bluuebunny/crossref_metadata_2025 huggingface dataset:
Fast and precise access to enantiomerization rate constants in dynamic chromatography
Authors: Trapp O.
Published: April 2006

An analytical solution of the unified equation to evaluate elution profiles of interconverting enantiomers in dynamic chromatography is presented. Rate constantsk1andk−1and Gibbs activation energies are directly obtained from the chromatographic parameters (retention timestandtof the interconverting enantiomers, the peak widths at half heightwAandwB,and the relative plateau heighthp), and the initial amountsA0andB0of the enantiomers without any iterative and time consuming computational step. Therefore, this equation is no longer limited to racemic analytes. The analytical solution presented here was validated by comparison with a dataset of 125,000 simulated elution profiles of enantiomerizations. Furthermore, it was found that the recovery rate from a defined dataset is on average 40% higher using the unified equation compared to evaluation methods based on iterative computer simulation. The new equation was applied to determine the enantiomerization rate constant of 1‐n‐butyl‐2‐tert‐butyldiaziridine by enantioselective gas chromatography. The activation parameters (ΔH‡= 112.6 ± 2.5 kJ/mol and ΔS‡= −27 ± 2 J/(K mol) were obtained from temperature‐dependent measurements between 100°C and 140°C in 10K steps. Chirality 18:489–497, 2006. © 2006 Wiley‐Liss, Inc.
Enantiomer separation of amino acids in immunoaffinity micro LC‐MS
Authors: Zeleke Jessica M. , Smith Gregory B. , Hofstetter Heike , Hofstetter Oliver
Published: April 2006

Chiral immunoaffinity microbore columns were directly interfaced with MS detection, and the effect of column length and temperature on the enantiomer separation of a number of underivatized aromatic and aliphatic amino acids was investigated utilizing an antibody chiral stationary phase that had been prepared by immobilizing a monoclonal anti‐D‐amino acid antibody onto silica. The stronger affinity of the antibody towards aromatic and bulky amino acids allowed separation of such analytes in a 0.75 × 150 mm column, while an increase in column length enabled separation of more weakly bound compounds. The strength of interaction between chiral selector and analytes could be modulated conveniently by lowering the temperature. For the first time, simultaneous enantiomer separation of mixtures of amino acids was achieved on antibody‐based chiral stationary phases using extracted ion chromatograms. Chirality 18:544–550, 2006. © 2006 Wiley‐Liss, Inc.
New Palladium Complexes with S‐ or Se‐Containing Schiff‐Base Ligands as Efficient Catalysts for the Suzuki–Miyaura Cross‐Coupling Reaction of Aryl Bromides with Phenylboronic Acid under Aerobic Conditions
Authors: Kostas Ioannis D. , Steele Barry R. , Terzis Aris , Amosova Svetlana V. , Martynov Alexander V. , Makhaeva Natalia A.
Published: April 2006

Four palladium chelate complexes with S‐ or Se‐containing substituted salicylaldehyde Schiff‐base derivatives have been synthesized. Spectroscopic and crystallographic data indicate that, in the complexes, the deprotonated salicylaldehyde ligand is bound to the metal in an O,N,S (or Se)‐terdentate coordination mode, forming one six‐ and one five‐membered chelate ring. The complexes are thermally and air stable and efficiently catalyze the Suzuki–Miyaura cross‐coupling of aryl bromides with phenylboronic acid in air.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)
Photochemistry of cis‐3‐Diazo‐5,6‐dimethyl‐1,4‐oxathian‐2‐one S‐Oxide in Argon Matrices
Authors: O’Sullivan Orlagh C. M. , Collins Stuart G. , Maguire Anita R. , Böhm Matthias , Sander Wolfram
Published: April 2006

The photochemistry of the α‐diazo sulfoxide 7 has been investigated in solid argon at 10 K by IR spectroscopy. The sulfinyl carbene was not detected directly but instead underwent photochemically induced hetero‐Wolff rearrangement to the sulfine 8 which could be detected and characterized following irradiation at 248 nm. Further photochemical reaction of this intermediate led to the oxathiirane 9 which was most readily detected on irradiation of 7 at 308 nm. The matrix‐isolated species were identified by comparison of experimental and calculated IR spectra. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)
Indium Triflate Catalyzed Rearrangement of Aryl‐Substituted Cyclopropyl Carbinols to 1,4‐Disubstituted 1,3‐Butadienes
Authors: Ranu Brindaban C. , Banerjee Subhash
Published: April 2006

Aryl‐substituted cyclopropyl carbinol derivatives undergo a facile stereoselective rearrangement catalyzed by In(OTf)3 in dichloromethane under sonication to produce the substituted conjugated all‐trans‐butadienes. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)
1,2,5‐Oxadiazole (Furazan) Derivatives from Benzoylnitromethane and Dipolarophiles in the Presence of DABCO: Structure and Intermediates
Authors: Cecchi Luca , De Sarlo Francesco , Faggi Cristina , Machetti Fabrizio
Published: April 2006

Furazan (1,2,5‐oxadiazole) derivatives are obtained along with isoxazolines from the reaction of benzoylnitromethane with dipolarophiles in the presence of DABCO. Furazans are shown to derive from the intermediate dibenzoylfuroxan (3,4‐dibenzoyl‐1,2,5‐oxadiazole‐5‐oxide) and dipolarophiles under hydrolytic conditions. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)
Genetic aberrations in prostate cancer by microarray analysis
Authors: Saramäki Outi R. , Porkka Kati P. , Vessella Robert L. , Visakorpi Tapio
Published: April 2006

The aim of this study was to screen genetic as well as expression alterations in prostate cancer. Array comparative genomic hybridization (aCGH) to a 16K cDNA microarray was performed to analyze DNA sequence copy number alterations in 5 prostate cancer cell lines and 13 xenografts. The aCGH confirmed the previously implicated common gains and losses, such as gains at 1q, 7, 8q, 16p and 17q and losses at 2q, 4p/q, 6q, 8p, 13q, 16q, 17p and 18q, which have previously been identified by chromosomal CGH (cCGH). Because of the higher resolution of aCGH, the minimal commonly altered regions were significantly narrowed‐down. For example, the gain of 8q was mapped to three independent regions, 8q13.3‐q21.11, 8q22.2 and 8q24.13‐q24.3. In addition, a novel recurrent gain at 9p13‐q21 was identified. The concomitant expression analysis indicated that genome‐wide DNA sequence copy number (gene dosage) was significantly associated with the expression level (p < 0.0001). The analyses indicated several individual genes whose expression was associated with the gene copy number. For example, gains of PTK2 and FZD6, were associated with the increased expression, whereas losses of TNFRSF10B (alias DR5) and ITGA4 with decreased expression. In conclusion, the aCGH mapping data will aid in the identification of genes altered in prostate cancer. The combined expression and copy number analysis suggested that even a low‐level copy number change may have significant effect on gene expression, and thus on the development of prostate cancer. © 2006 Wiley‐Liss, Inc.
Ideal and actual value patterns toward domains of scholarship in three types of colleges and universities
Authors: Braxton John M. , Luckey, Jr. William T. , Helland Patricia A.
Published: April 2006

The authors compare the ideal versus actual academic reward structures at a representative sample of nondoctoral four‐year institutions and make recommendations.
Encouraging multiple forms of scholarship in faculty reward systems: Have academic cultures really changed?
Authors: O'Meara KerryAnn
Published: April 2006

The author summarizes the findings from a study of 729 chief academic officers who identify both catalysts and barriers to the reform of faculty reward systems.
Low magnetic fields behavior of photon echo in
LuLiF4:Er3+
Authors: Lisin V N , Samartsev V V , Shegeda A M , Zuikov V A , Korableva S L
Published: April 2006

It is reported about the first observation and
studying of the photon echo in
LuLiF4:Er3+. The energy transition is
4I15/2→4F9/2 (λ=6536 Å). The
density of ErF3 is 0.025 wt%. The operation temperature is
1.9 K. Measurements were spent at low (up to 1200 Oe) and even
zero external magnetic fields. It was studied a behavior of the
photon echo intensity versus the magnetic field magnitude and
direction about the crystal axis C and versus the laser
pulse separation t
12. It was observed an exponential growth
and then, after some plateau, an exponential decreasing of the
photon echo intensity as a function of magnetic field with
increasing of the magnetic field from zero value. The parameters
describing the exponential growth and decreasing are not depended
on direction of magnetic field. Value of a magnetic field at which
the echo intensity accepts the maximum, and quantity of this
maximum decrease with increased the pulse separation t
12 and
the angle θ between the magnetic field and crystal axis.
The echo intensity exponentially decreases with increased
θ. The parameter describing the exponential decreasing is
not depended on the magnitude of the field. The echo intensity as
a function of pulse separation shows exponential decay. The phase
relaxation time is depended on the magnitude and direction of the
magnetic field. T
2 is equal to 202±16 ns at zero magnetic
field. Phenomenological formula is suggested, which qualitatively
presents the mentioned dependencies. Polarization properties of
the backward photon echo in this crystal are studied also.
Deviation from the mobile proton model in amino‐modified peptides: implications for multiple reaction monitoring analysis of peptides
Authors: Locke Steven J. , Leslie Andrew D. , Melanson Jeremy E. , Pinto Devanand M.
Published: April 2006

The study of peptide fragmentation is important to the understanding of chemical processes occurring in the gas phase and the more practical concern of peptide identification for proteomic analysis. Using the mobile proton model as a framework, we explore the effect of amino‐group modifications on peptide fragmentation. Three aldehydes are used to transform the peptides' primary amino groups into either a dimethylamino or a heterocyclic structure (five‐ or six‐membered). The observed fragmentation patterns deviate strongly from those observed for the analogous underivatised peptides. In particular, the a1 ion is the base peak in most tandem mass spectra of the derivatised peptides. The a1 ion intensity depends strongly on the N‐terminal amino acid, with tyrosine and phenylalanine having the strongest enhancement. Despite the change in fragmentation patterns of the derivatised peptides, they still provide high‐quality tandem mass spectra that, in many cases, are more amenable to database searching than the spectra of underivatised peptides. In addition, the reliable presence of the a1 ion facilitates rapid quantitative measurements using the multiple reaction monitoring approach. Copyright © 2006 John Wiley & Sons, Ltd.
Gravity currents: a personal perspective
Authors: HUPPERT HERBERT E.
Published: April 2006

Gravity currents, driven by horizontal differences in buoyancy, play a central role in fluid mechanics, with numerous important natural and industrial applications. The first quantitative, fluid-mechanical study of gravity currents, by von Kármán in 1940, was carried out before the birth of this Journal; the next important theoretical contribution was in 1968 by Brooke Benjamin, and appeared in this Journal more than a decade after its birth. The present paper reviews some of the material that has built on this auspicious start. Part of the fun and satisfaction of being involved in this field is that its development has been based on both theoretical and experimental contributions, which have at times been motivated and supported by field observations and measurements.
The motion of a finite mass of granular material down a rough incline
Authors: Savage S. B. , Hutter K.
Published: April 2006

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of anM-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce theM-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.
Onset of Rayleigh–Bénard convection in a rigid channel
Authors: Chana M. S. , Daniels P. G.
Published: April 2006

A two-dimensional Galerkin formulation of the three-dimensional Oberbeck-Boussinesq equations is used to describe the onset of convection in an infinite rigid horizontal channel uniformly heated from below. The dependence of the critical Rayleigh number on the channel aspect ratio is determined and results are compared with those of an idealized model studied by Davies-Jones (1970). Asymptotic results are derived for both narrow and wide channels, corresponding to limits of small and large aspect ratios respectively. In the latter case the main core flow, consisting of two-dimensional rolls with axes perpendicular to the vertical walls of the channel, can be represented by the solution of an amplitude equation. Close to the walls, however, the motion remains fully three-dimensional and a reversal of the vertical flow is associated with a local subdivision of each main roll into a pair of co-rotating rolls.
Frequency selection and asymptotic states in laminar wakes
Authors: Karniadakis George Em , Triantafyllou George S.
Published: April 2006

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.

It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.
Topographic waves in open domains. Part 2. Bay modes and resonances
Authors: Stocker Thomas F. , Johnson E. R.
Published: April 2006

The topographic wave equation is solved in a domain consisting of a channel with a terminating bay zone. For exponential depth profiles the problem reduces to an algebraic eigenvalue problem. In a flat channel adjacent to a shelf–like bay zone the solutions form a countably infinite set of orthogonal bay modes: the spectrum of eigenfrequencies is purely discrete. A channel with transverse topography allows wave propagation towards and away from the bay: the spectrum has a continuous part below the cutoff frequency of free channel waves. Above this cutoff frequency a finite number (possibly zero) of bay-trapped solutions occur. Bounds for this number are given. At particular frequencies below the cutoff the system is in resonance with the incident wave. These resonances are shown to be associated with bay modes.
The instability of a liquid film on a wall exposed to an air flow
Authors: Ludwieg H. , Hornung H.
Published: April 2006

The title problem, which is an important early element of the mechanism of the development of a surface oil flow visualization picture, is studied by a linear stability analysis that predicts the most strongly amplified wavenumber of transverse surface waves as a function of Reynolds number, surface tension, film viscosity and initial thickness of the film. Wall scaling virtually removes the additional dependence on Reynolds number. In a simple experiment the observed wavenumber agrees with the predicted most strongly amplified value to within the experimental accuracy.
Area-varying waves on curved vortex tubes with application to vortex breakdown
Authors: Lundgren T. S. , Ashurst W. T.
Published: April 2006

Equations which modify those derived by Widnall & Bliss (1971) and Moore & Saffman (1972) are presented in which jet-like flow along the axis of a vortex tube interacts with the motion of the tube. The equations describe two major effects. The first is the propagation of axial waves along the vortex tube which is similar to the flow of shallow water. A local decrease in cross-section area of the vortex tube produces higher swirling velocity and lower pressure. The resulting axial pressure gradient causes a propagating wave of area and axial velocity in order to move fluid into the region of smaller area. The second effect is instability to helical disturbances when the jet-like axial velocity is high enough to overcome the stabilizing effect of the swirling motion. An elementary nonlinear theory of vortex breakdown is presented which has an analogy with the formation of bores in shallow-water theory. A numerical example shows the growth of a helical disturbance behind a vortex breakdown front.
The relaxation of a turbulent boundary layer in an adverse pressure gradient
Authors: Cutler Andrew D. , Johnston James P.
Published: April 2006

The relaxation of a reattached turbulent boundary layer downstream of a wall fence has been investigated. The boundary layer has an adverse pressure gradient imposed upon it which is adjusted in an attempt to bring the boundary layer into equilibrium. This is done by adjusting the pressure gradient so as to bring the Clauser parameter (G) down to a value of about 11.4 and then maintain it constant. In the region from the reattachment point to 2 or 3 reattachment lengths downstream, the boundary layer recovers from the initial major effects of reattachment. Farther downstream (where G is constant) the pressure-gradient parameter changes very slowly and profiles of non-dimensionalized eddy viscosity appear self-similar. However, pressure gradient and eddy viscosity are both roughly twice as large as expected on the basis of previous studies of equilibrium turbulent boundary layers. It is not known whether equilibrium has been achieved in this downstream region. This is another illustration of the great sensitivity of boundary-layer structure to perturbations.
Nonlinear stability of a weakly supercritical mixing layer in a rotating fluid
Authors: Shukhman I. G.
Published: April 2006

A model has been constructed for a mixing layer of a rotating fluid with a large Reynolds number which is an analogue of a mixing-layer model for a plane flow widely used in the literature. The angular velocity profile in such a model has the form:\[ \Omega(r) = {\textstyle\frac{1}{2}}(\Omega_1 + \Omega_2)-{\textstyle\frac{1}{2}}(\Omega_1 - \Omega_2)\tan h\left(\frac{1}{D}\ln\frac{r}{R}\right), \]whereris the distance from the rotation axis; andR, Ω1,2, andDare the model's parameters. The model permits a relatively simple analytical study of the stability for two-dimensional disturbances. It is shown that the stability is defined by the ‘shear-width’ parameterD, namely the model is unstable whenD<Dcrit= ½. In a weakly supercritical flow (|D−Dcrit| [Lt ] 1), one mode with azimuthal numberm= 2 develops. In this case two vortices are produced in the vicinity of a critical layer (CL), i.e. a radius where the wave's azimuthal velocity Ωpcoincides with the rotation velocity Ω(r). A study is made of their nonlinear evolution corresponding to different CL regimes: viscous, nonlinear, and unsteady. It is found that the instability saturates at a low enough level and the equilibrium amplitude depends on the degree of supercriticality ΔD= |D−Dcrit|, but the character of this dependence is different in different regions of the supercriticality parameter ΔD.

It is shown that, despite the specific form of the velocity profile in the model under consideration, results concerning the critical-layer dynamics have a high degree of universality. In particular, it becomes possible to formulate the criterion that the instability will be saturated at a low level for an arbitrary weakly supercritical flow.
The role of transverse secondary instabilities in the evolution of free shear layers
Authors: Klaassen G. P. , Peltier W. R.
Published: April 2006

Linear stability analyses and nonlinear flow simulations reveal several important features of transverse secondary instabilities of two-dimensional Kelvin–Helmholtz billows and Stuart vortices. Vortex pairing is found to be the most rapidly amplified mode in a continuous spectrum of vortex merging instabilities. In certain not uncommon circumstances it is possible for more than two vortices to amalgamate in a single interaction, demonstrating that the phenomenon that has become known as the pairing resonance in fact has a rather low quality factor. Another form of merging instability in which a vortex is deformed and drained by its neighbours has been revealed by our linear stability analyses of nonlinear shear-layer disturbances. It appears, however, that this vortex draining instability may be important only in unstratified or very weakly stratified flows, since in moderately stratified Kelvin–Helmholtz flow, it is replaced by a highly localized instability which leads to a temporary distortion of the braids. Nonlinear simulations of vortex merging events in moderately stratified, high-Reynolds-number shear layers are compared to the theoretical predictions of our stability analyses. We investigate and quantify the sensitivity of merging events to variations in the initial conditions. The character of the flow after merging instability saturates and the nonlinear aspects of multiple merging events are also considered.
Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form
Authors: Childress S. , Ierley G. R. , Spiegel E. A. , Young W. R.
Published: April 2006

The time-dependent form of the classic, two-dimensional stagnation-point solution of the Navier-Stokes equations is considered. If the viscosity is zero, a class of solutions of the initial-value problem can be found in closed form using Lagrangian coordinates. These solutions exhibit singular behaviour in finite time, because of the infinite domain and unbounded initial vorticity. Thus, the blow-up found by Stuart in three dimensions using the stagnation-point form, also occurs in two. The singularity vanishes under a discrete, finite-dimensional ‘point vortex’ approximation, but is recovered as the number of vortices tends to infinity. We find that a small positive viscosity does not arrest the breakdown, but does strongly alter its form. Similar results are summarized for certain Boussinesq stratified flows.
The relationship between surface-renewal and bursting motions in an open-channel flow
Authors: Komori Satoru , Murakami Yasuhiro , Ueda Hiromasa
Published: April 2006

Surface-renewal motions in the interfacial region below a gas-liquid interface were experimentally investigated in relation to bursting motions in the wall region. To estimate the frequency of the appearance of surface-renewal eddies, mass-transport experiments with methylene-blue solution, together with velocity measurements, were done in an open-channel flow. The instantaneous concentration of methylene-blue tracer emitted from a point source positioned in the buffer layer was measured at the free surface downstream from the source by an optical probe. Instantaneous streamwise velocity was measured using a laser-Doppler velocimeter at a position in the buffer region. Frequencies of both surface-renewal and bursting events were computed from these concentration and velocity signals using a conditional-averaging method. In order to clarify whether the surface-renewal eddies actually dominate mass transfer across the gas-liquid interface, gas-absorption experiments were added. Carbon dioxide was absorbed into the water flow across the calm free surface and its mass-transfer coefficient on the liquid side was measured under the same flow conditions as used in the above mass-transport experiments. The results show that the surface-renewal motions originate in the bursting motions which vigorously occur in the buffer region. That is, the decelerated fluid which is strongly lifted towards the outer layer by bursting almost always arrives at the free surface and renews the free surface. The frequency of the surface renewal, as well as the bursting frequency, is uniquely determined by the wall variables or the outer-flow variables and the Reynolds number. Mass transfer across the gas-liquid interface is dominated by the large-scale surface-renewal eddies, and the mass-transfer coefficient on the liquid side is proportional to the square-root of the surface-renewal frequency.
Flow in curved ducts: bifurcation structure for stationary ducts
Authors: Daskopoulos P. , Lenhoff A. M.
Published: April 2006

In developed laminar flow in stationary curved ducts there is, in addition to the two-vortex secondary flow structure first analysed by Dean (1927), another solution branch with a four-vortex secondary flow. These two branches have recently been shown to be joined by a third branch, but stability characteristics and the possible presence of additional branches have yet to be described. In this paper orthogonal collocation is used in conjunction with continuation techniques to characterize the bifurcation structure for symmetric flows. The two- and four-vortex solutions are stable to symmetric disturbances, while the recently reported branch joining them is unstable. A more systematic exploration of the parameter space than has hitherto been reported is performed by examining the morphogenesis of the bifurcation structure within the general framework of properties described by Benjamin (1978). The starting point is the ‘perfect’ problem of flow in an infinite curved slit, which bifurcates to give rise to a cellular structure. Addition of ‘stickiness’ at the cell boundaries turns each pair of cells into a curved duct of rectangular cross-section which, by a geometry change, leads to the curved circular tube. For the perfect problem a large number of solution branches are present, but the addition of stickiness turns most of them into isolae which vanish before the no-slip limit is reached. The solution branches that remain include, in addition to the three described previously, another solution family not connected to the other one. This family comprises two branches, both four-vortex in character and unstable to symmetric disturbances.
Surface-tension effects in the contact of liquid surfaces
Authors: Oguz Hasan N. , Prosperetti Andrea
Published: April 2006

The process by which two surfaces of the same liquid establish contact, as when two drops collide or raindrops fall on water, is studied. The mathematical formulation is based on the assumption of an incompressible, inviscid fluid with surface tension. A model problem with a simplified geometry is solved numerically by means of a boundary-integral method. The results imply that a number of toroidal bubbles form and remain entrapped between the contacting surfaces. Experimental evidence for this process, which is important for boiling nucleation and the formation of condensation nuclei for rain drops, is found in the literature.
Note on shape oscillations of bubbles
Authors: Benjamin T. Brooke
Published: April 2006

By use of a virial equation introduced in a recent paper (Benjamin 1987), the main results of a second-order perturbation theory developed by Longuet-Higgins (1989a) are recovered in comparatively simple fashion. Asymmetric capillary vibrations of a gas bubble in an infinite incompressible liquid are confirmed to generate an increase in the volume of the bubble, a lowering of the mean pressure of the gas and a monopole component in the motion of the liquid. It is shown that the second effect remains when the bubble is incompressible.
Organized motions in a fully developed turbulent axisymmetric jet
Authors: Tso Jin , Hussain Fazle
Published: April 2006

An experiment has been conducted to study the occurrence, configuration and dynamics of large-scale coherent vortical motions in the fully developed region of a turbulent axisymmetric jet. The key idea is to use vorticity signals from a spatial grid to detect and sample large-scale vortical structures and then use the (smoothed) vorticity peaks of spatial vorticity patterns to align and ensemble average successive realizations to determine structure configuration and dynamics. Measurements were made in an air jet atReD= 69000 by employing a radial rake of seven × -wires to obtain the azimuthal vorticity map. Two additional conditioning probes were placed ± 90° away from the rake to determine the three-dimensional phase and hence the structure configuration. Structures with axisymmetric, helical and double helical configurations have been educed. Among them, the helical structures are far more dominant than the others, and the jet dynamics are thus discussed in terms of these helical structures. Helical structures move radially outward as they advect downstream. This radial movement, in conjunction with simultaneous local ejection of turbulent fluid and subsequent entrainment of the ejected fluid with ambient fluid, appears to be a major means of jet spreading. The shear strain rate is strong on the downstream side of the structure, causing intense small-scale turbulence production and mixing there.
Scaling of hard thermal turbulence in Rayleigh-Bénard convection
Authors: Castaing Bernard , Gunaratne Gemunu , Heslot François , Kadanoff Leo , Libchaber Albert , Thomae Stefan , Wu Xiao-Zhong , Zaleski Stéphane , Zanetti Gianluigi
Published: April 2006

An experimental study of Rayleigh-Bénard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 107 < Ra < 6 × 1012) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra. However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu, proportional to $Ra^{\frac{1}{3}}$ while experiment gives an index much closer to $\frac{2}{7}$. A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.
The viscous flow on surfaces with longitudinal ribs
Authors: Bechert D. W. , Bartenwerfer M.
Published: April 2006

The viscous sublayer of a turbulent boundary layer on a surface with fine longitudinal ribs (riblets) is investigated theoretically. The mean flow constituent of this viscous flow is considered. Using conformal mapping, the velocity distributions on various surface configurations are calculated. The geometries that were investigated include sawtooth profiles with triangular and trapezoidal grooves as well as profiles with thin blade-shaped ribs, ribs with rounded edges and ribs having sharp ridges and U-shaped grooves. (This latter riblet configuration is also found on the tiny scales of fast sharks.) Our calculations enable us to determine the location of the origin of the velocity profile that lies somewhat below the tips of the ridges. The distance between this origin and the tip of the ridge we call ‘protrusion height’. The upper limit for the protrusion height is found to be 22% of the lateral rib spacing; the coefficient 0.22 being the value of the expression π−1In 2. This limit is valid for two-dimensional riblet geometries. Analogous experiments with an electrolytic tank are carried out as an additional check on the theoretical calculations. This is also an easy way to determine experimentally the location of the origin of the velocity profile for arbitrary new riblet geometries. A possible connection between protrusion height and drag reduction in a turbulent boundary layer flow is discussed. Finally, the present theory also produces an orthogonal grid pattern above riblet surfaces which may be utilized in future numerical calculations of the whole turbulent boundary layer.
On the stabilization of a two-dimensional vortex strip by adverse shear
Authors: Dritschel David G.
Published: April 2006

An isolated strip of anomalous vorticity in a two-dimensional, inviseid, incompressible, unbounded fluid is linearly unstable - or is it? It is pointed out that an imposed uniform shear, opposing the shear due to the isolated strip alone, can prevent all linear instabilities if the imposed shear is of sufficient strength, and that this is highly relevant to current thinking about ‘two-dimensional turbulence’ and related problems. The linear stability result has been known and goes back to Rayleigh, but its implications for the behaviour of the thin strips of vorticity that are a ubiquitous feature of nonlinear two-dimensional flows, as revealed for instance in high-resolution experiments, appear not to have been widely recognized. In particular, these thin strips, or filaments, almost always behave quasi-passively when being wrapped around intense coherent vortices, and do not roll up into strings of miniature vortices as would an isolated strip. Nonlinear calculations presented herein furthermore show that substantially less adverse shear than suggested by linear theory is required to preserve a strip of vorticity. Taken together, and in conjunction with results showing the further stabilizing effect of a large-scale strain field, these results explain the observed quasi-passive behaviour.
Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary
Authors: Vogel A. , Lauterborn W. , Timm R.
Published: April 2006

The dynamics of laser-produced cavitation bubbles near a solid boundary and its dependence on the distance between bubble and wall are investigated experimentally. It is shown by means of high-speed photography with up to 1 million frames/s that jet and counterjet formation and the development of a ring vortex resulting from the jet flow are general features of the bubble dynamics near solid boundaries. The fluid velocity field in the vicinity of the cavitation bubble is determined with time-resolved particle image velocimetry. A comparison of path lines deduced from successive measurements shows good agreement with the results of numerical calculations by Kucera & Blake (1988). The pressure amplitude, the profile and the energy of the acoustic transients emitted during spherical bubble collapse and the collapse near a rigid boundary are measured with a hydrophone and an optical detection technique. Sound emission is the main damping mechanism in spherical bubble collapse, whereas it plays a minor part in the damping of aspherical collapse. The duration of the acoustic transients is 20-30 ns. The highest pressure amplitudes at the solid boundary have been found for bubbles attached to the boundary. The pressure inside the bubble and at the boundary reaches about 2.5 kbar when the maximum bubble radius is 3.5 mm. The results are discussed with respect to the mechanism of cavitation erosion.
Stability of Long's vortex at large flow force
Authors: Foster M. R. , Smith F. T.
Published: April 2006

Long's self-similar vortex is known to have two solutions for each supercritical value of the flow force. Each of those solutions is shown here to have a double structure if the flow force is large. We then investigate the inertial instabilities of one of those large-flow-force limit solutions, and find them to be related to the instabilities of the Bickley jet in one régime. However, the swirl in the vortex becomes important for long waves, very strongly modifying the sinuous and varicose Bickley modes. We find in particular that the asymptotic results obtained agree well with our numerical solutions for the sinuous mode, but not for the varicose mode, the difficulty in the latter case being apparently due to mode jumping. The asymptotics show a varicose long-wave neutral mode for positive azimuthal wavenumber, and two such modes for negative wavenumbers. The upper neutral sinuous mode occurs at much, larger wavenumber than in the Bickley case, and its structure is also presented. The study overall is aimed at providing a basis for the investigation of strongly nonlinear effects.
The motion of a rigid body in viscous fluid bounded by a plane wall
Authors: Hsu Richard , Ganatos Peter
Published: April 2006

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.

Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.

The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.
Extremal energy properties and construction of stable solutions of the Euler equations
Authors: Vallis G. K. , Carnevale G. F. , Young W. R.
Published: April 2006

Certain modifications of the Euler equations of fluid motion lead to systems in which the energy decays or grows monotonically, yet which preserve other dynamically important characteristics of the field. In particular, all topological invariants associated with the vorticity field are preserved. In cases where isolated energy extrema exist, a stable steady flow can be found. In two dimensions, highly constrained by vorticity invariants, it is shown that the modified dynamics will lead to at least one non-trivial stationary, generally stable, solution of the equations of motion from any initial conditions. Numerical implementation of the altered dynamics is straightforward, and thus provides a practical method for finding stable flows. The method is sufficiently general to be of use in other dynamical systems.

Insofar as three-dimensional turbulence is characterized by a cascade of energy, but not topological invariants, from large to small scales, the procedure has direct physical significance. It may be useful as a parameterization of the effects of small unresolved scales on those explicitly resolved in a calculation of turbulent flow.
Heating a salinity gradient from a vertical sidewall: linear theory
Authors: Kerr Oliver S.
Published: April 2006

When a body of fluid with a vertical salinity gradient is heated from a single vertical wall, instabilities have sometimes been observed experimentally (Thorpe, Hutt & Soulsby 1969; Chen, Briggs & Wirtz 1971; Tsinober & Tanny 1986). We present a linear stability analysis for this configuration and show that for strong salinity gradients the stability of the fluid to infinitesimal disturbances is governed by a single non-dimensional parameter,
\[
Q = \frac{(1-\tau)^6g(\alpha\Delta T)^6}{\nu\kappa_Sl^2(-\beta\overline{S}_z)^5}
\]
where g is the acceleration due to gravity, α the coefficient of thermal expansion, β the density change due to a unit change in the salinity, ΔT the change of temperature at the wall, $\overline{S}_z$ the vertical salinity gradient, l the horizontal lengthscale (kTt)½, v the kinematic viscosity, (κTt)½ the diffusivity of heat, kS the diffusivity of salt and τ the salt/heat diffusivity ratio. This non-dimensional parameter is related to the Rayleigh number, however, it involves two different lengthscales; the penetration depth of the thermal front, l, and the height by which a heated element of fluid would rise in the salinity gradient, $g\alpha \Delta T/(- \beta \overline{S}_z)$. This analysis is valid when the ratio of the vertical lengthscale to the horizontal lengthscale is small. This analysis gives good agreement with the published experimental results.
Hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas: resistance and mobility functions
Authors: Ying Ruoxian , Peters Michael H.
Published: April 2006

The problem of the hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas is treated following the singular perturbation scheme of Sone & Onishi (1978), valid at small, but finite, particle Knudsen numbers. In this method the solution to the linearized BGKW transport equation governing the gas molecular motion consists of two parts: one describing a Knudsen layer where the actual microscopic boundary conditions are applied and the other describing a Hilbert region where the Stokes equations of continuum hydrodynamics hold. The Knudsen-layer solution establishes the ‘slip’ boundary conditions for the Stokes equations. Here we clearly distinguish between particle ‘slip’ due to the type of boundary conditions and particle ‘slip’ due to lengthscale effects as measured by the Knudsen number. The present analysis has been carried out to first order in particle Knudsen number for the case of diffuse reflective molecular boundary conditions. General relationships between the first- and zero-order velocity fields, both of which are written in the form of Lamb's (1932) solution to the Stokes equation, are established. It is illustrated how these general relationships can be used to determine the force and torque acting on a single sphere translating and rotating in a slightly rarefied gas. Finally, we have treated the two-sphere problem in a slightly rarefied gas using the twin multipole expansion method of Jeffrey & Onishi (1984). Here again, general relationships are established between the solutions of the first-order fluid velocity field and the zero-order velocity field, the latter being shown to recover Jeffrey & Onishi's results for stick boundary conditions. These general relationships are subsequently used to determine the complete resistance and mobility matrices of the two-sphere system. The symmetric properties of the resistance and mobility matrices are demonstrated for slip boundary conditions, in agreement with the general proof of Landau & Lifshitz (1980) and Bedeaux, Albano & Mazur (1977).
Lagrangian statistics from direct numerical simulations of isotropic turbulence
Authors: Yeung P. K. , Pope S. B.
Published: April 2006

A comprehensive study is reported of the Lagrangian statistics of velocity, acceleration, dissipation and related quantities, in isotropic turbulence. High-resolution direct numerical simulations are performed on 643and 1283grids, resulting in Taylor-scale Reynolds numbers Rλin the range 38-93. The low-wavenumber modes of the velocity field are forced so that the turbulence is statistically stationary. Using an accurate numerical scheme, of order 4000 fluid particles are tracked through the computed flow field, and hence time series of Lagrangian velocity and velocity gradients are obtained.

The results reported include: velocity and acceleration autocorrelations and spectra; probability density functions (p.d.f.'s) and moments of Lagrangian velocity increments; and p.d.f.'s, correlation functions and spectra of dissipation and other velocity-gradient invariants. It is found that the acceleration variance (normalized by the Kolmogorov scales) increases as R½λ- a much stronger dependence than predicted by the refined Kolmogorov hypotheses. At small time lags, the Lagrangian velocity increments are distinctly non-Gaussian with, for example, flatness factors in excess of 10. The enstrophy (vorticity squared) is found to be more intermittent than dissipation, having a standard-deviation-to-mean ratio of about 1.5 (compared to 1.0 for dissipation). The acceleration vector rotates on a timescale about twice the Kolmogorov scale, while the timescales of acceleration magnitude, dissipation and enstrophy appear to scale with the Lagrangian velocity timescale.