bluuebunny/crossref_metadata_2025_split huggingface dataset:
Breaking of standing internal gravity waves through two-dimensional
instabilities
Authors: Bouruet-Aubertot Pascale , Sommeria J. , Staquet C. 
Published: April 2006

The evolution of an internal gravity wave is investigated by direct
numerical computations. We consider the case of a standing wave confined in
a bounded (square) domain, a case which can be directly compared with
laboratory experiments. A pseudo-spectral method with symmetries is used. We
are interested in the inertial dynamics occurring in the limit of large
Reynolds numbers, so a fairly high spatial resolution is used
(1292 or 2572), but the
computations are limited to a two-dimensional vertical plane.
We observe that breaking eventually occurs, whatever the wave amplitude:
the energy begins to decrease after a given time because of irreversible
transfers of energy towards the dissipative scales. The life time of the
coherent wave, before energy dissipation, is found to be proportional to the
inverse of the amplitude squared, and we explain this law by a simple
theoretical model. The wave breaking itself is preceded by a slow transfer
of energy to secondary waves by a mechanism of resonant interactions, and we
compare the results with the classical theory of this phenomenon: good
agreement is obtained for moderate amplitudes. The nature of the events
leading to wave breaking depends on the wave frequency (i.e. on the
direction of the wave vector); most of the analysis is restricted to the
case of fairly high frequencies.
The maximum growth rate of the inviscid wave instability occurs in the
limit of high wavenumbers. We observe that a well-organized secondary plane
wave packet is excited. Its frequency is half the frequency of the primary
wave, corresponding to an excitation by a parametric instability. The
mechanism of selection of this remarkable structure, in the limit of small
viscosities, is discussed. Once this secondary wave packet has reached a
high amplitude, density overturning occurs, as well as unstable shear
layers, leading to a rapid transfer of energy towards dissipative scales.
Therefore the condition of strong wave steepness leading to wave breaking is
locally attained by the development of a single small-scale parametric
instability, rather than a cascade of wave interactions. This fact may be
important for modelling the dynamics of an internal wave field.
The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow
Authors: Sakamoto Hiroshi , Haniu Hiroyuki 
Published: April 2006

Experiments to investigate the formation mechanism and frequency of vortex shedding from a sphere in uniform shear flow were conducted in a water channel using flow visualization and velocity measurement. The Reynolds number, defined in terms of the sphere diameter and approach velocity at its centre, ranged from 200 to 3000. The shear parameter K, defined as the transverse velocity gradient of the shear flow non-dimensionalized by the above two parameters, was varied from 0 to 0.25. The critical Reynolds number beyond which vortex shedding from the sphere occurred was found to be lower than that for uniform flow and decreased approximately linearly with increasing shear parameter. Also, the Strouhal number of the hairpin-shaped vortex loops became larger than that for uniform flow and increased as the shear parameter increased.The formation mechanism and the structure of vortex shedding were examined on the basis of series of photographs and subsequent image processing using computer graphics. The range of Reynolds number in the present investigation, extending up to 3000, could be classified into three regions on the basis of this study, and it was observed that the wake configuration did not differ substantially from that for uniform flow. Also, unlike the detachment point of vortex loops in uniform flow, which was irregularly located along the circumference of the sphere, the detachment point in shear flow was always on the high-velocity side.
The flow behind rings: bluff body wakes without end effects
Authors: Leweke T. , Provansal M. 
Published: April 2006

Recent studies have demonstrated the strong influence of end effects on low-Reynoldsnumber bluff body wakes, and a number of questions remain concerning the intrinsic nature of three-dimensional phenomena in two-dimensional configurations. Some of them are answered by the present study which investigates the wake of bluff rings (i.e. bodies without ends) both experimentally and by application of the phenomenological Ginzburg–Landau model. The model turns out to be very accurate in describing qualitative and quantitative observations in a large Reynolds number interval. The experimental study of the periodic vortex shedding regime shows the existence of discrete shedding modes, in which the wake takes the form of parallel vortex rings or ‘oblique’ helical vortices, depending on initial conditions. The Strouhal number is found to decrease with growing body curvature, and a global expression for the Strouhal–Reynolds number relation, including curvature and shedding angle, is proposed, which is consistent with previous straight cylinder results. A secondary instability of the helical modes at low Reynolds numbers is discovered, and a detailed comparison with the Ginzburg–Landau model identifies it as the Eckhaus modulational instability of the spanwise structure of the near-wake formation region. It is independent of curvature and its clear observation in straight cylinder wakes is inhibited by end effects.The dynamical model is extended to higher Reynolds numbers by introducing variable parameters. In this way the instability of periodic vortex shedding which marks the beginning of the transition range is characterized as the Benjamin–Feir instability of the coupled oscillation of the near wake. It is independent of the shear layer transition to turbulence, which is known to occur at higher Reynolds numbers. The unusual shape of the Strouhal curve in this flow regime, including the discontinuity at the transition point, is qualitatively reproduced by the Ginzburg–Landau model. End effects in finite cylinder wakes are found to cause important changes in the transition behaviour also: they create a second Strouhal discontinuity, which is not observed in the present ring wake experiments.
The motion of long bubbles in polygonal capillaries. Part 1. Thin films
Authors: Wong Harris , Radke C. J. , Morris S. 
Published: April 2006

Foam in porous media exhibits an unusually high apparent viscosity, making it useful in many industrial processes. The rheology of foam, however, is complex and not well understood. Previous pore-level models of foam are based primarily on studies of bubble flow in circular capillaries. A circular capillary, however, lacks the corners that characterize the geometry of the pores. We study the pressure–velocity relation of bubble flow in polygonal capillaries. A long bubble in a polygonal capillary acts as a leaky piston. The ‘piston’ is reluctant to move because of a large drag exerted by the capillary sidewalls. The liquid in the capillary therefore bypasses the bubble through the leaky corners at a speed an order higher than that of the bubble. Consequently, the pressure work is dissipated predominantly by the motion of the fluid and not by the motion of the bubble. This is opposite to the conclusion based on bubble flow in circular capillaries. The discovery of this new flow regime reconciles two groups of contradictory foam-flow experiments.Part 1 of this work studies the fluid films deposited on capillary walls in the limit Ca → 0 (Ca ≡ μU/σ, where μ is the fluid viscosity, U the bubble velocity, and σ the surface tension). Part 2 (Wong et al. 1995) uses the film profile at the back end to calculate the drag of the bubble. Since the bubble length is arbitrary, the film profile is determined here as a general function of the dimensionless downstream distance x. For 1 [Lt ] x [Lt ] Ca−1, the film profile is frozen with a thickness of order Ca2/3 at the centre and order Ca at the sides. For x ∼ Ca−1, surface tension rearranges the film at the centre into a parabolic shape while the film at the sides thins to order Ca4/3. For x [Gt ] Ca−1, the film is still parabolic, but the height decreases as film fluid leaks through the side constrictions. For x ∼ Ca−5/3, the height of the parabola is order Ca2/3. Finally, for x [Gt ] Ca−5/3, the height decreases as Ca1/4x−1/4.
On vapour flow in a hot porous layer
Authors: Fitzgerald Shaun D. , Woods Andrew W. 
Published: April 2006

The motion of isothermal vapour in a permeable rock is governed by a nonlinear diffusion equation for the vapour pressure. We analyse vapour flow described by this equation in both bounded and unbounded domains. We then apply these solutions to describe the controls on the rate of vaporization of liquid invading a hot permeable rock. In an unbounded domain, we determine asymptotic similarity solutions describing the motion of vapour when it is either supplied to or removed from the reservoir. Owing to the compressibility, these solutions have the property that vapour surfaces migrate towards the isobar on which the vapour has the maximum speed.In contrast, if vapour is supplied to or removed from a closed bounded system sufficiently slowly then the vapour density and pressure rapidly become approximately uniform. As more vapour is added, the mean pressure gradually increases and vapour surfaces become compressed. If liquid slowly invades a hot bounded porous layer and vaporizes, the vapour pressure becomes nearly uniform. As more liquid is added, the reservoir gradually becomes vapour saturated and the vaporization ceases.In an open bounded system, with a constant rate of vapour injection, the flux of vapour across the reservoir becomes uniform. If liquid is injected slowly and vaporizes then again the vapour flux becomes spatially uniform. However, the vapour flux now increases slowly as the liquid invades further into the rock, as a result of the decreased resistance to vapour flow from the interface to the far boundary.
Two-dimensional secondary instabilities in a strongly stratified shear layer
Authors: Staquet Chantal 
Published: April 2006

In a stably stratified shear layer, thin vorticity layers (‘baroclinic layers’) are produced by buoyancy effects and strain in between the Kelvin–Helmholtz vortices. A two-dimensional numerical study is conducted, in order to investigate the stability of these layers. Besides the secondary Kelvin–Helmholtz instability, expected but never observed previously in two-dimensional numerical simulations, a new instability is also found.The influence of the Reynolds number (Re) upon the dynamics of the baroclinic layers is first studied. The layers reach an equilibrium state, whose features have been described theoretically by Corcos & Sherman (1976). An excellent agreement between those predictions and the results of the numerical simulations is obtained. The baroclinic layers are found to remain stable almost up to the time the equilibrium state is reached, though the local Richardson number can reach values as low as 0.05 at the stagnation point. On the basis of the work of Dritschel et al. (1991), we show that the stability of the layer at this location is controlled by the outer strain field induced by the large-scale Kelvin–Helmholtz vortices. Numerical values of the strain rate as small as 3% of the maximum vorticity of the layer are shown to stabilize the stagnation point region.When non-pairing flows are considered, we find that only for Re ≤ 2000 does a secondary instability eventually amplify in the layer. (Re is based upon half the initial vorticity thickness and half the velocity difference at the horizontally oriented boundaries.) This secondary instability is not of the Kelvin–Helmholtz type. It develops in the neighbourhood of convectively unstable regions of the primary Kelvin–Helmholtz vortex, apparently once a strong jet has formed there, and moves along the baroclinic layer while amplifying. It next perturbs the layer around the stagnation point and a secondary instability, now of the Kelvin–Helmholtz type, is found to develop there.We next examine the influence of a pairing upon the flow behaviour. We show that this event promotes the occurrence of a secondary Kelvin–Helmholtz instability, which occurs for Re ≥ 400. Moreover, at high Reynolds number (≥ 2000), secondary Kelvin–Helmholtz instabilities develop successively in the baroclinic layer, at smaller and smaller scales, thereby transferring energy towards dissipative scales through a mechanism eventually leading to turbulence. Because the vorticity of such a two-dimensional stratified flow is no longer conserved following a fluid particle, an analogy with three-dimensional turbulence can be drawn.
Experiments on supersonic combustion ramjet propulsion in a shock tunnel
Authors: Paull A. , Stalker R. J. , Mee D. J. 
Published: April 2006

Measurements have been made of the propulsive effect of supersonic combustion ramjets incorporated into a simple axisymmetric model in a free piston shock tunnel. The nominal Mach number was 6, and the stagnation enthalpy varied from 2.8 to 8.5 MJ kg−1. A mixture of 13% silane and 87% hydrogen was used as fuel, and experiments were conducted at equivalence ratios up to approximately 0.8. The measurements involved the axial force on the model, and were made using a stress wave force balance, which is a recently developed technique for measuring forces in shock tunnels. A net thrust was experienced up to a stagnation enthalpy of 3.7 MJ kg−1, but as the stagnation enthalpy increased, an increasing net drag was recorded. Pilot and static pressure measurements showed that the combustion was supersonic.The results were found to compare satisfactorily with predictions based on established theoretical models, used with some simplifying approximations. The rapid reduction of net thrust with increasing stagnation enthalpy was seen to arise from increasing precombustion temperature, showing the need to control this variable if thrust performance was to be maintained over a range of stagnation enthalpies. Both the inviscid and viscous drag were seen to be relatively insensitive to stagnation enthalpy, with the combustion chambers making a particularly significant contribution to drag. The maximum fuel specific impulse achieved in the experiments was only 175 s, but the theory indicates that there is considerable scope for improvement on this through aerodynamic design.
Simple shear flows of dilute gas–solid suspensions
Authors: Tsao Heng-Kwong , Koch Donald L. 
Published: April 2006

Kinetic theory and numerical simulations are used to explore the dynamics of a dilute gas–solid suspension subject to simple shear flow. The particles experience a Stokes drag force and undergo solid-body interparticle collisions. Two qualitatively different steady-state behaviours are possible: an ignited state, in which the variance of the particle velocity is very large; and a quenched state, in which most of the particles follow the local fluid velocity. Theoretical results for the ignited state are obtained by perturbing from a Maxwell distribution, while predictions for the quenched state result from consideration of the collision of particles that initially move with the fluid. A composite theory, which includes effects of collisions driven by both the mean shear and the velocity fluctuations, predicts the existence of multiple steady states. Dynamic simulations and calculations using the direct-simulation Monte Carlo method confirm the result that, for certain volume fractions and shear rates, either the quenched or ignited state can be achieved depending on the initial velocity variance.Simulations are also performed for particles experiencing a nonlinear drag force. Both the theory of rapid granular flow, which neglects drag, and our theory for the ignited state with linear drag predict that the particle velocity variance can grow without bound as ϕ → 0, where ϕ is the volume fraction. The nonlinear drag force eliminates the divergence and leads to a particle velocity variance that will always decrease with decreasing volume fraction in the limit ϕ → 0.
Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio
Authors: Quon Charles , Ghil Michael 
Published: April 2006

For thermosolutal convection in an enclosure of arbitrary vertical aspect ratio, mixed boundary conditions – with salt flux and temperature prescribed on a horizontal boundary – can lead to symmetry breaking via pitchfork bifurcation. In the present paper we consider an enclosure of very small height-to-length aspect ratio δ, as encountered in the world's oceans. In this case, if the ratios of the vertical to horizontal components of viscosity, [Pscr ], and of diffusivity, [Lscr ], are of order unity, advective transport cannot set in even at very high Rayleigh numbers. The ratios [Pscr ] and [Lscr ] must be substantially less than unity in order for convection to dominate the heat and solute transport.We have investigated numerically the effects of monotonic and non-monotonic temperature and salinity boundary conditions in a two-dimensional domain at constant δ = 0.01 and constant [Pscr ] = [Lscr ] = 0.01. This ratio of eddy-mixing coefficients reflects the different scales of motion – vertical and horizontal – in the ocean, rather than a physically realizable laboratory fluid. It is found that when the salt-flux strength, γ, is sufficiently large, the system undergoes a second bifurcation for both types of boundary conditions. It is a Hopf bifurcation, leading from the asymmetric steady states produced by the first one to oscillatory solutions. These periodic solutions are stable and very robust. An approximate Hopf bifurcation diagram has been produced. We conclude that non-monotonic salt-flux conditions are neither necessary nor sufficient to induce the oscillations, while the strength of the salt flux is crucial.
Axisymmetric particle-driven gravity currents
Authors: Bonnecaze Roger T. , Hallworth Mark A. , Huppert Herbert E. , Lister John R. 
Published: April 2006

Axisymmetric gravity currents that result when a dense suspension intrudes under a lighter ambient fluid are studied theoretically and experimentally. The dynamics of and deposition from currents flowing over a rigid horizontal surface are determined for the release of either a fixed volume or a constant flux of a suspension. The dynamics of the current are assumed to be dominated by inertial and buoyancy forces, while viscous forces are assumed to be negligible. The fluid motion is modelled by the single-layer axisymmetric shallow-water equations, which neglect the effects of the overlying fluid. An advective transport equation models the distribution of particles in the current, and this distribution determines the local buoyancy force in the shallow-water equations. The transport equation is derived on the assumption that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through a viscous sublayer at the bottom of the current. No adjustable parameters are needed to specify the theoretical model. The coupled equations of the model are solved numerically, and it is predicted that after an early stage both constant-volume and constant-flux, particle-driven gravity currents develop an internal bore which separates a supercritical particle-free region upstream from a subcritical particle-rich region downstream near the head of the current. For the fixed-volume release, an earlier bore is also predicted to occur very shortly after the initial collapse of the current. This bore transports suspended particles away from the origin, which results in a maximum in the predicted deposition away from the centre.To test the model several laboratory experiments were performed to determine both the radius of an axisymmetric particle-driven gravity current as a function of time and its deposition pattern for a variety of initial particle concentrations, particle sizes, volumes and flow rates. For the release of a fixed volume and of a constant flux of suspension, the comparisons between the experimental results and the theoretical predictions are fairly good. However, for the current of fixed volume, we did not observe the bore predicted to occur shortly after the collapse of the current or the resulting maximum in deposition downstream of the origin. This is unlike the previous study of Bonnecaze et al. (1993) on two-dimensional currents, in which a strong bore was observed during the slumping phase. The radial extent R of the deposit from a fixed-volume current is accurately predicted by the model, and for currents whose particles settle sufficiently slowly, we find that R = 1.9(g′0V3 / v2s)1/8, where V is the volume of the current, vs is the settling velocity of a particle in the suspension and g’0 is the initial reduced gravity of the suspension.
Stability of the viscous flow of a fluid through a flexible tube
Authors: Kumaran V. 
Published: April 2006

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity η in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity ηs occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface.The transition velocity Γt for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities ηr = (ηs/η), the capillary number λ = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For ηr = 0 and λ = 0, the transition velocity Γt diverges in the limits k [Lt ] 1 and k [Gt ] 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for λ < 0 and ηr = 0, though there is an increase in λt in the limit k > 1. When the viscosity of the surface is non-zero (ηr < 0), however, there is a qualitative change in the λtvs. k curves. For ηr < 1, the transition velocity λt is finite only when k is greater than a minimum value kmin, while perturbations with wavenumber k < kmin are stable even for λ → ∞. For ηr > 1, λt is finite only for kmin < k < kmax, while perturbations with wavenumber k < kmin or k > kmax are stable in the limit λ → ∞. As H decreases or ηr increases, the difference kmax − kmin decreases. At a minimum value H = Hmin which is a function of ηr, the difference kmax − kmin = 0, and for H < Hmin, perturbations of all wavenumbers are stable even in the limit λ → ∞. The calculations indicate that Hmin shows a strong divergence proportional to exp (0.0832nr2) for ηr [Gt ] 1.