bluuebunny/crossref_metadata_2025 huggingface dataset:
Surface flow and vortex shedding of an impulsively started wing
Authors: HUANG R. F. , WU J. Y. , JENG J. H. , CHEN R. C.
Published: October 2003

The particle tracking flow visualization method (PTFV) and particle image velocimetry
(PIV) are used to obtain a clear picture of vortex evolution on the suction
surface of an impulsively started NACA 0012 wing. The experiments are conducted
in a towing water tank. The formation, evolution, and shedding of the vortex system
on the suction surface are observed and analysed by streak pictures of particle
images. Five characteristic vortex evolution regimes are identified in the parameter
domain of angle of attack and chord Reynolds number. The pathline patterns,
instantaneous streamlines, and vorticity of various vortex evolution processes are
presented. Stable vortex shedding in the wake is eventually established after the initial
period of complex vortex evolution on the suction surface of the wing. Various types
of instabilities in the wake, e.g. instability wave, surface vortex shedding, and bluff-body
vortex shedding, are found to correspond to different evolution processes of the
surface flow. The shedding frequency of the vortices is correlated and compared with
several conventional results. Topological critical points, separatrices, and alleyways
are identified and discussed to elucidate the unsteady structure of the instantaneous
streamline patterns. The topological rule for the number of singular points is verified.
Swash overtopping a truncated plane beach
Authors: PEREGRINE D. H. , WILLIAMS S. M.
Published: October 2003

Swash on a plane beach is modelled by using a solution of the shallow-water equations
due to Shen & Meyer (1963). The equations are used in a form appropriate for a
plane at a finite angle to the horizontal. The beach is cut-off at a level below that of
the maximum run-up, and the water is taken to fall freely over the end of the beach.
An explicit solution is found which permits evaluation of the overtopping flow and
total volume for one swash event.
On the slow draining of a gravity current moving through a layered permeable medium
Authors: PRITCHARD DAVID , WOODS ANDREW W. , HOGG ANDREW J.
Published: October 2003

We examine the gravitational dispersal of dense fluid through a horizontal permeable
layer, which is separated from a second underlying layer by a narrow band of much
lower permeability. We derive a series of analytical solutions which describe the
propagation of the fluid through the upper layer and the draining of the fluid into the
underlying region. The model predicts that the current initially spreads according to
a self-similar solution. However, as the drainage becomes established, the spreading
slows, and in fact the fluid only spreads a finite distance before it has fully drained into
the underlying layer. We examine the sensitivity of the results to the initial conditions
through numerical solution of the governing equations. We find that for sources
of sufficiently large initial aspect ratio (defined as the ratio of height to length), the
solution converges rapidly to the initially self-similar regime. For longer and shallower
initial source conditions, this convergence does not occur, but we derive estimates for
the run-out length of the current, which compare favourably with our numerical data.
We also present some preliminary laboratory experiments, which support the model.
Solid-body-type vortex solutions of the Euler equations
Authors: SHAPIRO ALAN
Published: October 2003

A class of unsteady vortex solutions of the Euler equations is investigated. The
solutions satisfy the von Kármán–Bödewadt similarity scalings and correspond to free
and forced oscillations of radially unbounded solid-body-type vortices with axially
varying rotation rates. The vortices may be of unbounded vertical extent or confined
by impermeable top and/or bottom plates. In the latter case the bounding plates
may be stationary or oscillatory. A solution breakdown result tends to support the
hypothesis that breakdown of viscous Bödewadt-type counter-rotating vortex flows
is an essentially inviscid process.
An exact form of Lilley's equation with a velocity quadrupole/temperature dipole source term
Authors: GOLDSTEIN M. E.
Published: October 2003

There have been several attempts to introduce approximations into the exact form
of Lilley's equation in order to express the source term as the sum of a quadrupole
whose strength is quadratic in the fluctuating velocities and a dipole whose strength
is proportional to the temperature fluctuations. The purpose of this note is to show
that it is possible to choose the dependent (i.e. the pressure) variable so that this type
of result can be derived directly from the Euler equations without introducing any
additional approximations.
Sensitive enhanced diffusivities for flows with fluctuating mean winds: a two-parameter study
Authors: BONN JAMES , McLAUGHLIN RICHARD M.
Published: October 2003

Enhanced diffusion coefficients arising from the theory of periodic homogenized
averaging for a passive scalar diffusing in the presence of a large-scale, fluctuating
mean wind superimposed upon a small-scale, steady flow with non-trivial topology are
studied. The purpose of the study is to assess how the extreme sensitivity of enhanced
diffusion coefficients to small variations in large-scale flow parameters previously
exhibited for steady flows in two spatial dimensions is modified by either the presence
of temporal fluctuation, or the consideration of fully three-dimensional steady flow.
We observe the various mixing parameters (Péclet, Strouhal and periodic Péclet
numbers) and related non-dimensionalizations. We document non-monotonic Péclet
number dependence in the enhanced diffusivities, and address how this behaviour is
camouflaged with certain non-dimensional groups. For asymptotically large Strouhal
number at fixed, bounded Péclet number, we establish that rapid wind fluctuations
do not modify the steady theory, whereas for asymptotically small Strouhal number
the enhanced diffusion coefficients are shown to be represented as an average over
the steady geometry. The more difficult case of large Péclet number is considered
numerically through the use of a conjugate gradient algorithm. We consider
Péclet-number-dependent Strouhal numbers, S = QPe−(1+γ), and
present numerical evidence documenting critical values of γ which distinguish the enhanced diffusivities as arising
simply from steady theory (γ < −1) for which fluctuation provides no averaging, fully
unsteady theory (γ ∈ (−1, 0)) with closure coefficients plagued by non-monotonic
Péclet number dependence, and averaged steady theory (γ > 0). The transitional case
with γ = 0 is examined in detail. Steady averaging is observed to agree well with
the full simulations in this case for Q [les ] 1, but fails for larger Q. For non-sheared
flow, with Q [les ] 1, weak temporal fluctuation in a large-scale wind is shown to reduce
the sensitivity arising from the steady flow geometry; however, the degree of this
reduction is itself strongly dependent upon the details of the imposed fluctuation.
For more intense temporal fluctuation, strongly aligned orthogonal to the steady
wind, time variation averages the sensitive scaling existing in the steady geometry,
and the present study observes a Pe1 scaling behaviour in the enhanced diffusion
coefficients at moderately large Péclet number. Finally, we conclude with the numerical
documentation of sensitive scaling behaviour (similar to the two-dimensional steady
case) in fully three dimensional ABC flow.
On the motion of multiple helical vortices
Authors: WOOD D. H. , BOERSMA J.
Published: October 2003

The analysis of the self-induced velocity of a single helical vortex (Boersma &
Wood 1999) is extended to include equally spaced multiple vortices. This arrangement
approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers,
or rotors in ascending, descending, or hovering flight. The problem is reduced to
finding, from the Biot–Savart law, the additional velocity of a helix due to an identical
helix displaced azimuthally. The resulting Biot–Savart integral is further reduced to a
Mellin–Barnes integral representation which allows the asymptotic expansions to be
determined for small and for large pitch. The Biot–Savart integral is also evaluated
numerically for a total of two, three and four vortices over a range of pitch values.
The previous finding that the self-induced velocity at small pitch is dominated by
a term inversely proportional to the pitch carries over to multiple vortices. It is
shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional
representation that leads to the Betz limit on the power output of wind
turbines. The small-pitch approximation then allows the determination of the blade&s
bound vorticity for optimum power extraction. The present analysis is shown to give
reasonable estimates for the vortex circulation in experiments using a single hovering
rotor and a four-bladed propeller.
On the different contributions of coherent structures to the spectra of a turbulent round jet and a turbulent boundary layer
Authors: NICKELS T. B. , MARUSIC IVAN
Published: October 2003

This paper examines and compares spectral measurements from a turbulent round jet
and a turbulent boundary layer. The conjecture that is examined is that both flows
consist of coherent structures immersed in a background of isotropic turbulence. In
the case of the jet, a single size of coherent structure is considered, whereas in the
boundary layer there are a range of sizes of geometrically similar structures. The
conjecture is examined by comparing experimental measurements of spectra for the
two flows with the spectra calculated using models based on simple vortex structures.
The universality of the small scales is considered by comparing high-wavenumber
experimental spectra. It is shown that these simple structural models give a good
account of the turbulent flows.
Experimental investigation of density
fluctuations in high-speed jets and correlation
with generated noise
Authors: PANDA J. , SEASHOLTZ R. G.
Published: October 2003

The air density fluctuations in the plumes of fully expanded, unheated free jets were
investigated experimentally using a Rayleigh-scattering-based technique. The point
measuring technique used a continuous-wave laser, fibre-optic transmission and photon counting electronics.
The radial and centreline profiles of time-averaged density
and root-mean-square density fluctuation provided a comparative description of jet
growth. To measure density fluctuation spectra a two-photomultiplier-tube (PMT)
technique was used. Cross-correlation between the two PMT signals significantly
reduced the electronic shot noise contribution. The density fluctuation spectra were
found to be remarkably similar for all Mach number jets. A detailed survey in fully
expanded Mach 0.95, 1.4 and 1.8 jets further confirmed that the distribution of various
Strouhal frequency fluctuations remained similar, except for a spatial stretching
with increased Mach number. In spite of this similarity in flow fluctuations the noise
sources in these three jets were found to be significantly different. Spark schlieren
photographs and near-field microphone measurements confirmed that Mach wave
radiation was present in the Mach 1.8 jet, and was absent in the Mach 0.95 jet. Direct
correlation measurement between the flow density fluctuation (cause) and far-field
sound pressure fluctuation (effect) shed further light on the sound generation process.
For this purpose a microphone was kept fixed at a far-field point, mostly at a distance
of 50 diameters and 30° to the flow direction, and the laser probe volume was moved
from point to point in the flow. In the Mach 1.8 jet, where the convective velocity
of Kelvin–Helmholtz instability waves exceeded the ambient sound speed, significant
correlation was measured from the peripheral shear layer, while in the Mach 0.95
jet, where the instability waves had subsonic convective speed, no correlation could
be measured. Although the same instability waves were present in both Mach 1.8
and 0.95 jets, the peripheral shear layer of the former was found to be an obvious
noise source, while that of the latter was not. Further correlation studies along the
jet centreline showed that behaviour in the region downstream of the potential core
was similar in all Mach number jets tested, 0:6[les ]M[les ]1:8. Good correlation at low
Strouhal frequencies was measured from this region, which started from downstream
of the potential core and extended many diameters from there.
Transient motion of a confined stratified fluid
induced simultaneously by sidewall thermal
loading and vertical throughflow
Authors: PARK JUN SANG , HYUN JAE MIN
Published: October 2003

An analytical study is made of the transient adjustment process of an initially
stationary, stably stratified fluid in a square container. The boundary walls are
highly conducting. The overall Rayleigh number Ra is large. Flow is initiated by the
simultaneous switch-on of a temperature increase (δT) at the vertical wall and a forced
vertical throughflow (Ra−1/4δw) at the horizontal walls. The principal characteristics
are found by employing the matched asymptotic expansion method. The flow field is
divided into the inviscid interior, vertical boundary layers and horizontal boundary
layers and analyses are conducted for each region. The horizontal boundary layers
are shown to be of double-layered structure, and explicit solutions are secured for
these layers. Evolutionary patterns of velocity and temperature in the whole flow
domain are illustrated. Both opposing (δw/δT > 0) and cooperating (δw/δT < 0)
configurations are considered. The flow character in the opposing configuration
can be classified into (a) a forced-convection dominant mode (δw/δT > 1/ √2),
(b) a buoyancy-convection-dominant mode (0 < δw/δT < 1/√2), and (c) a static
mode (δw/δT ≈ 1/√2). Global evolutionary processes are depicted, and physical
rationalizations are provided.
Moderate-Reynolds-number flow in a
wall-bounded porous medium
Authors: HILL REGHAN J. , KOCH DONALD L.
Published: October 2003

The transition to unsteady flow and the dynamics of moderate-Reynolds-number
flows in unbounded and wall-bounded periodic arrays of aligned cylinders are examined
using lattice-Boltzmann simulations. The simulations are compared to experiments,
which necessarily have bounding walls. With bounding walls, the transition
to unsteady flow is accompanied by a loss of spatial periodicity, and the temporal
fluctuations are chaotic at much smaller Reynolds numbers. The walls, therefore,
affect the unsteady flows everywhere in the domain. Consistency between experiments
and simulations is established by examining the wake lengths for steady flows and
the fundamental frequencies at higher Reynolds numbers, both as a function of the
Reynolds number. Simulations are used to examine the velocity fluctuations, flow
topologies, and the fluctuating forces on the cylinders.
Rayleigh–Bénard convection in liquid metal
layers under the influence of a horizontal
magnetic field
Authors: BURR ULRICH , MÜLLER ULRICH
Published: October 2003

This article presents an analytical and experimental study of magnetohydrodynamic
Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The
test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number
of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103<
Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.

When a horizontal magnetic field is imposed on a heated liquid metal layer, the
electromagnetic forces give rise to a transition of the three-dimensional convective roll
pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls
become more and more aligned with the magnetic field. A linear stability analysis
based on two-dimensional model equations shows that the critical Rayleigh number
for the onset of convection of quasi-two-dimensional flow is shifted to significantly
higher values due to Hartmann braking at walls perpendicular to the magnetic field.
This finding is experimentally confirmed by measured Nusselt numbers. Moreover,
the experiments show that the convective heat transport at supercritical conditions is
clearly diminished. Adjacent to the onset of convection there is a significant region
of stationary convection with significant convective heat transfer before the flow
proceeds to time-dependent convection. However, in spite of the Joule dissipation
effect there is a certain range of magnetic field intensities where an enhanced heat
transfer is observed. Estimates of the local isotropy properties of the flow by a four-element
temperature probe demonstrate that the increase in convective heat transport
is accompanied by the formation of strong non-isotropic time-dependent flow in the
form of large-scale convective rolls aligned with the magnetic field which exhibit a
simpler temporal structure compared to ordinary hydrodynamic flow and which are
very effective for the convective heat transport.
Collision of drops with inertia effects in strongly
sheared linear flow fields
Authors: PIGEONNEAU FRANCK , FEUILLEBOIS FRANÇOIS
Published: October 2003

The relative motion of drops in shear flows is responsible for collisions leading to
the creation of larger drops. The collision of liquid drops in a gas is considered here.
The drops are small enough for the Reynolds number to be low (negligible fluid
motion inertia), yet large enough for the Stokes number to be possibly of order unity
(non-negligible inertia in the motion of drops). Possible concurrent effects of Van der
Waals attractive forces and drop inertia are taken into account.

General expressions are first presented for the drag forces on two interacting drops
of different sizes embedded in a general linear flow field. These expressions are
obtained by superposition of solutions for the translation of drops and for steady
drops in elementary linear flow fields (simple shear flows, pure straining motions).
Earlier solutions adapted to the case of inertialess drops (by Zinchenko, Davis and
coworkers) are completed here by the solution for a simple shear flow along the line
of centres of the drops. A solution of this problem in bipolar coordinates is provided;
it is consistent with another solution obtained as a superposition of other elementary
flow fields.

The collision efficiency of drops is calculated neglecting gravity effects, that is
for strongly sheared linear flow fields. Results are presented for the cases of a
simple linear shear flow and an axisymmetric pure straining motion. As expected,
the collision efficiency increases with the Stokes numbers, that is with drop inertia.
On the other hand, the collision efficiency in a simple shear flow becomes negligible
below some value of the ratio of radii, regardless of drop inertia. The value of this
threshold increases with decreasing Van der Waals forces. The concurrence between
drop inertia and attractive van der Waals forces results in various anisotropic shapes
of the collision cross-section. By comparison, results for the collision efficiency in
an axisymmetric pure straining motion are more regular. This flow field induces
axisymmetric sections of collision and strong inertial effects resulting in collision
efficiencies larger than unity. Effects of van der Waals forces only appear when one
of the drops has a very low Stokes number.
On the spatio-temporal stability of primary and secondary crossflow vortices in a three-dimensional boundary layer
Authors: KOCH WERNER
Published: October 2003

To examine possible links between a global instability and laminar–turbulent breakdown
in a three-dimensional boundary layer, the spatio-temporal stability of primary
and secondary crossflow vortices has been investigated for the DLR swept-plate
experiment. In the absence of any available procedure for the direct verification of
pinching for three-dimensional wave packets the alternative saddle-point continuation
method has been applied. This procedure is known to give reliable results only in a
certain vicinity of the most unstable ray. Therefore, finding no absolute instability
by this method does not prove that the flow is absolutely stable. Accordingly, our
results obtained this way need to be confirmed experimentally or by numerical simulations.
A geometric interpretation of the time-asymptotic saddle-point result explains
certain convergence and continuation problems encountered in the numerical wave
packet analysis. Similar to previous results, all our three-dimensional wave packets
for primary crossflow vortices were found to be convectively unstable.

Due to prohibitive CPU time requirements the existing procedure for the verification
of pinching for two-dimensional wave packets of secondary high-frequency instabilities
could not be implemented. Again saddle-point continuation was used. Surprisingly, all
two-dimensional wave packets of high-frequency secondary instabilities investigated
were also found to be convectively unstable. This finding was corroborated by
recent spatial direct numerical simulations of Wassermann & Kloker (2001) for a
similar problem. This suggests that laminar–turbulent breakdown occurs after the
high-frequency secondary instabilities enter the nonlinear stage, and spatial marching
techniques, such as the parabolized stability equation method, should be applicable
for the computation of these nonlinear states.
Granular shear flows at the elastic limit
Authors: CAMPBELL CHARLES S.
Published: October 2003

This paper describes computer simulation studies of granular materials under dense
conditions where particles are in persistent contact with their neighbours and the
elasticity of the material becomes an important rheological parameter. There are two
regimes at this limit, one for which the stresses scale with both elastic and inertial
properties (called the elastic–inertial regime), and a non-inertial quasi-static regime in
which the stresses scale purely elastically (elastic–quasi-static). In these elastic regimes,
the forces are generated by internal force chains. Reducing the concentration slightly
causes a transition from an elastic to a purely inertial behaviour. This transition
occurs so abruptly that a 2% concentration reduction can be accompanied by nearly
three orders of magnitude of stress reduction. This indicates that granular flows near
this limit are prone to instabilities such as those commonly observed in shear cells.
Unexpectedly, there is no path between inertial (rapid) flow and quasi-static flow by
varying the shear rate at a fixed concentration; only by reducing the concentration
can one cause a transition from quasi-static to inertial flow. The solid concentrations
at which this transition occurs as well as the magnitude of the stresses in the elastic
regimes are strong functions of the particle surface friction, because the surface
friction strongly affects the strength of the force chains. A parametric analysis of the
elastic regime generated flowmaps showing the various regimes that might be realized
in practice. Many common materials such as sand require such large shear rates to
reach the elastic–inertial regime that it is unattainable for all practical purposes; such
materials will demonstrate either an elastic–quasi-static behaviour or a pure inertial
behaviour depending on the concentration – with many orders of magnitude of stress
change between them. Finally, the effects of nonlinear contacts are investigated and
an appropriate scaling is proposed that accounts for the nonlinear behaviour in the
elastic–quasi-static regime.
Self-organization mechanisms for the formation
of nearshore crescentic and transverse sand bars
Authors: CABALLERIA M. , COCO G. , FALQUÉS A. , HUNTLEY D. A.
Published: October 2003

The formation and development of transverse and crescentic sand bars in the coastal
marine environment has been investigated by means of a nonlinear numerical model
based on the shallow-water equations and on a simplified sediment transport parameterization. By assuming normally approaching waves and a saturated surf zone,
rhythmic patterns develop from a planar slope where random perturbations of
small amplitude have been superimposed. Two types of bedforms appear: one is a
crescentic bar pattern centred around the breakpoint and the other, herein modelled
for the first time, is a transverse bar pattern. The feedback mechanism related to the
formation and development of the patterns can be explained by coupling the water
and sediment conservation equations. Basically, the waves stir up the sediment and
keep it in suspension with a certain cross-shore distribution of depth-averaged concentration. Then, a current flowing with (against) the gradient of sediment concentration
produces erosion (deposition). It is shown that inside the surf zone, these currents
may occur due to the wave refraction and to the redistribution of wave breaking
produced by the growing bedforms. Numerical simulations have been performed in
order to understand the sensitivity of the pattern formation to the parameterization
and to relate the hydro-morphodynamic input conditions to which of the patterns
develops. It is suggested that crescentic bar growth would be favoured by high-energy
conditions and fine sediment while transverse bars would grow for milder waves and
coarser sediment. In intermediate conditions mixed patterns may occur.
Self-propelling slugs
Authors: BICO JOSÉ , QUÉRÉ DAVID
Published: October 2003

Surface coating is generally achieved by an active operation: painting with a brush;
withdrawing from a bath. Porous imbibition constitutes a more passive way: a porous
material just put in contact with a reservoir containing a wetting fluid is spontaneously
invaded. In this case, the material can eventually be filled by the fluid. If the aim
is to coat only the surface of the pores, the liquid excess must be actively removed.
We present an experiment in which a liquid train spontaneously moves in a capillary
tube because of the trail it leaves behind. From a practical point of view, this system
achieves a coating of the tube. The condition required for this motion and a model
for its dynamics are presented. We also show how these trains can drive extremely
viscous liquid slugs (or even solid bodies) in narrow tubes. We discuss the thickness of
the deposited films. Extensions and limits of this system in more complex geometries
are finally described, together with special cases such as the deposition of solid films.
Kármán–Howarth theorem for the Lagrangian-averaged Navier–Stokes–alpha model of turbulence
Authors: HOLM DARRYL D.
Published: October 2003

The Lagrangian averaged Navier–Stokes–alpha (LANS-α) model of turbulence is
found to possess a Kármán–Howarth (KH) theorem for the dynamics of its second-order
autocorrelation functions in homogeneous isotropic turbulence. This KH result
implies that alpha-filtering in the LANS-α model of turbulence does not affect
the exact Navier–Stokes relation between second and third moments at separation
distances large compared to the model's length scale α. Moreover, at separations r that
are smaller than α, the KH scaling between energy dissipation rate and longitudinal
third-order autocorrelation changes to match the scaling found in two-dimensional
incompressible flow. This is consistent with the corresponding change in scaling of
the kinetic energy spectrum from k−5/3 for larger scales with
kα < 1, which switches to k−3 for smaller scales
with kα > 1, as discovered in Foias, Holm & Titi (2001).
Internal hydraulic jumps and mixing
in two-layer flows
Authors: HOLLAND DAVID M. , ROSALES RODOLFO R. , STEFANICA DAN , TABAK ESTEBAN G.
Published: October 2003

Internal hydraulic jumps in two-layer flows are studied, with particular emphasis
on their role in entrainment and mixing. For highly entraining internal jumps, a
new closure is proposed for the jump conditions. The closure is based on two main
assumptions: (i) most of the energy dissipated at the jump goes into turbulence,
and (ii) the amount of turbulent energy that a stably stratified flow may contain
without immediately mixing further is bounded by a measure of the stratification. As
a consequence of this closure, surprising bounds emerge, for example on the amount
of entrainment that may take place at the location of the jump. These bounds are
probably almost achieved by highly entraining internal jumps, such as those likely to
develop in dense oceanic over flows. The values obtained here are in good agreement
with the existing observations of the spatial development of oceanic downslope
currents, which play a crucial role in the formation of abyssal and intermediate
waters in the global ocean.
Determination of surface shear viscosity via
deep-channel flow with inertia
Authors: HIRSA A. H. , LOPEZ J. M. , MIRAGHAIE R.
Published: October 2003

Results of an experimental and computational study of the flow in an annular
region bounded by stationary inner and outer cylinders and driven by the rotation
of the floor are presented. The top is a flat air/water interface, covered by an
insoluble monolayer. We develop a technique to determine the surface shear viscosity
from azimuthal velocity measurements at the interface which extends the range of
surface shear viscosity that can be measured using a deep-channel viscometer in the
usual Stokes flow regime by exploiting flow inertia. A Navier–Stokes-based model
of bulk flow coupled to a Newtonian interface that has surface shear viscosity as
the only interfacial property is developed. This is achieved by restricting the flow to
regimes where the surface radial velocity vanishes. The use of inertia results in an
improved signal-to-noise ratio of the azimuthal velocity measurements by an order of
magnitude beyond that available in the Stokes flow limit. Measurements on vitamin
K1 and stearic acid monolayers were performed, and their surface shear viscosities
over a range of concentrations are determined and found to be in agreement with
data in the literature.
Three-dimensional instability in flow over a
backward-facing step
Authors: BARKLEY DWIGHT , GOMES M. GABRIELA M. , HENDERSON RONALD D.
Published: October 2003

Results are reported from a three-dimensional computational stability analysis of flow
over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at
Reynolds numbers between 450 and 1050. The analysis shows that the first absolute
linear instability of the steady two-dimensional flow is a steady three-dimensional
bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized
to the primary separation bubble and has a flat roll structure with a spanwise
wavelength of 6.9 step heights. The system is further shown to be absolutely stable
to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra
and visualizations of the global modes of the system are presented for representative
Reynolds numbers.
Rheology of bidisperse granular mixtures via
event-driven simulations
Authors: ALAM MEHEBOOB , LUDING STEFAN
Published: October 2003

The bulk rheology of bidisperse mixtures of granular materials is examined under
homogeneous shear flow conditions using the event-driven simulation method. The
granular material is modelled as a system of smooth inelastic disks, interacting via
the hard-core potential. In order to understand the effect of size and mass disparities,
two cases were examined separately, namely, a mixture of different sized particles
with particles having either the same mass or the same material density. The relevant
macroscopic quantities are the pressure, the shear viscosity, the granular energy
(fluctuating kinetic energy) and the first normal stress difference.

Numerical results for pressure, viscosity and granular energy are compared with a
kinetic-theory constitutive model with excellent agreement in the low dissipation limit
even at large size disparities. Systematic quantitative deviations occur for stronger
dissipations. Mixtures with equal-mass particles show a stronger shear resistance
than an equivalent monodisperse system; in contrast, however, mixtures with equal-density
particles show a reduced shear resistance. The granular energies of the two
species are unequal, implying that the equi-partition principle assumed in most of the
constitutive models does not hold. Inelasticity is responsible for the onset of energy
non-equipartition, but mass disparity significantly enhances its magnitude. This lack of
energy equipartition can lead to interesting non-monotonic variations of the pressure,
viscosity and granular energy with the mass ratio if the size ratio is held fixed,
while the model predictions (with the equipartition assumption) suggest a monotonic
behaviour in the same limit. In general, the granular fluid is non-Newtonian with a
measurable first normal stress difference (which is positive if the stress is defined in
the compressive sense), and the effect of bidispersity is to increase the normal stress
difference, thus enhancing the non-Newtonian character of the fluid.
Weakly nonlinear surface waves over a
random seabed
Authors: MEI CHIANG C. , HANCOCK MATTHEW J.
Published: October 2003

We study the effects of multiple scattering of slowly modulated water waves by a
weakly random bathymetry. The combined effects of weak nonlinearity, dispersion
and random irregularities are treated together to yield a nonlinear Schrödinger
equation with a complex damping term. Implications for localization and side-band
instability are discussed. Transmission and nonlinear evolution of a wave packet past
a finite strip of disorder is examined.
The effect of base flow variation on flow stability
Authors: BOTTARO ALESSANDRO , CORBETT PETER , LUCHINI PAOLO
Published: October 2003

The Orr–Sommerfeld operator's eigenvalues determine the stability of exponentially growing disturbances in parallel and quasi-parallel flows. This work assesses the sensitivity of these eigenvalues to modifications of the base flow, which need not be infinitesimally small. Such base flow variations may represent differences between the laboratory flow and its ideal, theoretical counterpart. The worst case, i.e. the change in base flow with the most destabilizing effect on the eigenvalues, is found using variational techniques for the plane Couette flow. Relatively small changes in the base flow are shown to be destabilizing, although the ideal flow is unconditionally stable according to linear theory. These observations inspire a velocity-based definition of pseudospectra in the hydrodynamic stability context.
Transient dynamics at the onset of Taylor vortices
Authors: ABSHAGEN J. , MEINCKE O. , PFISTER G. , CLIFFE K. A. , MULLIN T.
Published: October 2003

The effect of boundary conditions on the ‘critical dynamics’ at the onset of Taylor vortices is investigated in a combined numerical and experimental study. Numerical calculations of Navier–Stokes equations with ‘stress-free’ boundary conditions show that the Landau amplitude equation provides a good model of the transient dynamics. However, this rapidly breaks down when the ‘no-slip’ condition is approached. Apparent ‘critical’ behaviour observed in experiments is shown to have a surprising dependence on the length of the system.
The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube
Authors: GHADIALI SAMIR N. , GAVER DONALD P.
Published: October 2003

We have utilized a computational model of semi-infinite air bubble progression in a
surfactant-doped, fluid-filled rigid capillary to investigate the continual interfacial
expansion dynamics that occur during the opening of collapsed pulmonary airways. This model
simulates mixed-kinetic conditions with nonlinear surfactant equations of state similar to
those of pulmonary surfactant. Several dimensionless parameters govern the system responses:
the capillary number (Ca) that relates viscous to surface tension forces; the elasticity
number (El), a measure of the ability of surfactant to modify the surface tension; the
bulk Péclet number (Pe), relating bulk convection rates to diffusion rates;
the adsorption and desorption Stanton numbers (Sta and
Std) that relate the adsorption/desorption rates to
surface convective rates; and finally the adsorption depth (λ), a dimensionless
bulk surfactant concentration parameter. We investigated this model by performing detailed
parameter variation studies at fixed and variable equilibrium concentrations. We find that
the surfactant properties can strongly influence the interfacial pressure drop through
modification of the surface tension and the creation of Marangoni stresses that influence
the viscous stresses along the interface. In addition, these studies demonstrate that,
depending upon the range of parameters, either film thickening or film thinning responses
are possible. In particular, we find that when Pe[Gt ]1 (as with pulmonary surfactant)
or when sorption rates are low, concentration profiles can substantially differ from near-equilibrium
approximations and can result in film thinning. These responses may influence stresses on
epithelial cells that line pulmonary airways and the stability of these airways, and may be
important to the delivery of exogenous surfactant to deep regions of the lung.
Experiments on the stability of sinusoidal flow over a circular cylinder
Authors: SARPKAYA TURGUT
Published: October 2003

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular
cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1
and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from
inception to chaos using several high-speed imagers and laser-induced fluorescence.
The instabilities ranged from small quasi-coherent structures, as in Stokes flow over
a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because
of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler
instability). These gave rise to streamwise-oriented counter-rotating vortices
or mushroom-shaped coherent structures as K approached the Kh values theoretically
predicted by Hall (1984). Further increases in K for a given β led first to complex
interactions between the coherent structures and then to chaotic motion. The mapping
of the observations led to the delineation of four states of flow in the (K, β)-plane:
stable, marginal, unstable, and chaotic.
Electric measurements of charged sprays emitted by cone-jets
Authors: GAMERO-CASTAÑO MANUEL , HRUBY VLADIMIR
Published: October 2003

We use time-of-flight and energy analysis techniques to measure in a vacuum the
charge, specific charge and stopping potential of primary and satellite droplets generated
by electrosprays of tributyl phosphate solutions. This information, of interest
in itself, is subsequently analysed to obtain the following relevant parameters of the
jet emanating from the Taylor cone: the velocity of the fluid at the breakup point,
the voltage difference between the liquid cone and jet breakup location, and the most
probable wavelength for varicose breakup. A large fraction of the electrospray needle
voltage is used to accelerate the jet. Indeed, for the solutions of lowest electrical
conductivities studied here, the voltage difference between electrospray needle and jet
breakup location becomes approximately 90% of the needle voltage. In addition, the
pressure of the jet fluid at the breakup point is negligible compared to its specific
kinetic energy. The specific charge distribution function of the main droplets produced
in the varicose breakup is remarkably narrow. Hence, the limiting and commonly
accepted case of varicose breakup at constant electric potential is not consistent with
this experimental observation. On the other hand, a scenario in which the electric
charge is bound to the jet surface seems to be a good approximation to simulate the
effect of charge on capillary breakup. It is also found that the effect of viscosity on the
formation of droplets is paramount in electrosprays of moderate and high electrical
conductivity. We expect that these measurements will guide the analytical modelling
of cone-jets.
Onset of menisci
Authors: CLANET CHRISTOPHE , QUÉRÉ DAVID
Published: October 2003

When a vertical solid is brought in contact with the surface of a wetting liquid, a
meniscus starts rising up the solid, until it reaches its steady state. We study this
dynamical phenomenon experimentally with liquids of low and high viscosity, and
taking as solids either large rods or small fibres. In the inviscid limit, we show that
the rising time scales as √(ρr30/σ), where ρ and σ are the density and surface tension
of the wetting liquid and r0 the radius of the fibre. This characteristic time holds for
small fibres, with radii smaller than the capillary length a. For large rods or planar
solids, r0 is replaced by a in the expression for the rising time. In the viscous limit, the
rising time scales as ηr0/σ where η is the dynamical viscosity. Again, r0 is replaced by
the capillary length a for large rods.
The manipulation of the streamwise vortex
instability in a natural convection boundary
layer along a heated inclined flat plate
Authors: TRAUTMAN MARK A. , GLEZER ARI
Published: October 2003

Flow instabilities leading to the formation of streamwise vortices in a natural convection boundary layer over a heated inclined plate submerged in a water tank are
manipulated using spanwise arrays of surface-mounted heating elements. The flow
over the plate is driven by a two-ply surface heater comprised of a uniform, constant-
heat flux heater and a mosaic of 32
×
12 individually controlled heating elements
that are used as control actuators. Surface temperature distributions are measured
using liquid crystal thermography and the fluid velocity in cross-stream planes is
measured using particle image velocimetry (PIV). Time-invariant spanwise-periodic
excitation over a range of spanwise wavelengths leads to the formation of arrays of
counter-rotating streamwise vortex pairs and to substantial modification of the surface
temperature and heat transfer. The increase in surface heat transfer is accompanied
by increased entrainment of ambient fluid and, as a consequence, higher streamwise flowrate. Subsequent spanwise-periodic merging of groups of vortices farther
downstream retards the streamwise increase of the surface heat transfer rate. Finally,
the suppression of small-amplitude spanwise disturbances by linear cancellation is
demonstrated.
Bubble collapse near a solid boundary: a numerical study of the influence of viscosity
Authors: POPINET STÉPHANE , ZALESKI STÉPHANE
Published: October 2003

The effect of viscosity on jet formation for bubbles collapsing near solid boundaries
is studied numerically. A numerical technique is presented which allows the Navier–Stokes
equations with free-surface boundary conditions to be solved accurately and
efficiently. Good agreement is obtained between experimental data and numerical
simulations for the collapse of large bubbles. However, the bubble rebound in our
simulation is larger than that observed in laboratory experiments. This leads us to
conclude that compressible and thermal effects should be taken into account to obtain
a correct model of the rebound. A parametric study of the effect of viscosity on jet
impact velocity is undertaken. The jet impact velocity is found to decrease as viscosity
increases and above a certain threshold jet impact is impossible. We study how this
critical Reynolds number depends on the initial radius and the initial distance from
the wall. A simple scaling law is found to link this critical Reynolds number to the
other non-dimensional parameters of the problem.
On the stability of a falling liquid curtain
Authors: SCHMID PETER J. , HENNINGSON DAN S.
Published: October 2003

The stability of a falling liquid curtain is investigated. The sheet of liquid is assumed
two-dimensional, driven by gravity and influenced by a compressible cushion of air
enclosed on one side of the curtain. The linear stability problem is formulated in
the form of an integro-differential eigenvalue problem. Although experimental efforts
have consistently reported a peak in the low-frequency range of the spectrum, the
linear stability results do not show instabilities at these frequencies. However, a
multi-modal approach combined with a projection onto low-frequency modes reveals a
dominant and robust instability feature that is in good agreement with experimental
measurements. This instability manifests itself as a wave packet, consisting of a linear
superposition of linear global modes, that travels down the curtain and causes a
strong pressure signal in the enclosed air cushion.
Kinetic ion gradient instability: bifurcation properties of a simple, kinetic ηi-unstable slab model
Authors: SIEKS O. , SPATSCHEK K. H.
Published: October 2003

The so-called ηi instability is driven by the ion-temperature gradient and
affects both particle and energy transport. Using a simple kinetic model, first the
onset of the instability is investigated by linear theory. In contrast to most treatments
in the literature, a non-local analysis is performed. It turns out that the
local approximation is only a very rough approximation, and may drastically overestimate
the instability conditions. A numerical solution of the full model confirms
the non-local stability analysis. In addition, it allows one to follow the nonlinear
development of the instability. Using a numerical scheme based on the Lagrange
structure of the equations of motion, the saturation values are obtained. A constriction
of the density profile is accompanied by a broadening of the ion-temperature
profile. The normal form of the bifurcation is obtained, together with the scaling of
the anomalous transport (in terms of the deviation from the marginal condition).
Stationary waves in a bi-ion plasma transverse to the magnetic field
Authors: McKENZIE J. F. , SAUER K. , DUBININ E.
Published: October 2003

We investigate the nature of stationary structures streaming at subfast
magnetosonic speeds perpendicular to the magnetic field in a bi-ion plasma consisting
of protons and a heavy ion species in which the magnetic field is frozen into the
electrons, whose inertia may be neglected. The study is based on the properties of
the structure equation for the system, which is derived from the equations of motion
and the Maxwell equations, and therefore reflects the coupling between the two ion
fluids and the electrons through the Lorentz forces and charge neutrality. The basic
features of the structure equation are elucidated by making use of conservation of
total momentum and charge neutrality, which provide relations between the ion
speeds in the unperturbed flow direction and the electron speed. This combination
of relations, which we call the momentum hodograph of the system, reveals the
structure of the flow and the magnetic field in a solitary-type pulse. In particular,
we find that in the initial portion of a compressive soliton, heavy ions run ahead
of the electrons and the protons lag between them until a point is reached where
they all once more attain the same speed, after which the protons run ahead and
are accelerated whereas the heavies now lag behind the continuously decelerating
electrons. The second half of the wave is a mirror image of the first portion. The
strength of the compression (the amplitude of the wave) is determined from the
momentum hodograph, and depends upon the initial Mach number, abundance ratio
of heavies to protons and the mass ratio. The analysis is relevant to subfast
flows of mass-loaded plasmas and pile-up boundaries, which appear near comets
and non-magnetic planets.