flapping. Parametric stability dependencies predicted by the linear analysis are confirmed by the nonlinear FSDS, and hysteresis in stability is explained with a nonlinear softening spring model. The chaotic flapping response shows up as a breaking of the limit cycle by inclusion of the 3/2 superharmonic. This occurs as the increased flapping amplitude yields a flapping Strouhal number (St=2Af/V) in the neighbourhood of the natural vortex wake Strouhal number, St ≃ 0.2. The limit-cycle von Karman vortex wake transitions in chaos to a wake with clusters of higher intensity vortices. For the largest mass ratios, strong vortex pairs are distributed away from the wake centreline during intermittent violent snapping events, characterized by rapid changes in tension and dynamic buckling.

Electro-osmotic slip and electroconvective instability

Abstract: Electric conduction from an electrolyte solution into a charge selective solid, such as ion exchange membrane or electrode, becomes unstable when the electrolyte concentration near the interface approaches zero owing to diffusion limitation. The sequence of events leading to instability is as follows: upon the decrease of the interface concentration, the electric double layer at the interface transforms from its common quasi-equilibrium structure to a different, non-equilibrium one. The key feature of this new structure is an extended space charge added to the usual one of the quasi-equilibrium electric double layer. The non-equilibrium electro-osmotic slip related to this extended space charge renders the quiescent conductance unstable. A unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibrium one, is developed and employed for derivation of a universal electro-osmotic slip formula. This formula is used for a linear stability study of quiescent electric conduction, yielding the precise parameter range of instability, compared with that in the full electroconvective formulation. The physical mechanism of instability is traced both kinematically, in terms of non-equilibrium electro-osmotic slip, and dynamically, in terms of forces acting in the electric double layer.

Recurrent motions within plane Couette turbulence

Abstract: The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low-speed fluid away from the wall, has been studied experimentally, theoretically and computationally for more than 50 years because of its importance to the three-dimensional structure of turbulent boundary layers. Five new three-dimensional solutions of turbulent plane Couette flow are produced, one of which is periodic while the other four are relative periodic. Each of these five solutions demonstrates the breakup and re-formation of near-wall coherent structures. Four of our solutions are periodic, but with drifts in the streamwise direction. More surprisingly, two of our solutions are periodic, but with drifts in the spanwise direction, a possibility that does not seem to have been considered in the literature. It is argued that a considerable part of the streakiness observed experimentally in the near-wall region could be due to spanwise drifts that accompany the breakup and re-formation of coherent structures. A new periodic solution of plane Couette flow is also computed that could be related to transition to turbulence. The violent nature of the bursting phenomenon implies the need for good resolution in the computation of periodic and relative periodic solutions within turbulent shear flows. This computationally demanding requirement is addressed with a new algorithm for computing relative periodic solutions one of whose features is a combination of two well-known ideas – namely the Newton–Krylov iteration and the locally constrained optimal hook step. Each of the six solutions is accompanied by an error estimate. Dynamical principles are discussed that suggest that the bursting phenomenon, and more generally fluid turbulence, can be understood in terms of periodic and relative periodic solutions of the Navier–Stokes equation.

Detection of Lagrangian coherent structures in three-dimensional turbulence

Abstract: We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that despite additional computational cost, the DLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. As a further advantage, the DLE method requires no velocity derivatives, which are often too noisy to be useful in the study of a turbulent flow. We study the evolution of a single hairpin vortex into a packet of similar structures, and show that the birth of a secondary vortex corresponds to a loss of hyperbolicity of the Lagrangian coherent structures.

The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

Abstract: Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a three-dimensional rough surface geometrically similar to the honed pipe roughness used by Shockling, Allen & Smits (J. Fluid Mech. vol. 564, 2006, p. 267). The present work covers a wide Reynolds-number range (Re θ = 2180–27 100), spanning the hydraulically smooth to the fully rough flow regimes for a single surface, while maintaining a roughness height that is a small fraction of the boundary-layer thickness. In this investigation, the root-mean-square roughness height was at least three orders of magnitude smaller than the boundary-layer thickness, and the Karman number (δ+), typifying the ratio of the largest to the smallest turbulent scales in the flow, was as high as 10100. The mean velocity profiles for the rough and smooth walls show remarkable similarity in the outer layer using velocity-defect scaling. The Reynolds stresses and higher-order turbulence statistics also show excellent agreement in the outer layer. The results lend strong support to the concept of outer layer similarity for rough walls in which there is a large separation between the roughness length scale and the largest turbulence scales in the flow.

Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high-pressure burner

Abstract: Nitric oxide formation in gas turbine combustion depends on four key factors: flame stabilization, heat transfer, fuel–air mixing and combustion instability. The design of modern gas turbine burners requires delicate compromises between fuel efficiency, emissions of oxides of nitrogen (NOx) and combustion stability. Burner designs allowing substantial NOx reduction are often prone to combustion oscillations. These oscillations also change the NOx fields. Being able to predict not only the main species field in a burner but also the pollutant and the oscillation levels is now a major challenge for combustion modelling. This must include a realistic treatment of unsteady acoustic phenomena (which create instabilities) and also of heat transfer mechanisms (convection and radiation) which control NOx generation.In this work, large-eddy simulation (LES) is applied to a realistic gas turbine combustion chamber configuration where pure methane is injected through multiple holes in a cone-shaped burner. In addition to a non-reactive simulation, this article presents three reactive simulations and compares them to experimental results. The first reactive simulation neglects effects of cooling air on flame stabilization and heat losses by radiation and convection. The second reactive simulation shows how cooling air and heat transfer affect nitric oxide emissions. Finally, the third reactive simulation shows the effects of combustion instability on nitric oxide emissions. Additionally, the combustion instability is analysed in detail, including the evaluation of the terms in the acoustic energy equation and the identification of the mechanism driving the oscillation.Results confirm that LES of gas turbine combustion requires not only an accurate chemical scheme and realistic heat transfer models but also a proper description of the acoustics in order to predict nitric oxide emissions and pressure oscillation levels simultaneously.

Effects of upstream boundary layer on the unsteadiness of shock-induced separation

Abstract: The relationship between the upstream boundary layer and the low-frequency, large-scale unsteadiness of the separated flow in a Mach 2 compression ramp interaction is investigated by performing wide-field particle image velocimetry (PIV) and planar laser scattering (PLS) measurements in streamwise–spanwise planes. Planar laser scattering measurements in the upstream boundary layer indicate the presence of spanwise strips of elongated regions of uniform momentum with lengths greater than 40?. These long coherent structures have been observed in a Mach 2 supersonic boundary layer (Ganapathisubramani, Clemens & Dolling 2006) and they exhibit strong similarities to those that have been found in incompressible boundary layers (Tomkins & Adrian 2003; Ganapathisubramani, Longmire & Marusic 2003). At a wall-normal location of y/?=0.2, the inferred instantaneous separation line of the separation region is found to oscillate between x/?=?3 and ?1 (where x/?=0 is the ramp corner). The instantaneous spanwise separation line is found to respond to the elongated regions of uniform momentum. It is shown that high- and low-momentum regions are correlated with smaller and larger size of the separation region, respectively. Furthermore, the instantaneous separation line exhibits large-scale undulations that conform to the low- and high-speed regions in the upstream boundary layer. The low-frequency unsteadiness of the separation region/shock foot observed in numerous previous studies can be explained by a turbulent mechanism that includes these elongated regions of uniform momentum

Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders

Abstract: Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Benard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Benard flow can be introduced, . In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Benard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.

Structure of turbulent flow over regular arrays of cubical roughness

Abstract: The structure of turbulent flow over large roughness consisting of regular arrays of cubical obstacles is investigated numerically under constant pressure gradient conditions. Results are analysed in terms of first- and second-order statistics, by visualization of instantaneous flow fields and by conditional averaging. The accuracy of the simulations is established by detailed comparisons of first- and second-order statistics with wind-tunnel measurements. Coherent structures in the log region are investigated. Structure angles are computed from two-point correlations, and quadrant analysis is performed to determine the relative importance of Q2 and Q4 events (ejections and sweeps) as a function of height above the roughness. Flow visualization shows the existence of low-momentum regions (LMRs) as well as vortical structures throughout the log layer. Filtering techniques are used to reveal instantaneous examples of the association of the vortices with the LMRs, and linear stochastic estimation and conditional averaging are employed to deduce their statistical properties. The conditional averaging results reveal the presence of LMRs and regions of Q2 and Q4 events that appear to be associated with hairpin-like vortices, but a quantitative correspondence between the sizes of the vortices and those of the LMRs is difficult to establish; a simple estimate of the ratio of the vortex width to the LMR width gives a value that is several times larger than the corresponding ratio over smooth walls. The shape and inclination of the vortices and their spatial organization are compared to recent findings over smooth walls. Characteristic length scales are shown to scale linearly with height in the log region. Whilst there are striking qualitative similarities with smooth walls, there are also important differences in detail regarding: (i) structure angles and sizes and their dependence on distance from the rough surface; (ii) the flow structure close to the roughness; (iii) the roles of inflows into and outflows from cavities within the roughness; (iv) larger vortices on the rough wall compared to the smooth wall; (v) the effect of the different generation mechanism at the wall in setting the scales of structures.

Shear instability and coherent structures in shallow flow adjacent to a porous layer

Abstract: Results are presented from an experimental study of shallow flow in a channel partially obstructed by an array of circular cylinders. The cylinder array is a model for emergent vegetation in an open channel, but also represents a simple sparse porous medium. A shear layer with regular vortex structures forms at the edge of the array, evolving downstream to an equilibrium width and vortex size. The vortices induce nearly periodic oscillations with a frequency that matches the most unstable linear mode for a parallel shear flow. The shear layer is asymmetric about the array interface and has a two-layer structure. An inner region of maximum shear near the interface contains a velocity inflection point and establishes the penetration of momentum into the array. An outer region, resembling a boundary layer, forms in the main channel, and establishes the scale of the vortices. The vortex structure, educed by conditional sampling, shows strong crossflows with sweeps from the main channel and ejections from the array, which create significant momentum and mass fluxes across the interface. The sweeps maintain the coherent structures by enhancing shear and energy production at the interface. A linear stability analysis is consistent with the experimental results and demonstrates that the instability is excited by the differential drag between the channel and the array.

Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics

Abstract: One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 4096 3 grid points. The DNS consist of two series of runs; one is with k max η∼ 1 (Series 1) and the other is with k max η∼2 (Series 2), where k max is the maximum wavenumber and η the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number R λ in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on R λ of the skewness and flatness factors (S and F). The DNS data suggest that the R λ dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S∼-0.32R λ 0.11 and F∼1.14R λ 0.34 , in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with R λ similarly to each other at R λ >00, in contrast to R λ < 100. Regarding the statistics of time derivatives, the second-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at R λ ≈430. The flatness factors of the Eulerian and Lagrangian accelerations increase with R λ approximately proportional to R λ αE and R λ αL , respectively, where α E ≈0.5 and α L ≈1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to R λ βE and R λ βL , respectively, where β E ≈1.5 and β L ≈3.0.

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

Abstract: The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

On the front velocity of gravity currents

Abstract: Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 10 5 ,1 .5×10 6 and 10 7 , respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments

Abstract: A systematic procedure for initializing supersonic and hypersonic turbulent boundary layers at controlled Mach number and Reynolds number conditions is described. The initialization is done by locally transforming a true direct numerical simulation flow field, and results in a nearly realistic initial magnitude of turbulent fluctuations, turbulence structure and energy distribution. The time scales necessary to forget the initial condition are studied. The experimental conditions of previous studies are simulated. The magnitude of velocity and temperature fluctuations, as well as the turbulent shear stresses given by the direct numerical simulations are in agreement with the experimental data.

Numerical simulation of active separation control by a synthetic jet

Abstract: Direct numerical simulation (DNS) and large-eddy simulation (LES) are carried out to investigate the frequency effect of zero-net-mass-flux forcing (synthetic jet) on a generic separated flow. The selected test case is a rounded ramp at a Reynolds number based on the step height of 28 275. The incoming boundary layer is fully turbulent with Rθ=1410. The whole flow in the synthetic jet cavity is computed to ensure an accurate description of the actuator effect on the flow field. In a first step, DNS is used to validate LES of this particular flow. In a second step, the effect of a synthetic jet at two reduced frequencies of 0.5 and 4 (based on the separation length of the uncontrolled case and the free-stream velocity) is investigated using LES. It is demonstrated that, with a proper choice of the oscillating frequency, separation can be drastically reduced for a velocity ratio between the jet and the flow lower than one. The low frequency is close to the natural vortex shedding frequency. Two different modes of the synthetic jet have been identified. A vorticity-dominated mode is observed in the low-frequency forcing case for which the separation length is reduced by 54%, while an acoustic-dominated mode is identified in the high-frequency forcing case for which the separation length is increased by 43%. The decrease of the separation length in the low-frequency forcing case is correlated with an increase of the turbulent kinetic energy level and consequently with an increase of the entrainment in the separated zone. A linear inviscid stability analysis shows that the increase of the separation length in the high-frequency forcing case is due to a modification of the mean velocity profile suggested by Stanek and coworkers. The result is a lower amplification of the perturbations and consequently, a lower entrainment into the mixing layer. To our knowledge, it is the first time that Stanek's hypothesis has been assessed, thanks to numerical simulations of fully turbulent flow.

Dynamics of transient cavities

Abstract: We study the collapse of a transient cavity of air in water created by the impact of a solid body. Experimentally, we characterize the dynamics of the cavity from its creation (t = 0) until it collapses (t = τ) in the limit where inertia dominates viscous and capillary effects. Theoretically, we find in this regime an approximate analytical solution which describes the time evolution of the shape of the cavity. This theoretical solution predicts the existence of two different types of cavities that we also observe experimentally.

Numerical investigation of the tone noise mechanism over laminar airfoils

Abstract: This paper presents the first numerical investigation via direct numerical simulation of the tone noise phenomenon occurring in the flow past laminar airfoils. This phenomenon corresponds to the radiation of discrete acoustic tones in some specific flow conditions, and has received much attention since the 1970s, and several experimental studies have been carried out to identify and understand the underlying physical mechanisms. However, several points remain to be clarified in order to provide a complete explanation of its origin. The flow around a two-dimensional NACA0012 airfoil is considered in order to have a deeper understanding of the tone noise phenomenon. Consistently with previous experimental studies, it is shown that depending on the Reynolds number and angle of attack, two different types of acoustic spectrum are observed: one which exhibits a broadband contribution with a dominant frequency together with a sequence of regularly spaced discrete frequencies, while the other one is only characterized by a simple broadband contribution. The first configuration is typical of the tone noise phenomenon. The present work shows that in this case, the mean flow on the pressure side of the airfoil exhibits a separation bubble near the trailing edge and the main tone frequency is close to the most amplified frequency of the boundary layer. The mechanism proposed in previous works for the main tone generation – which implies the existence of a separation bubble at the pressure side – is therefore validated by numerical simulation. On the other hand, the analysis of the suction side boundary layer reveals that there is no separation and that the most amplified frequency is different from the main tonal one. However, the suction side boundary layer is highly receptive to the tone frequency. Finally, an original explanation for the existence of the secondary discrete frequencies observed in the radiated pressure spectrum is given. They are associated to a bifurcation of the airfoil wake from a symmetric to a non-symmetric vortex pattern. A possible explanation for the existence of this bifurcation is the interaction between the disturbances which are the most amplified by the suction side boundary layer and those originating in the forcing of the suction side flow by the main tone noise mechanism.

Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

Abstract: A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as v T =(C s δ)2(| S |—|〈 S 〉|): the magnitude of the mean shear |〈 S 〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor | S |; CS is the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Re τ = 395 and Re τ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.

An analysis of the correlations between the turbulent flow and the sound pressure fields of subsonic jets

Abstract: Noise generation is investigated in subsonic isothermal round jets at Mach numbers M = 0.6 and M = 0.9, with Reynolds numbers Re D = 1700 and Re D ≥ 10 5 , using causality methods on data provided by large-eddy simulations. The correlations between broadband sound pressure signals and broadband turbulence signals along the jet axis and the shear layer are calculated. The normalized correlations are found to be significant between the pressure emitted in the downstream direction and centreline flow quantities. They are much smaller in the cases involving flow quantities along the shear layer, and fall for large emission angles. The maximum correlations obtained between centreline turbulence and downstream sound pressure are observed just at the end of the potential core for time delays corresponding to the times of propagation evaluated along ray paths. They also appear to be lower as the Mach number is reduced, and to be enhanced as the Reynolds number is decreased. These correlation levels can reasonably be attributed to the noise source which is predominant at small emission angles. This source is therefore located on the jet centreline at the end of the potential core, in a flow region which is shown to be characterized by a dominant Strouhal number over a large axial distance, by a strong level of intermittency, and by a high convection velocity. This supports the contention that the downstream jet-noise component is connected to the periodic and intermittent intrusion of vortical structures into the jet core.

On transition to cellularity in expanding spherical flames

Abstract: The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuelx–oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional–thermal instabilities. Experimental results show that the transition Peclet number, Pec = RclL, assumes an almost constant value for the near-equidiffusive acetylene flames with wide ranges in the mixture stoichiometry, oxygen concentration and pressure, where Rc is the flame radius at transition and lL the laminar flame thickness. However, for the non-equidiffusive hydrogen and propane flames, Pec respectively increases and decreases somewhat linearly with the mixture equivalence ratio. Evaluation of Pec using previous theory shows complete qualitative agreement and satisfactory quantitative agreement, demonstrating the insensitivity of Pec to all system parameters for equidiffusive mixtures, and the dominance of the Markstein number, Ze(Le – 1), in destabilization for non-equidiffusive mixtures, where Ze is the Zel'dovich number and Le the Lewis number. The importance of using locally evaluated values of lL, Ze and Le, extracted from either computationally simulated one-dimensional flame structure with detailed chemistry and transport, or experimentally determined response of stretched flames, in the evaluation of Pec is emphasized.

Marine ice-sheet dynamics. Part 1. The case of rapid sliding

Abstract: Marine ice sheets are continental ice masses resting on bedrock below sea level. Their dynamics are similar to those of land-based ice sheets except that they must couple with the surrounding floating ice shelves at the grounding line, where the ice reaches a critical flotation thickness. In order to predict the evolution of the grounding line as a free boundary, two boundary conditions are required for the diffusion equation describing the evolution of the grounded-ice thickness. By analogy with Stefan problems, one of these conditions imposes a prescribed ice thickness at the grounding line and arises from the fact that the ice becomes afloat. The other condition must be determined by coupling the ice sheet to the surrounding ice shelves. Here we employ matched asymptotic expansions to study the transition from ice-sheet to ice-shelf flow for the case of rapidly sliding ice sheets. Our principal results are that the ice flux at the grounding line in a two-dimensional ice sheet is an increasing function of the depth of the sea floor there, and that ice thicknesses at the grounding line must be small compared with ice thicknesses inland. These results indicate that marine ice sheets have a discrete set of steady surface profiles (if they have any at all) and that the stability of these steady profiles depends on the slope of the sea floor at the grounding line.