bluuebunny/crossref_metadata_2025 huggingface dataset:
Bragg scattering of random surface gravity waves by irregular seabed topography
Authors: ARDHUIN FABRICE , HERBERS T. H. C.
Published: August 2008

The Bragg scattering of random, non-stationary surface gravity waves by random
topography on a gently sloping bottom is investigated. A correction is given of
previously published expressions for the triad wave–wave–bottom interaction source
term in the spectral energy balance equation, and the result is reconciled with
deterministic theories for the reflection of waves from sinusoidal seabed undulations.
For both normal and oblique incidence, the stochastic and deterministic theories are
equivalent in the limit of long propagation distances. Even for relatively short distances
(for example two bottom undulations), the reflected energy predicted by the stochastic
source term formulation is generally within 15% of values predicted by deterministic
theories. The detuning of Bragg resonance by refraction and shoaling is discussed,
suggesting practical validity conditions for the stochastic theory. The effect of bottom
scattering on swell propagation is illustrated with numerical model computations for
the North Carolina continental shelf using high-resolution bathymetry and an efficient
semi-implicit scheme to evaluate the bottom scattering source term and integrate
the energy balance equation. Model results demonstrate the importance of forward
scattering of waves that propagate at large oblique angles over bottom features
with typical scales of one to several surface wavelengths. This process contributes
significantly to the directional spread of swell on the continental shelf by diffusing
energy, in the spectrum, around the mean wave direction. Back-scattering, caused by
bottom features with crests parallel to those of the surface waves and wavelengths
close to half the surface wavelength, is weak, owing to the sharp roll-off of the bottom
elevation spectrum at high wavenumbers. Model predictions are consistent with field
measurements.
Subcritical transition in channel flows
Authors: CHAPMAN S. JONATHAN
Published: August 2008

Certain laminar flows are known to be linearly stable at all Reynolds numbers, R,
although in practice they always become turbulent for sufficiently large R. Other
flows typically become turbulent well before the critical Reynolds number of linear
instability. One resolution of these paradoxes is that the domain of attraction for
the laminar state shrinks for large R (as Rγ say, with γ < 0), so that small but
finite perturbations lead to transition. Trefethen et al. (1993) conjectured that in fact
γ <−1. Subsequent numerical experiments by Lundbladh, Henningson & Reddy
(1994) indicated that for streamwise initial perturbations γ =−1 and −7/4 for plane
Couette and plane Poiseuille flow respectively (using subcritical Reynolds numbers
for plane Poiseuille flow), while for oblique initial perturbations γ =−5/4 and −7/4
Here, through a formal asymptotic analysis of the Navier–Stokes equations, it is found
that for streamwise initial perturbations γ =−1 and −3/2 for plane Couette and plane
Poiseuille flow respectively (factoring out the unstable modes for plane Poiseuille flow),
while for oblique initial perturbations γ =−1 and −5/4. Furthermore it is shown why
the numerically determined threshold exponents are not the true asymptotic values.
Generation of slow large scales in forced rotating stratified turbulence
Authors: SMITH LESLIE M. , WALEFFE FABIAN
Published: August 2008

Numerical simulations are used to study homogeneous, forced turbulence in three-dimensional
rotating, stably stratified flow in the Boussinesq approximation, where the
rotation axis and gravity are both in the zˆ-direction. Energy is injected through a three-dimensional
isotropic white-noise forcing localized at small scales. The parameter
range studied corresponds to Froude numbers smaller than an O(1) critical value,
below which energy is transferred to scales larger than the forcing scales. The values
of the ratio N/f range from ≈1/2 to ∞, where N is the Brunt–Väisälä frequency
and f is twice the rotation rate. For strongly stratified flows (N/f[Gt ]1), the slow
large scales generated by the fast small-scale forcing consist of vertically sheared
horizontal flow. Quasi-geostrophic dynamics dominate, at large scales, only when
1/2 [les ] N/f [les ] 2, which is the range where resonant triad interactions cannot occur.
Start-up flows in a three-dimensional rectangular
driven cavity of aspect ratio 1:1:2 at Re = 1000
Authors: GUERMOND J.-L. , MIGEON C. , PINEAU G. , QUARTAPELLE L.
Published: August 2008

This paper provides comparisons between experimental data and numerical results
for impulsively started flows in a three-dimensional rectangular lid-driven cavity of
aspect ratio 1:1:2 at Reynolds number 1000. The initial evolution of this flow is
studied up to the dimensionless time t = 12 and is found both experimentally and
numerically to exhibit high sensitivity to geometrical perturbations. Three different
flow developments generated by very small changes in the boundary geometry are
found in the experiments and are reproduced by the numerics. This indicates that even
at moderate Reynolds numbers the predictability of three-dimensional incompressible
viscous flows in bounded regions requires controlling the shape of the boundary and
the values of the boundary conditions more carefully than needed in two dimensions.
Instability of an annular jet surrounded by a viscous gas in a pipe
Authors: CHEN J. N. , LIN S. P.
Published: August 2008

The onset of instability in a liquid annular jet enclosing another fluid, and surrounded
by a gas in a pipe is analysed by use of a spectra-collocation method. The dynamic
responses to the variation of different flow parameters are elucidated by use of
numerical results. Two linearly independent convectively unstable interfacial modes
of disturbances are found. In general, the para-sinuous mode has a larger amplification
rate than the para-varicose mode. It is shown that to initiate encapsulation of core
fluid with a uniform shell fluid, the growth of the para-sinuous mode must be
promoted and the para-varicose mode must be suppressed. Suppression of the
paravaricose mode in a finite range of wavenumbers is possible by varying the flow
parameters. The effects of ten relevant parameters on instability are discussed. In
certain parameter space, the annular jet becomes absolutely unstable with respect to
the sinuous mode. The transition Weber number below which the flow is absolutely
unstable and above which the flow is convectively unstable is found as a function
of the Reynolds number when the rest of flow parameters are given. A successful
encapsulation of core fluid with a uniform shell fluid is possible if the process is
carried out outside of the parameter space of absolute instability, and if an external
forcing is introduced at a frequency within a band in which the para-varicose mode
is stable but the para-sinuous mode is convectively unstable.
Convection in a spherical capacitor
Authors: AMARA KAMEL , HEGSETH JOHN
Published: August 2008

Real-time holographic interferometry and shadowgraph visualization are used to study
convection in the fluid between two concentric spheres when two distinct buoyancy
forces are applied to the fluid. The heated inner sphere has a constant temperature that
is greater than the constant temperature of the outer sphere by ΔT. In addition to the
usual gravitational buoyancy from temperature induced density differences, another
radial buoyancy is imposed by applying an a.c. voltage difference, ΔV between the
inner and outer spheres. The resulting electric field gradient in this spherical capacitor
produces a central polarization force. The temperature dependence of the dielectric
constant results in the second buoyancy force that is especially large near the inner
sphere. The normal buoyancy is always present and, within the parameter range
explored in our experiment, always results in a large-scale cell that is axisymmetric
about the vertical. We have found that this flow becomes unstable to toroidal or
spiral rolls that form near the inner sphere and travel vertically upward when ΔT
and ΔV are suffciently high. These rolls start near the centre sphere's equator and
travel upward toward its top. The onset of this instability depends on both the
temperature difference at onset ΔTc and the voltage difference at onset ΔVc and
these two quantities appear to be related, within the parameter range accessible to
our experimental system, by a power law ΔVc ∝ ΔT1/3c. Measurements of the heat
transfer show that these travelling rolls increase the heat transfer at onset. Far above
onset, the heat transfer may actually decrease with increasing ΔT. The travelling
roll's frequency increases with increasing ΔT near onset and with increasing ΔV far
above onset. These results have been interpreted in terms of a flow structure that
includes a thermal boundary-layer-like behaviour. This layer has a radial width that
increases from the bottom pole to an unstable ‘latitude’ near the equator where the
rolls appear.
Direct numerical simulation of turbulent channel
flow with permeable walls
Authors: HAHN SEONGHYEON , JE JONGDOO , CHOI HAECHEON
Published: August 2008

The main objectives of this study are to suggest a proper boundary condition at the
interface between a permeable block and turbulent channel flow and to investigate
the characteristics of turbulent channel flow with permeable walls. The boundary
condition suggested is an extended version of that applied to laminar channel flow
by Beavers & Joseph (1967) and describes the behaviour of slip velocities in the
streamwise and spanwise directions at the interface between the permeable block
and turbulent channel flow. With the proposed boundary condition, direct numerical
simulations of turbulent channel flow that is bounded by the permeable wall
are performed and significant skin-friction reductions at the permeable wall are
obtained with modification of overall flow structures. The viscous sublayer thickness
is decreased and the near-wall vortical structures are significantly weakened by the
permeable wall. The permeable wall also reduces the turbulence intensities, Reynolds
shear stress, and pressure and vorticity fluctuations throughout the channel except
very near the wall. The increase of some turbulence quantities there is due to the
slip-velocity fluctuations at the wall. The boundary condition proposed for the
permeable wall is validated by comparing solutions with those obtained from a separate
direct numerical simulation using both the Brinkman equation for the interior of a
permeable block and the Navier–Stokes equation for the main channel bounded by a
permeable block.
Oscillating structures in a stretched–compressed
vortex
Authors: ABID MALEK , ANDREOTTI BRUNO , DOUADY STÉPHANE , NORE CAROLINE
Published: August 2008

The dynamics of a vortex subject to a localized stretching is numerically investigated.
The structure of the flow is analysed in the case of an initially two-dimensional vortex
surrounded by a periodic array of vortex rings localized far from its core. Amplified
oscillations of both the axial vorticity and the stretching are found, in strong contrast
with Burgers-like vortices. The resulting dynamics is the appearance, around the
vortex, of successive vortical structures of smaller and smaller radius and alternate
sign embedded in the previous vortical rings. The frequency scaling of the oscillations
is recovered by linear analysis (Kelvin modes) but not the amplification nor the
shape of the successive tori. An inviscid model based on structures is presented,
which compares better with the numerical computations. These results suggest that
the formalism of Kelvin waves is not sufficient to describe the full dynamics, which
is instead related to the feedback of rotation on stretching and more conveniently
described in terms of localized structures. We finally discuss the relative timescales of
vortex stretching and of vortex reaction. The Burgers-like vortices, where there is no
such reaction, turn out to correspond to a nearly pure strain field, slightly disturbed
by rotation.
Aerodynamic flow-vectoring of a planar jet in a co-flowing stream
Authors: LIM DAVID W. , REDEKOPP LARRY G.
Published: August 2008

The vectoring of an incompressible, two-dimensional jet in a co-flowing stream is
investigated by means of direct numerical simulation. The control input used to
stimulate jet vectoring is accomplished through distributed suction from blunt-faced
lips at the exit of the jet. The thrust vector methodology is based on suppression
of global instabilities in the wake-shear layers formed between the co-flow and the
jet. Once a critical suction volume flux needed to suppress these global instabilities
is exceeded, local flow control can be realized through varying the distribution of
suction across the base of the jet lips. It is found that the critical suction flux scales
primarily with the ambient co-flow, not with the jet speed, and that lift-to-thrust
ratios exceeding 15% can be realized. The effects of jet Reynolds number, jet-to-
ambient velocity ratio, boundary-layer thickness, and geometric parameters on various
performance characteristics are examined. It is also shown that the asymmetric flow
control approach used for vectoring the jet can also be implemented in a symmetric
configuration to enhance jet spreading. Significant increases in jet spreading can be
realized when the symmetrically applied suction flux is sufficient to stimulate the
sinuous mode of instability of the jet such that energetic apping motion ensues.
Fluidization of 1204 spheres: simulation and experiment
Authors: PAN T.-W. , JOSEPH D. D. , BAI R. , GLOWINSKI R. , SARIN V.
Published: August 2008

In this paper we study the fluidization of 1204 spheres at Reynolds numbers in the
thousands using the method of distributed Lagrange multipliers. The results of the
simulation are compared with an experiment. This is the first direct numerical
simulation of a fluidized bed at the finite Reynolds numbers encountered in applications.
The simulations are processed to give straight lines in log–log plots leading to power
laws as in the celebrated experimental correlations of Richardson & Zaki (1954).
The numerical method allows the first direct calculation of the slip velocity and
other averaged values used in two-fluid continuum models. The computation and the
experiment show that a single particle may be in balance with respect to weight and
drag for an interval of fluidizing velocities; the expectation that the fluidizing velocity
is unique is not realized. The numerical method reveals that the dynamic pressure
decreases slowly with the fluidizing velocity. Tentative interpretations of these new
results are discussed.
Some observations of the effects of
micro-organisms growing on the bed of an open
channel on the turbulence properties
Authors: NIKORA V. I. , GORING D. G. , BIGGS B. J. F.
Published: August 2008

In this paper we report the results of an experimental study of periphyton–flow
interactions conducted in a specially designed outdoor hydraulic flume. ‘Periphyton’
is a collective term for the micro-organisms which grow on stream beds, and includes
algae, bacteria, and fungi, with algae usually the dominant and most conspicuous
component. The main goals of the study are to identify potential effects of periphyton–flow interactions as
well as the potential mechanisms of mass transfer in the near-bed
region, which could influence periphyton growth and losses. The main results of the
study may be summarized as follows.

A linear velocity distribution in the interfacial sublayer (i.e. below the roughness
tops), and a logarithmic distribution above the roughness tops appeared to be reasonable
approximations for both flow types, with and without periphyton on the
bed. However, the appearance of periphyton on a rough bed shifts the origin of the
bed upwards, increases the roughness length zo by 16–21%, and reduces the ratio of
the mean velocity at the level of roughness tops to the shear velocity by
≈30%. In general, below the roughness tops the periphyton suppresses the mean velocities, the
turbulent stresses, turbulence intensities, and vertical turbulent fluxes of the turbulent
energy and turbulent shear stresses.

It was found that in flows without periphyton large-scale eddies successfully penetrate
the interfacial sublayer. However, tufts of periphyton on the tops of the
roughness elements significantly weaken the penetration processes leading to spatial
de-correlation in the velocity field within the interfacial sublayer. The appearance of
periphyton on the bed does not change appreciably the velocity spectra above the
roughness tops but reduces the total spectral energy and generates a wide spectral
peak in the interfacial sublayer. Most probably, this peak is formed by penetration
of sweep events into the interfacial sublayer, ‘filtered’ by the periphyton tufts. Thus,
sweep events may be the main mechanism responsible for the delivery of nutrients
from the outer region to the biologically active interfacial sublayer. The potential
effects of flow properties on the periphyton community are also discussed.
Spatial versions of the Zakharov and Dysthe
evolution equations for deep-water gravity waves
Authors: KIT ELIEZER , SHEMER LEV
Published: August 2008

A spatial two-dimensional version of the Zakharov equation describing the evolution
of deep-water gravity waves is used to derive two fourth-order evolution equations,
for the amplitudes of the surface elevation and of the velocity potential. The scaled
form of the equations is presented.
Density-driven unstable flows of miscible fluids in a Hele-Shaw cell
Authors: FERNANDEZ J. , KUROWSKI P. , PETITJEANS P. , MEIBURG E.
Published: August 2008

Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are
investigated by means of experimental measurements, as well as two- and three-dimensional
numerical simulations. The experiments focus on the early stages of the
instability growth, and they provide detailed information regarding the growth rates
and most amplified wavenumbers as a function of the governing Rayleigh number Ra.
They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime
in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in
which the length scale of the instability is 5±1 times the gap width. The experiments
are compared to a recent linear stability analysis based on the Brinkman equation.
The analytical dispersion relationship for a step-like density profile reproduces the
experimentally observed trend across the entire Ra range. Nonlinear simulations
based on the two- and three-dimensional Stokes equations indicate that the high-Ra
regime is characterized by an instability across the gap, wheras in the low-Ra regime
a spanwise Hele-Shaw mode dominates.
Density-driven instabilities of miscible fluids in a
Hele-Shaw cell: linear stability analysis of the
three-dimensional Stokes equations
Authors: GRAF F. , MEIBURG E. , HÄRTEL C.
Published: August 2008

We consider the situation of a heavier fluid placed above a lighter one in a vertically
arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this
configuration, experiments and nonlinear simulations recently reported by Fernandez
et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability
mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on
the order of five times the gap width. These findings are in disagreement with linear
stability results based on the gap-averaged Hele-Shaw approach, which predict much
smaller wavelengths. Similar observations have been made for immiscible flows as
well (Maxworthy 1989).

In order to resolve the above discrepancy, we perform a linear stability analysis
based on the full three-dimensional Stokes equations. A generalized eigenvalue problem
is formulated, whose numerical solution yields both the growth rate and the
two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise
wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion
relations confirm that the optimally amplified wavelength is about five times the gap
width, with the exact value depending on the interface thickness. The corresponding
growth rate is in very good agreement with the experimental data as well. The eigenfunctions
indicate that the predominant fluid motion occurs within the plane of the
Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified,
for which there is no motion in the spanwise direction. Scaling laws are provided
for the dependence of the maximum growth rate, the corresponding wavenumber, and
the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present
results are compared both with experimental data, as well as with linear stability
results obtained from the Hele-Shaw equations and a modified Brinkman equation.
Sand bars in tidal channels
Part 2. Tidal meanders
Authors: SOLARI L. , SEMINARA G. , LANZONI S. , MARANI M. , RINALDO A.
Published: August 2008

Careful analysis of new field observations on the geometry of meandering tidal
channels reveals that the values of meander wavelengths as well as curvatures,
conveniently scaled by local channel width, fall within a fairly restricted range,
suggesting the existence of some mechanistic process controlling meander formation.
A three-dimensional model is then proposed to predict flow and bed topography in
weakly meandering tidal channels. The analysis is developed for meander wavelengths
much smaller than the tidal wavelength and assuming that sediment is transported
both as bedload and as suspended load. Both conditions are typically met in nature.
Due to the symmetry of the meander pattern investigated, the theory indicates that
oscillations associated with the basic flow give rise to symmetric oscillations of the
point bar–pool pattern around the locations of maximum curvature. However, no
net migration in a tidal cycle is present, at least for periodic tides with zero mean.
Suspended load leads both to an enhanced bottom deformation and to a downstream
shifting of the position of the point bar. The model then provides the basis of a
planimetric instability theory of the type developed for river meanders (Blondeaux &
Seminara 1985). Though the available data do not yet allow a detailed quantitative
comparison, it is shown that the wavelengths selected by the ‘bend mechanism’ are
somewhat larger than those typically encountered in nature. The geomorphology of
the process of meander formation in tidal environments is then discussed and, upon
comparison with observational evidence, points out the need for various developments
of the present model.
A study of the flow-field evolution and mixing
in a planar turbulent jet using direct
numerical simulation
Authors: STANLEY S. A. , SARKAR S. , MELLADO J. P.
Published: August 2008

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion,
combustion and environmental flows. While considerable experimental research has
been performed on planar jets, very few computational studies exist. To the authors'
knowledge, this is the first computational study of spatially evolving three-dimensional
planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well
as the mean velocity, mean scalar and Reynolds stress profiles compare well with
experimental data. Coherency spectra, vorticity visualization and autospectra are
obtained to identify inferred structures. The development of the initial shear layer
instability, as well as the evolution into the jet column mode downstream is captured
well.

The large- and small-scale anisotropies in the jet are discussed in detail. It is
shown that, while the large scales in the flow field adjust slowly to variations in
the local mean velocity gradients, the small scales adjust rapidly. Near the centreline
of the jet, the small scales of turbulence are more isotropic. The mixing process
is studied through analysis of the probability density functions of a passive scalar.
Immediately after the rollup of vortical structures in the shear layers, the mixing
process is dominated by large-scale engulfing of fluid. However, small-scale mixing
dominates further downstream in the turbulent core of the self-similar region of the
jet and a change from non-marching to marching PDFs is observed. Near the jet
edges, the effects of large-scale engulfing of coflow fluid continue to influence the
PDFs and non-marching type behaviour is observed.
Dependence of the non-stationary form of Yaglom’s equation on the Schmidt number
Authors: ORLANDI P. , ANTONIA R. A.
Published: August 2008

The dynamic equation for the second-order moment of a passive scalar increment is
investigated in the context of DNS data for decaying isotropic turbulence at several
values of the Schmidt number Sc, between 0.07 and 7. When the terms of the equation
are normalized using Kolmogorov and Batchelor scales, approximate independence
from Sc is achieved at sufficiently small r/ηB (r is the separation across which
the increment is estimated and ηB is the Batchelor length scale). The results imply
approximate independence of the mixed velocity-scalar derivative skewness from Sc
and underline the importance of the non-stationarity. At small r/ηB, the contribution
from the non-stationarity increases as Sc increases.
Wilton ripples generated by a moving pressure distribution
Authors: VANDEN-BROECK J.-M.
Published: August 2008

The two-dimensional steady potential free surface flow due to a pressure distribution
moving at a constant velocity at the surface of a fluid of infinite depth is considered.
The effects of gravity and surface tension are included in the dynamic boundary
condition. The fully nonlinear problem is solved numerically by a boundary integral
equation method and the results are compared with those of the linear theory of
Rayleigh (1883). It is found that for some values of the capillary number, the nonlinear
solutions do not approach the linear solution of Rayleigh as the magnitude of the
pressure distribution approaches zero. Appropriate linear and nonlinear solutions are
constructed.
Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration
Authors: FABRE DAVID , JACQUIN LAURENT , LOOF ANTOINE
Published: August 2008

We consider the instability of two vortex pairs in a counter-rotating configuration.
Such configurations model vortex wakes observed behind aircraft with inboard vortices
produced at the inboard flap edges and at the tips of the horizontal tail. The
instability potential is characterized by an optimal perturbation analysis. This extends
the analysis of Fabre & Jacquin (2000) which was restricted to particular stationary
configurations, and that of Crouch (1997) which considered co-rotating configurations.
A complete mapping of the optimal perturbations is presented. The optimal
perturbations grow faster than the Crow (1970) instability. However, they correspond
to short-wavelength perturbations mainly affecting the weaker inboard vortices. A
possible strategy which consists of forcing a long wavelength is then investigated. Application
of both the optimal and the long-wave optimal perturbations to reduction
of vortex wake danger is discussed.
A study of compressibility effects in the
high-speed turbulent shear layer using
direct simulation
Authors: PANTANO C. , SARKAR S.
Published: August 2008

Direct simulations of the turbulent shear layer are performed for subsonic to supersonic
Mach numbers. Fully developed turbulence is achieved with profiles of mean
velocity and turbulence intensities that agree well with laboratory experiments. The
thickness growth rate of the shear layer exhibits a large reduction with increasing
values of the convective Mach number, Mc. In agreement with previous investigations,
it is found that the normalized pressure–strain term decreases with increasing Mc,
which leads to inhibited energy transfer from the streamwise to cross-stream fluctuations,
to the reduced turbulence production observed in DNS, and, finally, to reduced
turbulence levels as well as reduced growth rate of the shear layer. An analysis, based
on the wave equation for pressure, with supporting DNS is performed with the result
that the pressure–strain term decreases monotonically with increasing Mach number.
The gradient Mach number, which is the ratio of the acoustic time scale to the flow
distortion time scale, is shown explicitly by the analysis to be the key quantity that
determines the reduction of the pressure–strain term in compressible shear flows. The
physical explanation is that the finite speed of sound in compressible flow introduces
a finite time delay in the transmission of pressure signals from one point to an
adjacent point and the resultant increase in decorrelation leads to a reduction in the
pressure–strain correlation.

The dependence of turbulence intensities on the convective Mach number is investigated.
It is found that all components decrease with increasing Mc and so does the
shear stress.

DNS is also used to study the effect of different free-stream densities parameterized
by the density ratio, s = ρ2/ρ1, in the high-speed case. It is found that changes in the
temporal growth rate of the vorticity thickness are smaller than the changes observed
in momentum thickness growth rate. The momentum thickness growth rate decreases
substantially with increasing departure from the reference case, s = 1. The peak value
of the shear stress, uv, shows only small changes as a function of s. The dividing
streamline of the shear layer is observed to move into the low-density stream. An
analysis is performed to explain this shift and the consequent reduction in momentum
thickness growth rate.
The ejecta sheet generated by the impact of a drop
Authors: THORODDSEN S. T.
Published: August 2008

When a drop impacts on a liquid layer it ejects a thin horizontal sheet of liquid,
emanating from the neck region connecting the two liquid masses. Dual-frame imaging
and pulsed lasers are used to study the origin, speed and evolution of this ejecta sheet
for a range of viscosities. The initial ejecta speed can be more than 10 times the
impact velocity of the drop. Visualizations using fluorescent dye show the sheet
originating from the underlying liquid layer, not the drop liquid. The sheet undergoes
a characteristic instability, bending out of its plane and hitting the bottom layer. For
some impact conditions the sheet folds in on itself.
Four-phase merging in sessile compound drops
Authors: MAHADEVAN L. , ADDA-BEDIA M. , POMEAU Y.
Published: August 2008

We consider the statics of compound droplets made of two immiscible fluids on a
rigid substrate, in the limit when gravity is dominated by capillarity. In particular,
we show that the merging of four phases along a single contact line is a persistent
and robust phenomenon from a mechanical and thermodynamic perspective; it can
and does occur for a range of interfacial energies and droplet volumes. We give an
interpretation for this in the context of the macroscopic Young–Laplace law and
its microscopic counterpart due to van der Waals, and show that the topological
transitions that result can be of either a continuous or discontinuous type depending
on the interfacial energies in question.
Vibration-induced drop atomization and
bursting
Authors: JAMES A. J. , VUKASINOVIC B. , SMITH MARC K. , GLEZER A.
Published: August 2008

A liquid drop placed on a vibrating diaphragm will burst into a fine spray of
smaller secondary droplets if it is driven at the proper frequency and amplitude. The
process begins when capillary waves appear on the free surface of the drop and then
grow in amplitude and complexity as the acceleration amplitude of the diaphragm
is slowly increased from zero. When the acceleration of the diaphragm rises above
a well-defined critical value, small secondary droplets begin to be ejected from the
free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected
from the vibrating diaphragm in the form of a spray. This event is the result of an
interaction between the fluid dynamical process of droplet ejection and the vibrational
dynamics of the diaphragm. During droplet ejection, the effective mass of the
drop–diaphragm system decreases and the resonance frequency of the system increases. If
the initial forcing frequency is above the resonance frequency of the system, droplet
ejection causes the system to move closer to resonance, which in turn causes more
vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting.
In this paper, the basic phenomenon of vibration-induced drop atomization and drop
bursting will be introduced, demonstrated, and characterized. Experimental results
and a simple mathematical model of the process will be presented and used to explain
the basic physics of the system.
Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave
Authors: FASEL HERMANN F.
Published: August 2008

Direct numerical simulations (DNS) of the Navier–Stokes equations are used to
investigate the role of the Klebanoff-mode in laminar–turbulent transition in a
flatplate boundary layer. To model the effects of free-stream turbulence, volume forces
are used to generate low-frequency streamwise vortices outside the boundary layer.
A suction/blowing slot at the wall is used to generate a two-dimensional Tollmien–Schlichting (TS) wave inside the boundary layer. The characteristics of the fluctuations
inside the boundary layer agree very well with those measured in experiments. It is
shown how the interaction of the Klebanoff-mode with the two-dimensional TS-wave
leads to the formation of three-dimensional TS-wavepackets. When the disturbance
amplitudes reach a critical level, a fundamental resonance-type secondary instability
causes the breakdown of the TS-wavepackets into turbulent spots.
Kinematics and statistics of dense, slow granular flow through vertical channels
Authors: K. S. ANANDA , MOKA SUDHESHNA , NOTT PRABHU R.
Published: August 2008

We have investigated the flow of dry granular materials through vertical channels in the regime of dense slow flow using video imaging of the particles adjacent to a transparent wall. Using an image processing technique based on particle tracking velocimetry, the video movies were analysed to obtain the velocities of individual particles. Experiments were conducted in two- and three-dimensional channels. In the latter, glass beads and mustard seeds were used as model granular materials, and their translational velocities were measured. In the former, aluminium disks with a dark diametral stripe were used and their translational velocities and spin were measured. Experiments in the three-dimensional channels were conducted for a range of the channel width W, and for smooth and rough sidewalls. As in earlier studies, we find that shearing takes place predominantly in thin layers adjacent to the walls, while the rest of the material appears to move as a plug. However, there are large velocity fluctuations even in the plug, where the macroscopic deformation rate is negligibly small. The thickness of the shear layer, scaled by the particle diameter dp, increases weakly with W/dp. The experimental data for the velocity field are in good agreement with the Cosserat plasticity model proposed recently. We also measured the mean spin of the particles in the two-dimensional channel, and its deviation from half the vorticity. There is a clear, measurable deviation, which too is in qualitative agreement with the Cosserat plasticity model. The statistics of particle velocity and spin fluctuations in the two-dimensional channel were analysed by determining their probability distribution function, and their spatial and temporal correlation. They were all found to be broadly similar to previous observations for three-dimensional channels, but some differences are evident. The spatial correlation of the velocity fluctuations are much stronger in the two-dimensional channel, implying a pronounced solid-like motion superimposed over an uncorrelated fluid-like motion. The strong spatial correlation over large distances has led us to propose a mechanism for the production of velocity fluctuations in the absence of a macroscopic deformation rate.
The acceleration of solid particles subjected to cavitation nucleation
Authors: BORKENT BRAM M. , ARORA MANISH , OHL CLAUS-DIETER , DE JONG NICO , VERSLUIS MICHEL , LOHSE DETLEF , MØRCH KNUD AAGE , KLASEBOER EVERT , KHOO BOO CHEONG
Published: August 2008

The cavity–particle dynamics at cavitation inception on the surface of spherical particles suspended in water and exposed to a strong tensile stress wave is experimentally studied with high-speed photography. Particles, which serve as nucleation sites for cavitation bubbles, are set into a fast translatory motion during the explosive growth of the cavity. They reach velocities of ~40 ms−1and even higher. When the volume growth of the cavity slows down, the particle detaches from the cavity through a process of neck-breaking, and the particle is shot away. The experimental observations are simulated with (i) a spherical cavity model and (ii) with an axisymmetric boundary element method (BEM). The input for both models is a pressure pulse, which is obtained from the observed radial cavity dynamics during an individual experiment. The model then allows us to calculate the resulting particle trajectory. The cavity shapes obtained from the BEM calculations compare well with the photographs until neck formation occurs. In several cases we observed inception at two or more locations on a single particle. Moreover, after collapse of the primary cavity, a second inception was often observed. Finally, an example is presented to demonstrate the potential application of the cavity–particle system as a particle cannon, e.g. in the context of drug delivery into tissue.
The circular internal hydraulic jump
Authors: THORPE S. A. , KAVCIC I.
Published: August 2008

Circular hydraulic jumps are familiar in single layers. Here we report the discovery of similar jumps in two-layer flows. A thin jet of fluid impinging vertically onto a rigid horizontal plane surface submerged in a deep layer of less-dense miscible fluid spreads radially, and a near-circular internal jump forms within a few centimetres from the point of impact with the plane surface. A jump is similarly formed as a jet of relatively less-dense fluid rises to the surface of a deep layer of fluid, but it appears less stable or permanent in form. Several experiments are made to examine the case of a downward jet onto a horizontal plate, the base of a square or circular container. The inlet Reynolds numbers, Re, of the jet range from 112 to 1790. Initially jumps have an undular, laminar form with typically 2–4 stationary waves on the interface between the dense and less-dense layers but, as the depth of the dense layer beyond the jump increases, the transitions become more abrupt and turbulent, resulting in mixing between the two layers. During the transition to a turbulent regime, single and sometimes moving multiple cusps are observed around the periphery of jumps. A semi-empirical model is devised that relates the parameters of the laboratory experiment, i.e. flow rate, inlet nozzle radius, kinematic viscosity and reduced gravity, to the layer depth beyond the jump and the radius at which an undular jump occurs. The experiments imply that surface tension is not an essential ingredient in the formation of circular hydraulic jumps and demonstrate that stationary jumps can exist in stratified shear flows which can be represented as two discrete layers. No stationary circular undular jumps are found, however, in the case of a downward jet of dense fluid when the overlying, less-dense, fluid is stratified, but a stationary turbulent transition is observed. This has implications for the existence of stationary jumps in continuously stratified geophysical flows: results based on two-layer models may be misleading. It is shown that the Froude number at which a transition of finite width occurs in a radially diverging flow may be less than unity.
An analytical model for bore-driven run-up
Authors: PRITCHARD DAVID , GUARD PAUL A. , BALDOCK TOM E.
Published: August 2008

We use a hodograph transformation and a boundary integral method to derive a new analytical solution to the shallow-water equations describing bore-generated run-up on a plane beach. This analytical solution differs from the classical Shen–Meyer runup solution in giving significantly deeper and less asymmetric swash flows, and also by predicting the inception of a secondary bore in both the backwash and the uprush in long surf. We suggest that this solution provides a significantly improved model for flows including swash events and the run-up following breaking tsunamis.
Vortex flow and cavitation in diesel injector nozzles
Authors: ANDRIOTIS A. , GAVAISES M. , ARCOUMANIS C.
Published: August 2008

Flow visualization as well as three-dimensional cavitating flow simulations have been employed for characterizing the formation of cavitation inside transparent replicas of fuel injector valves used in low-speed two-stroke diesel engines. The designs tested have incorporated five-hole nozzles with cylindrical as well as tapered holes operating at different fixed needle lift positions. High-speed images have revealed the formation of an unsteady vapour structure upstream of the injection holes inside the nozzle volume, which is referred to as ‘string-cavitation’. Computation of the flow distribution and combination with three-dimensional reconstruction of the location of the strings inside the nozzle volume has revealed that strings are found at the core of recirculation zones; they originate either from pre-existing cavitation sites forming at sharp corners inside the nozzle where the pressure falls below the vapour pressure of the flowing liquid, or even from suction of outside air downstream of the hole exit. Processing of the acquired images has allowed estimation of the mean location and probability of appearance of the cavitating strings in the three-dimensional space as a function of needle lift, cavitation and Reynolds number. The frequency of appearance of the strings has been correlated with the Strouhal number of the vortices developing inside the sac volume; the latter has been found to be a function of needle lift and hole shape. The presence of strings has significantly affected the flow conditions at the nozzle exit, influencing the injected spray. The cavitation structures formed inside the injection holes are significantly altered by the presence of cavitation strings and are jointly responsible for up to 10% variation in the instantaneous fuel injection quantity. Extrapolation using model predictions for real-size injectors operating at realistic injection pressures indicates that cavitation strings are expected to appear within the time scales of typical injection events, implying significant hole-to-hole and cycle-to-cycle variations during the corresponding spray development.
Viscoelastic effects on the jetting–dripping transition in co-flowing capillary jets
Authors: MONTANERO J. M. , GAÑÁN-CALVO A. M.
Published: August 2008

Linear hydrodynamics stability analysis is used to determine the influence of elasticity on the jetting–dripping transition and on the temporal stability of non-axisymmetric modes in co-flowing capillary jets. The critical Weber number for which axisymmetric perturbations undergo a transition from convective to absolute instability is calculated from the spatio-temporal analysis of the dispersion relation for Oldroyd-B liquids, as a function of the density and viscosity ratios, and the Reynolds and Deborah numbers. Elasticity increases the critical Weber number for all cases analysed and, consequently, fosters the transition from jetting to dripping. The temporal analysis of the dispersion relation for them= 1 lateral mode shows that elasticity does not affect its stability.
On the initial-value problem in a rotating circular cylinder
Authors: ZHANG KEKE , LIAO XINHAO
Published: August 2008

The initial-value problem in rapidly rotating circular cylinders is revisited. Four different but related analyses are carried out: (i) we derive a modified asymptotic expression for the viscous decay factors valid for the inertial modes of a broad range of frequencies that are required for an asymptotic solution of the initial value problem at an arbitrarily small but fixed Ekman number; (ii) we perform a fully numerical analysis to estimate the viscous decay factors, showing satisfactory quantitative agreement between the modified asymptotic expression and the fuller numerics; (iii) we derive a modified time-dependent asymptotic solution of the initial value problem valid for an arbitrarily small but fixed Ekman number and (iv) we perform fully numerical simulations for the initial value problem at a small Ekman number, showing satisfactory quantitative agreement between the modified time-dependent solution and the numerical simulations.
Dynamics of volatile liquid droplets on heated surfaces: theory versus experiment
Authors: SODTKE CHRISTOF , AJAEV VLADIMIR S. , STEPHAN PETER
Published: August 2008

We consider the evaporation of volatile liquid droplets deposited on a heated substrate in a pure saturated vapour environment. A mathematical model is developed that incorporates the effects of surface tension, evaporation, thermocapillarity, gravity, disjoining pressure, as well as unsteady heat conduction in the solid substrate. The apparent contact line is treated mathematically as a transition region between the macroscopic droplet shape and the adsorbed film of liquid on the heated substrate. Theoretical parametric studies are conducted to clarify the effects of thermocapillarity and wetting properties on the droplet dynamics. An experimental study is conducted in a closed container with de-ionized water droplets on a stainless steel foil heated by an electric current. The interface shapes are recorded together with the temperature profiles under the droplets, measured using thermochromic liquid crystals. Experiment and theory are in very good agreement as long as the conditions of applicability of our lubrication-type mathematical model are satisfied.
On the Lamb vector divergence in Navier–Stokes flows
Authors: HAMMAN CURTIS W. , KLEWICKI JOSEPH C. , KIRBY ROBERT M.
Published: August 2008

The mathematical and physical properties of the Lamb vector divergence are explored. Toward this aim, the instantaneous and mean dynamics of the Lamb vector divergence are examined in several analytic and turbulent flow examples relative to its capacity to identify and characterize spatially localized motions having a distinct capacity to effect a time rate of change of momentum. In this context, the transport equation for the Lamb vector divergence is developed and shown to accurately describe the dynamical mechanisms by which adjacent high- and low-momentum fluid parcels interact to effect a time rate of change of momentum and generate forces such as drag. From this, a transport-equation-based framework is developed that captures the self-sustaining spatiotemporal interactions between coherent motions, e.g. ejections and sweeps in turbulent wall flows, as predicted by the binary source–sink distribution of the Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of the Lamb vector divergence.