bluuebunny/crossref_metadata_2025 huggingface dataset:
A turbulent equilibrium boundary layer near separation
Authors: Skåre Per Egil , Krogstad Per-åge
Published: April 2006

The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from Kl ≈ 0.41 to Kl ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y/δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.
Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity
Authors: Neves João C. , Moin Parviz , Moser Robert D.
Published: April 2006

Convex transverse curvature effects in wall-bounded turbulent flows are significant if the boundary-layer thickness is large compared to the radius of curvature (large γ = δ/a). The curvature affects the inner part of the flow if a+, the cylinder radius in wall units, is small.

Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). Statistical and structural data were extracted from the computed flow fields. The effects of the transverse curvature were identified by comparing the present results with those of the plane channel simulation of Kim, Moin & Moser (1987), performed at a similar Reynolds number. As the curvature increases, the skin friction increases, the slope of the logarithmic region decreases and turbulence intensities are reduced. Several turbulence statistics are found to scale with a curvature dependent velocity scale derived from the mean momentum equation. Near the wall, the flow is more anisotropic than in the plane channel with a larger percentage of the turbulent kinetic energy resulting from the streamwise velocity fluctuations. As the curvature increases, regions of strong normal vorticity develop near the wall.
On the 3-D inverse potential target pressure problem. Part 1. Theoretical aspects and method formulation
Authors: Chaviaropoulos P. , Dedoussis V. , Papailiou K. D.
Published: April 2006

An inverse potential methodology is introduced for the solution of the fully 3-D target pressure problem. The method is based on a potential function/stream function formulation, where the physical space is mapped onto a computational one via a body-fitted coordinate transformation. A potential function and two stream vectors are used as the independent natural coordinates, whilst the velocity magnitude, the aspect ratio and the skew angle of the elementary streamtube cross-section are assumed to be the dependent ones. A novel procedure based on differential geometry and generalized tensor analysis arguments is employed to formulate the method. The governing differential equations are derived by requiring the curvature tensor of the flat 3-D physical Eucledian space, expressed in terms of the curvilinear natural coordinates, to be zero. The resulting equations are discussed and investigated with particular emphasis on the existence and uniqueness of their solution. The general 3-D inverse potential problem, with ‘target pressure’ boundary conditions only, seems to be illposed accepting multiple solutions. This multiplicity is alleviated by considering elementary streamtubes with orthogonal cross-sections. The assumption of orthogonal stream surfaces reduces the number of dependent variables by one, simplifying the governing equations to an elliptic p.d.e. for the velocity magnitude and to a second-order o.d.e. for the streamtube aspect ratio. The solution of these two equations provides the flow field. Geometry is determined independently by integrating Frenet equations along the natural coordinate lines, after the flow field has been calculated. The numerical implementation as well as validation test cases for the proposed inverse methodology are presented in the companion paper (Paper 2).
The stabilizing effect of compressibility in turbulent shear flow
Authors: Sarkar S.
Published: April 2006

Direct numerical simulation of turbulent homogeneous shear flow is performed in order to clarify compressibility effects on the turbulence growth in the flow. The two Mach numbers relevant to homogeneous shear flow are the turbulent Mach number Mt and the gradient Mach number Mg. Two series of simulations are performed where the initial values of Mg and Mt are increased separately. The growth rate of turbulent kinetic energy is observed to decrease in both series of simulations. This ‘stabilizing’ effect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value of Mg is changed. A systematic comparison of the different DNS cases shows that the compressibility effect of reduced turbulent energy growth rate is primarily due to the reduced level of turbulence production and not due to explicit dilatational effects. The reduced turbulence production is not a mean density effect since the mean density remains constant in compressible homogeneous shear flow. The stabilizing effect of compressibility on the turbulence growth is observed to increase with the gradient Mach number Mg in the homogeneous shear flow DNS. Estimates of Mg for the mixing layer and the boundary layer are obtained. These estimates show that the parameter Mg becomes much larger in the high-speed mixing layer relative to the high-speed boundary layer even though the mean flow Mach numbers are the same in the two flows. Therefore, the inhibition of turbulent energy production and consequent ‘stabilizing’ effect of compressibility on the turbulence (over and above that due to any mean density variation) is expected to be larger in the mixing layer relative to the boundary layer, in agreement with experimental observations.
Stability of eccentric core–annular flow
Authors: Huang Adam , Joseph Daniel D.
Published: April 2006

Perfect core-annular flows are two-phase flows, for example of oil and water, with the oil in a perfectly round core of constant radius and the water outside. Eccentric core flows can be perfect, but the centre of the core is displaced off the centre of the pipe. The flow is driven by a constant pressure gradient, and is unidirectional. This kind of flow configuration is a steady solution of the governing fluid dynamics equations in the cases when gravity is absent or the densities of the two fluids are matched. The position of the core is indeterminate so that there is a family of these eccentric core flow steady solutions. We study the linear stability of this family of flows using the finite element method to solve a group of PDEs. The large asymmetric eigenvalue problem generated by the finite element method is solved by an iterative Arnoldi's method. We find that there is no linear selection mechanism; eccentric flow is stable when concentric flow is stable. The interface shape of the most unstable mode changes from varicose to sinuous as the eccentricity increases from zero.
Three-dimensional structure of straight and curved plane wakes
Authors: Weygandt James H. , Mehta Rabindra D.
Published: April 2006

The formation and evolution of the three-dimensional structure of straight and mildly curved ($b/\bar{R} < 2\%$) flat plate wakes at relatively high Reynolds numbers (Reb = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.
Instability of strained vortex layers and vortex tube formation in homogeneous turbulence
Authors: Passot T. , Politano H. , Sulem P.L. , Angilella J.R. , Meneguzzi M.
Published: April 2006

A modulational perturbation analysis is presented which shows that when a strained vortex layer becomes unstable, vorticity concentrates into steady tubular structures with finite amplitude, in quantitative agreement with the numerical simulations of Lin & Corcos (1984). Elaborated three-dimensional visualizations suggest that this process, due to a combination of compression and self-induced rotation of the layer, is at the origin of intense and long-lived vortex tubes observed in direct numerical simulations of homogeneous turbulence.
Computer simulations of Brownian motion of complex systems
Authors: Grassia P. S. , Hinch E. J. , Nitsche L. C.
Published: April 2006

Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models; firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.
Mixing induced by oscillatory stratified flow past a right-circular cylinder
Authors: Perera M. J. A. M. , Fernando H. J. S. , Boyer D. L.
Published: April 2006

A series of laboratory experiments was performed to investigate the overall mixing characteristics of oscillatory stratified flow past an isolated topography. The experiments were conducted by oscillating a right-circular cylinder in an otherwise quiescent linearly stratified fluid contained in a rectangular basin. The mixing was largely confined to the turbulent ‘core’ region around the cylinder. This mixed fluid was then injected into the fluid interior of the basin by numerous intrusive tongues. These intrusions were accompanied by return currents of unmixed stratified fluid into the turbulent core. The overall effect of this mixing process was to increase the potential energy of the fluid in the basin. An expression is derived to relate the rate of change of potential energy of the system to the basin-averaged buoyancy flux. This formula was then used to calculate the mean buoyancy flux from measurements of the rate of change of potential energy of the fluid system. Basin-averaged diapycnal eddy diffusivities for the experiments were evaluated and the results were found to be in good agreement with the predictions of a heuristic model based on the energetics of the mixing. Observations on the spreading of intrusions and the evolution of the density field are also presented.
Bifurcation for flow past a cylinder between parallel planes
Authors: Chen J.-H. , Pritchard W. G. , Tavener S. J.
Published: April 2006

Numerical experiments are described to ascertain how the steady flow past a circular cylinder loses stability as the Reynolds number is increased. A novel feature of the present study is that the cylinder is confined between parallel planes, allowing a more definitive specification of the flow, both experimentally and computationally, than is possible for the unbounded case. Since the structure of the bifurcation is unclear from the extant literature, with the experimental and computational evidence not in good agreement, a critical appraisal of both sets of evidence is presented.

A study has been made of the formation of the steady vortex pair behind the cylinder, and it has been determined that the first appearance of the vortices is not associated with a bifurcation of the full dynamical problem but instead it is probably associated with a bifurcation of a restricted kinematical problem.

A set of numerical experiments has been made in which the steady flow past the cylinder was perturbed slightly and the ensuing time-dependent motions were computed. These experiments revealed that, for a given blockage ratio, the perturbation would die away at small Reynolds numbers but that, above a critical Reynolds number, the disturbance would be amplified and the flow would eventually settle down to a new state comprising a time-periodic motion.

Experiments were also carried out to determine the bifurcation point numerically by considering an eigenvalue problem based on a linearization about the computed steady flow past the cylinder. The calculations showed that stability is lost through a symmetry-breaking Hopf bifurcation and that, for a given blockage ratio, the critical Reynolds number was in very good agreement with that estimated from the time-dependent computations.
On the stability of large-amplitude geostrophic flows in a two-layer fluid: the case of ‘strong’ beta-effect
Authors: Benilov E. S.
Published: April 2006

This paper examines the stability of two-layer geostrophic flows with large displacement of the interface and strong β-effect. Attention is focused on flows with non-monotonic interface profiles which are not covered by the Rayleigh-style stability theorems proved by Benilov (1992a, b) and Benilov & Cushman-Roisin (1994). For such flows the coefficient of the highest derivative in the corresponding boundary-value problem vanishes at the point where the depth profile has an extremum. Although this singularity is similar to a critical level, it cannot be regularized by the simplistic introduction of infinitesimal viscosity through the assumption that the phase speed of the disturbance is complex. In order to regularize the singularity properly, one should consider the problem within the framework of the original ageostrophic viscous equations and, having obtained the boundary-value problem for harmonic disturbance, take the limit Rossby number → 0, viscosity → 0.

The results obtained analytically and (for special cases) numerically indicate that the stability of flows with non-monotonic profiles strongly depends on the depth of the upper layer. If the upper layer is ‘thick’ (i.e. if the average depth H1 of the upper layer is of the order of the total depth of the fluid H0), the stability boundary-value problem does not have any solutions at all, which means stability (however, this stability is structurally unstable, and the flow, generally speaking, can be made weakly unstable by any small effect such as external forcing, viscosity, or ageostrophic corrections). In the case of ‘thin’ upper layer (H1/H0 [lsim ] Ro), the order of the singularity changes and all non-monotonic flows are unstable regardless of their profiles. It is also demonstrated that thin-upper-layer flows do not have to be non-monotonic to be unstable: if u–βR20 (where u is the zonal velocity, β is the β-parameter, and R0 is the deformation radius) changes sign somewhere in the flow, the stability boundary-value problem has another singular point which leads to instability.
On coupling between the Poincaré equation and the heat equation: non-slip boundary condition
Authors: Zhang K.
Published: April 2006

In contrast to the well-known columnar convection mode in rapidly rotating spherical fluid systems, the viscous dissipation of the preferred convection mode at sufficiently small Prandtl numberPrtakes place only in the Ekman boundary layer. It follows that different types of velocity boundary condition lead to totally different forms of the asymptotic relationship between the Rayleigh numberRand the Ekman numberEfor the onset of convection. We extend both perturbation and numerical analyses with the stress-free boundary condition (Zhang 1994) in rapidly rotating spherical systems to those with the non-slip boundary condition. Complete analytical solutions – the critical parameters for the onset of convection and the corresponding flow and temperature structure – are obtained and a new asymptotic relation betweenRandEis derived. While an explicit solution of the Ekman boundary-layer problem can be avoided by constructing a proper surface integral in the case of the stress-free boundary problem, an explicit solution of the spherical Ekman boundary layer is required and then obtained to derive the solvability condition for the present problem. In the corresponding numerical analysis, velocity and temperature are expanded in terms of spherical harmonics and Chebychev functions. Accurate numerical solutions are obtained in the asymptotic regime of smallEandPr, and comparison between the analytical and numerical solutions is then made to demonstrate that a satisfactory quantitative agreement between the analytical and numerical analyses is reached.
Gas flow in micro-channels
Authors: Harley John C. , Huang Yufeng , Bau Haim H. , Zemel Jay N.
Published: April 2006

An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 μm wide, 104 μm long, and ranged in depth from 0.5 to 20 μm. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.
Asymptotic vorticity structure and numerical simulation of slender vortex filaments
Authors: Klein Rupert , Knio Omar M.
Published: April 2006

A new asymptotic analysis of slender vortices in three dimensions, based solely on the vorticity transport equation and the non-local vorticity–velocity relation gives new insight into the structure of slender vortex filaments. The approach is quite different from earlier analyses using matched asymptotic solutions for the velocity field and it yields additional information. This insight is used to derive three different modifications of the thin-tube version of a numerical vortex element method. Our modifications remove an O(1) error from the node velocities of the standard thin-tube model and allow us to properly account for any prescribed physical vortex core structure independent of the numerical vorticity smoothing function. We demonstrate the performance of the improved models by comparison with asymptotic solutions for slender vortex rings and for perturbed slender vortex filaments in the Klein–Majda regime, in which the filament geometry is characterized by small-amplitude–short-wavelength displacements from a straight line. These comparisons represent a stringent mutual test for both the proposed modified thin-tube schemes and for the Klein–Majda theory. Importantly, we find a convincing agreement of numerical and asymptotic predictions for values of the Klein–Majda expansion parameter ε as large as ½. Thus, our results support their findings in earlier publications for realistic physical vortex core sizes.
Numerical simulation of nonlinear kink instabilities on supersonic shear layers
Authors: Bassett Gene M. , Woodward Paul R.
Published: April 2006

Nonlinear kink instabilities of high-Reynolds-number supersonic shear layers have been studied using high-resolution computer simulations with the piecewise-parabolic-method (PPM). The transition region between the two fluids of the shear layer is spread out over many computational zones to avoid numerical effects introduced on the smallest lengthscales. Mach number, density contrast, and perturbation speed and amplitude were varied to study their effects on the growth of the kink instabilities. In response to a perturbing sound wave, a travelling kink mode grows in amplitude until enough of a disturbance on the shear layer has been created for it to roll up and rapidly grow in thickness. The time it takes for this rapid growth to be initiated is proportional to the initial shear-layer thickness and increases for increasing Mach number or decreasing perturbation amplitude. For equal density, Mach 4 shear layers, perturbed by a sound wave with a 2% amplitude at the travelling mode velocity, the growth time is τg= (546 ± 24) δ/c, wherecis the sound speed and δ the half-width of the shear layer.
Trapping of water waves by submerged plates using hypersingular integral equations
Authors: Parsons Neil F. , Martin P. A.
Published: April 2006

The trapping of surface water waves by a thin plate in deep water is reduced to finding non-trivial solutions of a homogeneous, hypersingular integral equation for the discontinuity in velocity potential across the plate. The integral equation is discretized using an expansion-collocation method, involving Chebyshev polynomials of the second kind. A non-trivial solution to the problem is given by the vanishing of the determinant inherent in such a method. Results are given for inclined flat plates, and for curved plates that are symmetric with respect to a line drawn vertically through their centre. Comparisons with published results for horizontal flat plates (in water of finite depth) and for circular cylinders are made.
Interaction of oblique instability waves with weak streamwise vortices
Authors: Goldstein M. E. , Wundrow David W.
Published: April 2006

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien–Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed.
Inertial effects in chaotic mixing with diffusion
Authors: Dutta Pradip , Chevray Rene
Published: April 2006

The role of diffusion and transient velocities in the dispersal of
passive scalars by chaotic advection produced in a low Reynolds number
periodic journal-bearing flow is studied numerically and experimentally. The
transient velocity field, which occurs whenever the cylinders switch motion,
is obtained by solving the Navier–Stokes equations numerically in the
eccentric annulus. It is observed, numerically, that the transient effects,
along with diffusion, significantly enhance the separation of chaotically
advected particles even when the Reynolds number is very low. Corresponding
experimental observations are found to be in good qualitative agreement with
the numerical results obtained by including the effect of transient
velocities, which are seen to add to the overall separation of
particles.
Mixing due to grid-generated turbulence of a two-layer scalar
profile
Authors: Huq Pablo , Britter Rex E.
Published: April 2006

In this experimental study the mixing of passive scalars that arises
from shear-free decaying grid-generated turbulence is examined. The flow
configuration consists of two homogeneous layers of equal density separated
by a sharp interface between different mean concentrations of passive
scalar. Both layers flow through a turbulence-generating grid. To determine
the effect of diffusivity the scalar was heat in one experiment and salt in
a second. The Schmidt number – the ratio of momentum to species diffusivity
– was 7 and 700 for heat and salt respectively. Velocity, scalar and flux
fields were mapped and flow visualization was undertaken to study the
flows.

Integral lengthscales and (scalar) flux were determined to be
independent of diffusivity, whereas the scalar Taylor microscales varied
with Schmidt number,
Sc,
thus illustrating the disparate effects of diffusivity on large and small
scales. The time series of signals showed a correspondence between locations
of wθ extrema and uw
extrema. Flux wθ arose from intermittent events;
and the magnitude of the time-averaged flux $\overline{w\theta}$ was found to depend on the
frequency, rather than on variations in the amplitude of
wθ events.
On the identification of a vortex
Authors: Jeong Jinhee , Hussain Fazle
Published: April 2006

Considerable confusion surrounds the longstanding question of what
constitutes a vortex, especially in a turbulent flow. This question,
frequently misunderstood as academic, has recently acquired particular
significance since coherent structures (CS) in turbulent flows are now
commonly regarded as vortices. An objective definition of a vortex should
permit the use of vortex dynamics concepts to educe CS, to explain formation
and evolutionary dynamics of CS, to explore the role of CS in turbulence
phenomena, and to develop viable turbulence models and control strategies
for turbulence phenomena. We propose a definition of a vortex in an
incompressible flow in terms of the eigenvalues of the symmetric tensor
${\bm {\cal S}}^2 + {\bm
\Omega}^2$; here ${\bm {\cal S}}$ and ${\bm \Omega}$ are respectively the
symmetric and antisymmetric parts of the velocity gradient tensor
${\bm \Delta}{\bm
u}$. This definition captures the pressure minimum
in a plane perpendicular to the vortex axis at high Reynolds numbers, and
also accurately defines vortex cores at low Reynolds numbers, unlike a
pressure-minimum criterion. We compare our definition with prior
schemes/definitions using exact and numerical solutions of the Euler and
Navier–Stokes equations for a variety of laminar and turbulent flows. In
contrast to definitions based on the positive second invariant of
${\bm \Delta}{\bm
u}$ or the complex eigenvalues of
${\bm \Delta}{\bm
u}$, our definition accurately identifies the
vortex core in flows where the vortex geometry is intuitively
clear.
Streamline topology in eccentric Taylor vortex flow
Authors: Ashwin P. , King G. P.
Published: April 2006

We investigate an asymptotic model of DiPrima & Stuart
(1972b, 1975) describing steady Taylor vortex
flow between eccentric cylinders, under the assumption that the eccentricity
ε, the clearance ratio δ and the Taylor vortex amplitude
A satisfy ε, δ and
A small. By solving a boundary value problem
for the radial eigenfunctions we numerically obtain the flow field of
DiPrima & Stuart and investigate its topology, after correcting
higher-order terms to ensure that the flow preserves volume. We find regions
of chaotic streamlines at all eccentricities and discuss the reason for
their existence. We make an analogy between the full model and a modulated
vortex flow field which qualitatively displays the same behaviour.

For large eccentricities, we examine the flow field and the topology of
its streamlines, especially where the two-dimensional flow contains a
separated region of recirculation. In this case Taylor vortices give rise to
transport of fluid particles in and out of the separated region. We find
that the onset of Taylor vortices encourages recirculation in the inflow
plane, whilst discouraging it in the outflow plane.
Rayleigh streaming at large Reynolds number and its effect on shear
flow
Authors: Vainshtein P.
Published: April 2006

A fluid contained between two parallel walls, one of which is at rest
and the other moving in the longitudinal direction with a constant velocity,
is examined when a standing sound wave is imposed in the transverse
direction. Vortical acoustic streaming appears in the region between the
walls. The streaming is not affected by the main flow. A qualitative
analysis is presented for the Navier–Stokes equations governing the
steady-streaming component of the motion. The study considers the case of
flow with high streaming Reynolds number and makes an explicit determination
of the vorticity in the inviscid core region. The effect of the streaming
upon the shear flow in the longitudinal direction is then analysed
asymptotically. A periodic structure of the wall shear stress in the
transverse direction is detected in which vast areas of vanishing wall shear
stress alternate with narrow regions where it increases significantly. A
relation expressing the mean wall shear stress in terms of the streaming
Reynolds number is derived. Results obtained show that acoustic streaming
results in a marked enhancement of the mean wall shear stress at the
walls.
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 primary and inverse instabilities of directional viscous
fingering
Authors: Reinelt D. A.
Published: April 2006

Consider two infinitely long cylinders of different radii with one
inside the other but off-centred. The gap between the two cylinders is
partially filled with a viscous fluid. As the cylinders rotate with
independent velocities U1
and U2, a thin liquid film
coats each of their surfaces all the way around except in the region where
the viscous fluid completely fills the gap. Interface conditions that
connect solutions of averaged equations in the viscous fluid region with
solutions in the thin film region are derived. For the two-interface problem
analysed here, two types of instabilities occur depending on the amount of
viscous fluid between the cylinders. For large fluid volume, the primary
supercritical instability occurs when the front interface becomes unstable
as the cylinder velocities are increased. For small fluid volume, the back
interface passes through the region where the gap width is a minimum to the
same side as the front interface. Steady state solutions with straight
interface edges exhibit a turning point with respect to the cylinder
velocities. The back interface becomes unstable at the turning point; this
inverse instability is subcritical.
Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow
Authors: Borue Vadim , Orszag Steven A. , Staroselsky Ilya
Published: April 2006

We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.
The effects of laterally sloping upper and lower boundaries on waves and instability in stratified shear flows
Authors: Thorpe S. A. , Holt J. T.
Published: April 2006

The dispersion relation for internal waves travelling in the horizontal direction of a two-dimensional stratified shear flow is affected by the presence of topography, or upper and lower boundaries, which vary only in the horizontal direction normal to that of the flow. This is in accordance with Grimshaw's (1978) findings for long internal waves. Such topography, however, imposes boundary conditions which affect both the growth rates and orientation of the crests of unstable disturbances. Predictions are derived for the particular case of instability of a fluid with a thin interface separating two fluids of different densities in relative flow, which are confined in a tube with horizontal generators but which has upper and lower parallel plane boundaries inclined to the horizontal at an angle α. These predictions are compared with laboratory experiments. There is good qualitative agreement and some quantitative agreement, at least when the predicted angle, γ, between the crest lines of the disturbances and the cross-flow direction, is small. Relatively small disturbances, or billow, amplitudes are found along the centreline of the tube. At large γ, however, the disturbance crests becomes less well-ordered, with billows on one side of the tube centreline connecting with neighbouring pairs on the other, so evolving a zigzag pattern. The results have application to naturally occurring flows in estuaries and channels, and to the development of instability in the stratified atmosphere.
Quantitative characteristics of a laminar, unsteady necklace vortex system at a rectangular block-flat plate juncture
Authors: Seal C. V. , Smith C. R. , Akin O. , Rockwell D.
Published: April 2006

The unsteady laminar necklace vortex system formed at the junction of a rectangular bluff body and a flat plate was studied experimentally using hydrogen bubble flow visualization and particle image velocimetry (PIV). The vortex system was found to exhibit unsteady behaviour similar to that described by other investigators for cylinder-flat plate junctures, and is characterized by the periodic formation of necklace vortices upstream of the body that subsequently break away and advect towards the block. Detailed analysis of PIV measurements on the plane of symmetry indicates that the dominant mechanism for vorticity balance in the vortex system is the cross-cancellation of the vorticity of the necklace vortex with vorticity of opposite sign generated by interaction of the necklace vortex with the approach surface to the body.
Multi-mode models of flow and of solute dispersion in shallow water. Part 2. Logarithmic velocity profiles
Authors: Smith R.
Published: April 2006

A two-mode model for velocity and solute concentration in shallow-water flows is derived which allows for departures from the logarithmic velocity profile and from vertically well-mixed concentrations. The modelling is tested against exact results for a buoyancy-driven transverse flow and for a modified logarithmic velocity profile.
Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 2. Free jet flow
Authors: Dillmann Andreas
Published: April 2006

By extending the methods of Part 1, the general problem of steady cylindrical supersonic free jet flow is treated in a similar manner to the flow in quasi-cylindrical ducts. It is shown that the presence of a finite pressure jump at the nozzle lip gives rise to a periodic singularity pattern in the flow field. Basic examples of free jet flows are discussed, and for the case of a nearly ideally expanded axisymmetric jet, theoretical Mach—Zehnder interferograms are calculated by analytical integration of the density field. Excellent agreement with experiment proves the validity of linear theory even close to the singularities and far downstream of the nozzle orifice. Furthermore, it is shown that Pack's formula for the wavelength of the shock cell structure is inconsistent; the correct formula is derived and excellent agreement with Emden's empirical fit is found.
A numerical study of the shearing motion of emulsions and foams
Authors: Li Xiaofan , Zhou Hua , Pozrikidis C.
Published: April 2006

A numerical study is presented of the motion of two-dimensional, doubly periodic, dilute and concentrated emulsions of liquid drops with constant surface tension, subject to a simple shear flow. The numerical method is based on a boundary integral formulation that employs a Green's function for doubly periodic Stokes flow, computed using the Ewald summation method. Under the assumption that the viscosity of the drops is equal to that of the ambient fluid, the motion is examined in a broad range of capillary numbers, volume fractions, and initial geometrical configurations. The latter include square and hexagonal lattices of circular and closely packed hexagonal drops with rounded corners. Based on the nature of the asymptotic motion at large times, a phase diagram is constructed separating regions where periodic motion is established, or the emulsion is destabilized due to continued elongation or coalescence of intercepting drops. Comparisons with previous computations for bounded systems illustrate the significance of the walls on the evolution and rheological properties of an emulsion. It is shown that the shearing flow is able to stabilize a concentrated emulsion against the tendency of the drops to become circular and coalesce, thereby allowing for periodic evolution even when the volume fraction of the suspended phase might be close to that for dry foam. This suggests that the imposed shearing flow plays a role similar to that of the disjoining pressure for stationary foam. At high volume fractions, the geometry of the microstructure and flow at the Plateau borders and within the thin films separating adjacent drops are illustrated and discussed with reference to the predictions of the quasi-steady theory of foam. Although the accuracy of certain fundamental assumptions underlying the quasi-steady theory is not confirmed by the numerical results, we find qualitative agreement regarding the basic geometrical features of the evolving microstructure and effective rheological properties of the emulsion.
Another look at unidirectional turbulent flow
Authors: Reynolds A. J. , Wieghardt K.
Published: April 2006

Here we consider the mean velocity profile in the core region of a unidirectional turbulent flow, that is, a flow in which the turbulent motion is superposed upon parallel time-averaged streamlines. A kinematical variational principle, originally developed for three-dimensional free-turbulent motions, is shown to be applicable to significant parts of the velocity profiles for flows of both Couette and Poiseuille types. In addition to pure plane Couette and pure plane Poiseuille flows, the motions considered include a variety of admixtures produced by blowing through a wide flat channel one of whose walls comprises a belt which moves either in the direction of the blowing or counter to it.
Asymptotic solution of shock tube flows with homogeneous condensation
Authors: Delale Can F. , Schnerr Günter H. , Zierep Jürgen
Published: April 2006

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.
The stability of an interface between viscous fluids subjected to a high-frequency magnetic field and consequences for electromagnetic casting
Authors: Deepak  , Evans J. W.
Published: April 2006

The stability of an interface between inviscid fluids subjected to a high-frequency magnetic field has been examined previously by Garnier & Moreau (1983). The present paper extends that study to include the viscosity of both fluids in order to estimate the damping rates of the perturbations. Furthermore, Garnier & Moreau made an assumption that the frequency of oscillation of the interface could be neglected compared to the frequency of the applied field; they concluded that the applied field was not destabilizing. That (apparently reasonable) assumption has been lifted in the present work and the consequence is that the magnetic field is seen to lead to instability over a significant range of wavelengths. Application of this analysis to the electromagnetic casting of aluminium is discussed.
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.
Effect of wire separation on X-probe measurements in a turbulent flow
Authors: Zhu Y. , Antonia R. A.
Published: April 2006

The effect of the separation between hot wires in a crossed wire or X-probe on Reynolds stress measurements has been studied analytically and experimentally. Wyn-gaard's (1968) spectral analysis, which assumes isotropic turbulence, has been modified to include the effect of the tangential velocity component and possible asymmetries of the probe. The relaxation of the assumption of isotropy to one of homogeneity allows corrections to be made to Reynolds stress measurements obtained when the separation between the wires is in the spanwise direction. Measurements with two inclined hot wires in the central region of a fully developed turbulent channel flow provide reasonable support for the modified analysis. In the anisotropic wall region, the measurements provide reasonable support for the correction ratios which have been derived by assuming that turbulence is homogeneous in a plane parallel to the wall.