bluuebunny/crossref_metadata_2025_split huggingface dataset:
Melting driven by vigorous compositional convection
Authors: Kerr Ross C. 
Published: April 2006

The melting of a solid in contact with a hot fluid is quantified for the case in which a difference between the densities of the fluid and of the melted solid is able to drive vigorous compositional convection. A scaling analysis is first used to obtain a theoretical expression for the melting rate that is valid for a certain range of Stefan numbers. This expression is then compared with melting velocities measured in laboratory experiments in which ice and wax are melted when they are overlain or underlain by hot aqueous solutions. The melting velocities are consistent with the theoretical expression, and are found to depend on the heats of solution that are released when the melted solids mix with the solutions. The experiments also indicate that, for vigorous convection to occur during the melting of a floor, the unstable compositional buoyancy needs to be at least twice the stabilizing thermal buoyancy.An important geological situation in which melting occurs is when large volumes of basaltic magma are intruded into the Earth's continental crust. The theoretical and experimental results are used and extended to examine quantitatively the melting of the floor and walls of the magma chamber, and of crustal blocks that fall into the chamber.
A stationary potential-flow approximation for a breaking-wave crest
Authors: Jenkins Alastair D. 
Published: April 2006

The flow in a breaking-wave crest is represented by a complex velocity potential on a Riemann surface, satisfying the Bernoulli condition on two free boundaries. The flow is assumed to be stationary in the reference frame which moves with the wave crest, and at large distances approximates Stokes corner flow in the main part of the fluid and a parabolic descending flow in the jet. The interaction of the jet with the rest of the fluid is neglected.The solution is obtained by means of a conformal transformation from a bounded, teardrop-shaped domain, using a Faber polynomial expansion. The Bernoulli condition is applied at a number of discrete points on the boundaries, and the resulting nonlinear equations for the expansion coefficients are solved iteratively. The resulting surface form is similar to that obtained by laboratory experiments and time-dependent numerical simulations of waves up to the point of breaking, with a stagnation point at the top of the crest, an overturning loop with major axis$\ap 8g^{-\frac{1}{3}}\Psi^{\frac{2}{3}}$, and a maximum acceleration of ≈ 5.4g, wheregis the gravitational acceleration and ψ is the flux in the jet.
On the stability of flow in an elliptic pipe which is nearly circular
Authors: Davey A. , Salwen H. 
Published: April 2006

In an earlier paper (Davey 1978) the first author investigated the linear stability of flow in a straight pipe whose cross-section was an ellipse, of small ellipticity e, by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. That paper contained some serious errors which we correct herein. We show analytically that for the most important mode n = 1, for which the circular problem has a double eigenvalue c0 as the ‘swirl’ can be in either direction, the ellipticity splits the double eigenvalue into two separate eigenvalues c0 ± e2c12, to leading order, when the cross-sectional area of the pipe is kept fixed. The imaginary part of c12 is non-zero and so the ellipticity always makes the flow less stable. This specific problem is generic to a much wider class of fluid dynamical problems which are made less stable when the symmetry group of the dynamical system is reduced from S1 to Z2.In the Appendix, P. G. Drazin describes simply the qualitative structure of this problem, and other problems with the same symmetries, without technical detail.
Nonlinear interaction of shear flow with a free surface
Authors: Dimas Athanassios A. , Triantafyllou George S. 
Published: April 2006

In this paper the nonlinear evolution of two-dimensional shear-flow instabilities near the ocean surface is studied. The approach is numerical, through direct simulation of the incompressible Euler equations subject to the dynamic and kinematic boundary conditions at the free surface. The problem is formulated using boundary-fitted coordinates, and for the numerical simulation a spectral spatial discretization method is used involving Fourier modes in the streamwise direction and Chebyshev polynomials along the depth. An explicit integration is performed in time using a splitting scheme. The initial state of the flow is assumed to be a known parallel shear flow with a flat free surface. A perturbation having the form of the fastest growing linear instability mode of the shear flow is then introduced, and its subsequent evolution is followed numerically. According to linear theory, a shear flow with a free surface has two linear instability modes, corresponding to different branches of the dispersion relation: Branch I, at low wavenumbers; and Branch II, at high wavenumbers for low Froude numbers, and low wavenumbers for high Froude numbers. Our simulations show that the two branches have a distinctly different nonlinear evolution.Branch I: At low Froude numbers, Branch I instability waves develop strong oval-shaped vortices immediately below the ocean surface. The induced velocity field presents a very sharp shear near the crest of the free-surface elevation in the horizontal direction. As a result, the free-surface wave acquires steep slopes, while its amplitude remains very small, and eventually the computer code crashes suggesting that the wave will break.Branch II: At low Froude numbers, Branch II instability waves develop weak vortices with dimensions considerably smaller than their distance from the ocean surface. The induced velocity field at the ocean surface varies smoothly in space, and the free-surface elevation takes the form of a propagating wave. At high Froude numbers, however, the growing rates of the Branch II instability waves increase, resulting in the formation of strong vortices. The free surface reaches a large amplitude, and strong vertical velocity shear develops at the free surface. The computer code eventually crashes suggesting that the wave will break. This behaviour of the ocean surface persists even in the infinite-Froude-number limit.It is concluded that the free-surface manifestation of shear-flow instabilities acquires the form of a propagating water wave only if the induced velocity field at the ocean surface varies smoothly along the direction of propagation.
The influence of coherent structures and microfronts on scaling laws using global and local transforms
Authors: Mahrt L. , Howell J. F. 
Published: April 2006

This study examines the influence of coherent structures and attendant microfronts on scaling laws. Toward this goal, we analyse atmospheric observations of turbulence collected 45 m above a flat surface during the Lammefjord Experiment in Denmark. These observations represent more than 40 hours of nearly stationary strong wind conditions and include more than 1600 samples of the main coherent structures. These samples occupy about 40% of the total record and explain the majority of the Reynolds stress.To study the dependence of the scaling laws on the choice of basis set, the time series of velocity fluctuations are decomposed into Fourier modes, the local Haar basis set and eigenvectors of the lagged covariance matrix. The three decompositions are compared by formulating joint projections. The decompositions are first applied to the samples of phased-locked coherent structures centred about eddy microfronts. The eigenvector decomposition is able to partially separate the small-scale variances due to the coherent eddy microfronts from that due to the small-scale structure with random phase. In the Fourier spectrum, both of these contributions to the variance appear together at the higher wavenumbers and their individual contributions cannot be separated. This effect is relatively minor for the scale distribution of energy but exerts an important influence on higher-moment statistics. Deviations from the −$\frac53$ scaling are observed to be slight and depend on choice of basis set.The microfronts strongly influence the higher-order statistics such as the sixth-order structure function traditionally used to estimate the energy transfer variance. The intermittency of fine-scale structure, energy transfer variance and dissipation are not completely characterized by random phase, as often assumed, but are partly associated with microfronts characterized by systematic phase with respect to the main transporting eddies. These conclusions are supported by both the higher-order structure function and the higher-order Haar transform.The Fourier and Haar spectra are also computed for the entire record. The peak of the Haar energy spectrum occurs at smaller scales than those of the Fourier spectrum. The Haar transform is local and emphasizes the width of the events. The Fourier spectrum peaks at the scale of the main periodicity, if it exists, which includes the spacing between the events.
Stability analysis and large-eddy simulation of rotating turbulence with organized eddies
Authors: Cambon Claude , Benoit Jean-Pierre , Shao Liang , Jacquin Laurent 
Published: April 2006

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame.The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Ω, maximum destabilization is obtained for zero tilting vorticity (½W + 2Ω = 0) whereas stability occurs for zero absolute vorticity (2Ω = 0) These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number $B=2\Omega(W+2\Omega)/W^2$ is not always a good indicator of the flow stability.
Instantaneous three-dimensional concentration measurements in the self-similar region of a round high-Schmidt-number jet
Authors: Yoda M. , Hesselink L. , Mungal M. G. 
Published: April 2006

The virtually instantaneous three-dimensional concentration fields in the self-similar region of natural or unexcited, circularly excited and weakly buoyant round jets of Reynolds number based on nozzle diameter of 1000 to 4000 are measured experimentally at a spatial resolution of the order of the Kolmogorov length scale. Isoconcentration surfaces are extracted from the concentration field. These surfaces along with their geometrical parameters are used to deduce the structure and modal composition of the jet. The concentration gradient field is calculated, and its local topology is classified using critical-point concepts.Large-scale structure is evident in the form of ‘clumps’ of higher-concentration jet fluid. The structure, which has a downstream extent of about the local jet diameter, is roughly axisymmetric with a conical downstream end. This structure appears to be present only in fully turbulent jets. The antisymmetric two-dimensional images previously thought to be axial slices of an expanding spiral turn out in our data to instead be slices of a simple sinusoid in three dimensions. This result suggests that the helical mode, when present, is in the form of a pair of counter-rotating spirals, or that the +1 and −1 modes are simultaneously present in the flow, with their relative phase set by initial conditions.In terms of local structure, regions with a large magnitude in concentration gradient are shown to have a local topology which is roughly axisymmetric and compressed along the axis of symmetry. Such regions, which would be locally planar and sheet-like, may correspond to the superposition of several of the layer-like structures which are the basic structure of the fine-scale passive scalar field (Buch & Dahm 1991; Ruetsch & Maxey 1991).
Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors
Authors: Broze George , Hussain Fazle 
Published: April 2006

Conclusive experimental evidence is presented for the existence of a low-dimensional temporal dynamical system in an open flow, namely the near field of an axisymmetric, subsonic free jet. An initially laminar jet (4 cm air jet in the Reynolds number range 1.1 × 104[Lt ]ReD× 9.1 × 104) with a top-hat profile was studied using single-frequency, longitudinal, bulk excitation. Two non-dimensional control parameters – forcing frequencyStD(≡fexD/Ue, wherefezis the excitation frequency,Dis the jet exit diameter andUeis the exit velocity) and forcing amplitudeaf(≡u’f/Ue, whereu’fis the jet exit r.m.s. longitudinal velocity fluctuation at the excitation frequency) – were varied over the ranges 10-4<af< 0.3 and 0.3 <StD< 3.0 in order to construct a phase diagram. Periodic and chaotic states were found over large domains of the parameter space. The periodic attractors correspond to stable pairing (SP) and stable double pairing (SDP) of rolled-up vortices. One chaotic attractor, near SP in the parameter space, results from nearly periodic modulations of pairing (NPMP) of vortices. At large scales (i.e. approximately the size of the attractor) in phase space, NPMP exhibits approximately quasi-periodic behaviour, including modulation sidebands around ½fexinu-spectra, large closed loops in its Poincaré sections, correlation dimensionv∼ 2 and largest Lyapunov exponent λ1∼ 0. But investigations at smaller scales (i.e. distances greater than, but of the order of, trajectory separation) in phase space reveal chaos, as shown byv> 2 and λ1> 0. The other chaotic attractor, near SDP, results from nearly periodic modulations of the first vortex pairing but chaotic modulations of the second pairing and has a broadband spectrum, a dimension 2.5 [Lt ]v[Lt ] 3 and the largest Lyapunov exponent 0.2 [Lt ] λ1[Lt ] 0.7 bits per orbit (depending on measurement locations in physical and parameter spaces).A definition that distinguishes between physically and dynamically open flows is proposed and justified by our experimental results. The most important conclusion of this study is that a physically open flow, even one that is apparently dynamically open due to convective instability, can exhibit dynamically closed behaviour as a result of feedback. A conceptual model for transitional jets is proposed based on twodimensional instabilities, subharmonic resonance and feedback from downstream vortical structures to the nozzle lip. Feedback was quantified and shown to affect the exit fundamental–subharmonic phase difference ϕ – a crucial variable in subharmonic resonance and, hence, vortex pairing. The effect of feedback, the sensitivity of pairings to ϕ, the phase diagram, and the documented periodic and chaotic attractors demonstrate the validity of the proposed conceptual model.
Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity
Authors: Neves João C. , Moin Parviz , Moser Robert D. 
Published: April 2006

Convex transverse curvature effects in wall-bounded turbulent flows are significant if the boundary-layer thickness is large compared to the radius of curvature (large γ = δ/a). The curvature affects the inner part of the flow if a+, the cylinder radius in wall units, is small.Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). Statistical and structural data were extracted from the computed flow fields. The effects of the transverse curvature were identified by comparing the present results with those of the plane channel simulation of Kim, Moin & Moser (1987), performed at a similar Reynolds number. As the curvature increases, the skin friction increases, the slope of the logarithmic region decreases and turbulence intensities are reduced. Several turbulence statistics are found to scale with a curvature dependent velocity scale derived from the mean momentum equation. Near the wall, the flow is more anisotropic than in the plane channel with a larger percentage of the turbulent kinetic energy resulting from the streamwise velocity fluctuations. As the curvature increases, regions of strong normal vorticity develop near the wall.
Bifurcation for flow past a cylinder between parallel planes
Authors: Chen J.-H. , Pritchard W. G. , Tavener S. J. 
Published: April 2006

Numerical experiments are described to ascertain how the steady flow past a circular cylinder loses stability as the Reynolds number is increased. A novel feature of the present study is that the cylinder is confined between parallel planes, allowing a more definitive specification of the flow, both experimentally and computationally, than is possible for the unbounded case. Since the structure of the bifurcation is unclear from the extant literature, with the experimental and computational evidence not in good agreement, a critical appraisal of both sets of evidence is presented.A study has been made of the formation of the steady vortex pair behind the cylinder, and it has been determined that the first appearance of the vortices is not associated with a bifurcation of the full dynamical problem but instead it is probably associated with a bifurcation of a restricted kinematical problem.A set of numerical experiments has been made in which the steady flow past the cylinder was perturbed slightly and the ensuing time-dependent motions were computed. These experiments revealed that, for a given blockage ratio, the perturbation would die away at small Reynolds numbers but that, above a critical Reynolds number, the disturbance would be amplified and the flow would eventually settle down to a new state comprising a time-periodic motion.Experiments were also carried out to determine the bifurcation point numerically by considering an eigenvalue problem based on a linearization about the computed steady flow past the cylinder. The calculations showed that stability is lost through a symmetry-breaking Hopf bifurcation and that, for a given blockage ratio, the critical Reynolds number was in very good agreement with that estimated from the time-dependent computations.
On the stability of large-amplitude geostrophic flows in a two-layer fluid: the case of ‘strong’ beta-effect
Authors: Benilov E. S. 
Published: April 2006

This paper examines the stability of two-layer geostrophic flows with large displacement of the interface and strong β-effect. Attention is focused on flows with non-monotonic interface profiles which are not covered by the Rayleigh-style stability theorems proved by Benilov (1992a, b) and Benilov & Cushman-Roisin (1994). For such flows the coefficient of the highest derivative in the corresponding boundary-value problem vanishes at the point where the depth profile has an extremum. Although this singularity is similar to a critical level, it cannot be regularized by the simplistic introduction of infinitesimal viscosity through the assumption that the phase speed of the disturbance is complex. In order to regularize the singularity properly, one should consider the problem within the framework of the original ageostrophic viscous equations and, having obtained the boundary-value problem for harmonic disturbance, take the limit Rossby number → 0, viscosity → 0.The results obtained analytically and (for special cases) numerically indicate that the stability of flows with non-monotonic profiles strongly depends on the depth of the upper layer. If the upper layer is ‘thick’ (i.e. if the average depth H1 of the upper layer is of the order of the total depth of the fluid H0), the stability boundary-value problem does not have any solutions at all, which means stability (however, this stability is structurally unstable, and the flow, generally speaking, can be made weakly unstable by any small effect such as external forcing, viscosity, or ageostrophic corrections). In the case of ‘thin’ upper layer (H1/H0 [lsim ] Ro), the order of the singularity changes and all non-monotonic flows are unstable regardless of their profiles. It is also demonstrated that thin-upper-layer flows do not have to be non-monotonic to be unstable: if u–βR20 (where u is the zonal velocity, β is the β-parameter, and R0 is the deformation radius) changes sign somewhere in the flow, the stability boundary-value problem has another singular point which leads to instability.
Mixing due to grid-generated turbulence of a two-layer scalar
profile
Authors: Huq Pablo , Britter Rex E. 
Published: April 2006

In this experimental study the mixing of passive scalars that arises
from shear-free decaying grid-generated turbulence is examined. The flow
configuration consists of two homogeneous layers of equal density separated
by a sharp interface between different mean concentrations of passive
scalar. Both layers flow through a turbulence-generating grid. To determine
the effect of diffusivity the scalar was heat in one experiment and salt in
a second. The Schmidt number – the ratio of momentum to species diffusivity
– was 7 and 700 for heat and salt respectively. Velocity, scalar and flux
fields were mapped and flow visualization was undertaken to study the
flows.
Integral lengthscales and (scalar) flux were determined to be
independent of diffusivity, whereas the scalar Taylor microscales varied
with Schmidt number,
Sc,
thus illustrating the disparate effects of diffusivity on large and small
scales. The time series of signals showed a correspondence between locations
of wθ extrema and uw
extrema. Flux wθ arose from intermittent events;
and the magnitude of the time-averaged flux $\overline{w\theta}$ was found to depend on the
frequency, rather than on variations in the amplitude of
wθ events.
Streamline topology in eccentric Taylor vortex flow
Authors: Ashwin P. , King G. P. 
Published: April 2006

We investigate an asymptotic model of DiPrima & Stuart
(1972b, 1975) describing steady Taylor vortex
flow between eccentric cylinders, under the assumption that the eccentricity
ε, the clearance ratio δ and the Taylor vortex amplitude
A satisfy ε, δ and
A small. By solving a boundary value problem
for the radial eigenfunctions we numerically obtain the flow field of
DiPrima & Stuart and investigate its topology, after correcting
higher-order terms to ensure that the flow preserves volume. We find regions
of chaotic streamlines at all eccentricities and discuss the reason for
their existence. We make an analogy between the full model and a modulated
vortex flow field which qualitatively displays the same behaviour.
For large eccentricities, we examine the flow field and the topology of
its streamlines, especially where the two-dimensional flow contains a
separated region of recirculation. In this case Taylor vortices give rise to
transport of fluid particles in and out of the separated region. We find
that the onset of Taylor vortices encourages recirculation in the inflow
plane, whilst discouraging it in the outflow plane.