bluuebunny/crossref_metadata_2025_split huggingface dataset:
Supersonic cooling by shock–vortex interaction
Authors: Fox M. D. , Kurosaka M. 
Published: April 2006

The subject of total temperature separation in jets was treated in Fox et al. (1993) for subsonic jets. When we extended this study to the case of supersonic jets, we found the presence of a different mechanism of cooling, an effect which does not appear to have been known in the past. Named the ‘shock-induced total temperature separation’, this cooling can be of much greater magnitude than the subsonic cooling treated previously; it is caused by the interaction of convected vortical structures near the jet exhaust with the shock structure of the supersonic jet.In studying this phenomenon, we focus our attention on overexpanded jets exiting a convergent-divergent nozzle. The theoretical results for the shock-induced cooling which are based on a linearized, unsteady supersonic analysis are shown to agree favourably with experiments.When an impingement plate is inserted, the shock-induced cooling would manifest itself as wall cooling, whose magnitude is significantly larger than the subsonic counterpart. This has implications for heat transfer not only in jets, but wherever vortical structures may interact with shock waves.
Filling flows, cliff erosion and cleaning flows
Authors: Peregrine D. H. , Kalliadasis S. 
Published: April 2006

The flows considered here are those where a container or confined region is being filled by a substantial flow of liquid. The case of especial interest is where the incoming flow fills a large part of the cross-section of the container, for example where a nearly full flowing conduit has one end suddenly closed and hence fills rapidly, or where a water wave propagates close to the under surface of a horizontal structure and then rapidly fills the available space. These flows are taken to be so rapid that gravity is unimportant and yet not so violent that compressibility effects become significant. Important features, such as the greatly enhanced pressures and a thin high-velocity return jet are evaluated. The calculated pressures are very significantly greater than those associated with the incoming flow velocity and can be especially large when there is little clearance between the flow and the container boundary. One of many possible applications is in the extension of cracks and openings in coastal cliffs and structures. The flows could also be relevant to estimating the forces on the underside of some marine structures. A simple two-dimensional irrotational free-surface solution is found for the flow, which is steady in a suitably moving frame of reference.Reversing the direction of one of these filling flows gives the case of a narrow high-speed jet which may be used to flush liquid out of cavities and containers. The optimum size of jet is calculated.
The structure and development of a wing-tip vortex
Authors: Devenport William J. , Rife Michael C. , Liapis Stergios I. , Follin Gordon J. 
Published: April 2006

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.
Linear and nonlinear dynamics of a differentially heated slot under gravity modulation
Authors: Farooq A. , Homsy G. M. 
Published: April 2006

In this paper we consider the effect of sinusoidal gravity modulation of size ε on a differentially heated infinite slot in which a vertical temperature stratification is imposed on the walls. The slot problem is characterized by a Rayleigh number, Prandtl number, and the imposed uniform stratification on the walls. When ε is small, we show by regular perturbation expansion in ε that the modulation interacts with the natural mode of the system to produce resonances, confirming the results of Farooq & Homsy (1994). For ε ∼ O(1) we show that the modulation can potentially destabilize the longwave eigenmodes of the slot problem. This is achieved by projecting the governing equations onto the least-damped eigenmode, and investigating the resulting Mathieu equation via Floquet theory. No instability was found at large values of the Prandtl number and also low stratification, when there are no travelling modes present.To understand the nonlinear saturation mechanisms of this growth, we consider a two-mode model of the slot problem with the primary mode being the least-damped travelling parallel-flow mode as before and a secondary mode of finite wavenumber. By projecting the governing equations onto these two modes we obtained the equations for temporal evolution of the two modes. For modulation amplitudes above critical, the growth of the primary mode is saturated resulting in a stable weak nonlinear synchronous oscillation of the primary mode. An unexpected and intriguing feature of the coupling is that the secondary mode exhibits very high-frequency bursts which appear once every cycle of the forcing frequency.
Second-order horizontal steady forces and moment on a floating body with small forward speed
Authors: Aranha J. A. P. 
Published: April 2006

In a recent work, a simple formula was derived for the ‘wave drift damping’ in a two-dimensional floating body and the obtained expression is exact within the context of the related theory, where only leading-order terms in the forward speed are retained. This formula is now generalized for a three-dimensional problem and the coefficients of the ‘wave drift damping matrix’ are given explicitly in terms of the standard second-order steady forces and moment in the horizontal plane; Munk's yaw moment, related with the steady second-order potential and discussed in Grue & Palm (1993), is not analysed in this paper and the effect of an eventual small angular velocity around the vertical axis is also not considered.Numerical results agree in general with the proposed formula although in a specific case a consistent disagreement has been observed, as discussed in §5.
Stability of a potential vorticity front: from quasi-geostrophy to shallow water
Authors: Boss E. , Paldor N. , Thompson L. 
Published: April 2006

The linear stability of a simple two-layer shear flow with an upper-layer potential vorticity front overlying a quiescent lower layer is investigated as a function of Rossby number and layer depths. This flow configuration is a generalization of previously studied flows whose results we reinterpret by considering the possible resonant interaction between waves. We find that instabilities previously referred to as ‘ageostrophic’ are a direct extension of quasi-geostrophic instabilities.Two types of instability are discussed: the classic long-wave quasi-geostrophic baroclinic instability arising from an interaction of two vortical waves, and an ageostrophic short-wave baroclinic instability arising from the interaction of a gravity wave and a vortical wave (vortical waves are defined as those that exist due to the presence of a gradient in potential vorticity, e.g. Rossby waves). Both instabilities are observed in oceanic fronts. The long-wave instability has length scale and growth rate similar to those found in the quasi-geostrophic limit, even when the Rossby number of the flow is O(1).We also demonstrate that in layered shallow-water models, as in continuously stratified quasi-geostrophic models, when a layer intersects the top or bottom boundaries, that layer can sustain vortical waves even though there is no apparent potential vorticity gradient. The potential vorticity gradient needed is provided at the top (or bottom) intersection point, which we interpret as a point that connects a finite layer with a layer of infinitesimal thickness, analogous to a temperature gradient on the boundary in a continuously stratified quasi-geostrophic model.
Near-wake structure of an oscillating cylinder: effect of controlled shear-layer vortices
Authors: Chyu C. K. , Rockwell D. 
Published: April 2006

The instantaneous structure of the near wake of a cylinder subjected to small-amplitude perturbations is characterized using high-image-density particle image velocimetry. Emphasis is on control of the small-scale shear-layer vortices, which feed into the Kármán vortices. Modifications of the Kármán vortex formation are classified according to patterns of modulated and locked-on shear-layer vortices. The formation length of the Kármán vortices can be dramatically shortened and, in the limiting case, occur adjacent to the base of the cylinder when it is perturbed at the inherent instability frequency of the shear layer and its subharmonics. Moreover, the induced shear-layer vortices can lead to large-amplitude transverse undulations of the entire near-wake region during formation of the Kármán vortices.These variations of the near-wake structure are further elucidated by considering the transient response of the wake, induced by abrupt cessation and onset of periodic motion of the cylinder. Distinctive intermediate states of the wake arise during relaxation to its asymptotic state; such relaxation requires a very large number of periods of the inherent instability of the shear layer.
Dynamical flow characterization of transitional and chaotic regimes in converging–diverging channels
Authors: Guzmán A. M. , Amon C. H. 
Published: April 2006

Numerical investigation of laminar, transitional and chaotic flows in converging–diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as timedelay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos.Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging–diverging channels. Autocorrelation functions, pseudophase space representations and Poincaré maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincaré maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging–diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.
Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients
Authors: Yeung P. K. 
Published: April 2006

The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.
Expanding gas clouds of ellipsoidal shape: new exact solutions
Authors: Gaffet B. 
Published: April 2006

We consider a model of a freely expanding gas cloud of tri-axial ellipsoidal shape, Gaussian density profile, proposed by Dyson (1968). The ellipsoids are deformable, but are further constrained here to have principal axes maintaining a fixed orientation in space: the study of the more general rotating flows is deferred to a future work. Our main result is that, when the fluid is a monatomic gas with adiabatic index γ = 5/3, the model is completely integrable by quadratures. Solutions starting from a state of rest are describable by elliptic functions; the generic solution however is a more general transcendent that cannot be reduced to elliptic type.The complete integrability of Dyson's model may be ascribed to the fact that it possesses the Painlevé property (Ince 1956; Ablowitz & Segur 1977), meaning, essentially, that the solutions are meromorphic functions of the independent variable, admitting only pole singularities. However, the correct choice of independent variable here is not just the physical time t: rather, it is the thermasy (van Danzig 1939) u = ∫ Tdt, which is one of the potentials occurring in the Clebsch transformation.Further investigation will be required to test Dyson's full ‘spinning gas cloud’ model for an eventual Painlevé property.
The instability and breakdown of tall columnar vortices in a quasi-geostrophic fluid
Authors: Dritschel David G. , JuáRez Manuel De La Torre 
Published: April 2006

We examine the linear stability of elliptical columns of uniform potential vorticity subject to two-dimensional (horizontal) straining within a rapidly rotating, stratified (quasi-geostrophic) fluid. We find that horizontal straining can promote the exponential growth of three-dimensional disturbances when the vortex height-to-width aspect ratio exceeds, qualitatively, three times the ratio of the Coriolis parameter to the buoyancy frequency. This instability is not related to the usual baroclinic instability which operates on shallow vortex columns whose potential vorticity changes sign with height. The nonlinear development of these instabilities is investigated numerically using a high-resolution contour surgery algorithm. Simulations are conducted for both a Boussinesq (ocean-like) fluid and a compressible (atmospheric-like) fluid having exponentially decreasing density with height. The simulations reveal a generic nonlinear development that results in a semi-ellipsoidal baroclinic vortex dome at the lower surface and, in the case of a Boussinesq fluid, another such dome at the upper surface.The related problem of two interacting vortex columns is also examined. A generic three-dimensional instability and nonlinear development occurs no matter how great the distance between the vortex columns, provided that they are sufficiently tall.Our results may bear upon the observed structure of many atmospheric and oceanic vortices, whose height-to-width aspect ratios are consistent with our findings. Remarkably, even strongly ageostrophic vortices, such as tropical cyclones, fit the pattern. Our results furthermore re-open questions about the long-time nature of freely decaying quasi-geostrophic turbulence, for which recent simulations indicate a progressive two-dimensionalization by vortex alignment, while earlier simulations have indicated long-lived baroclinic vortices, not unlike what we find here.
Writing therapy in brief workplace counselling: Collaborative writing as inquiry
Authors: Wright Jeannie K. 
Published: April 2006

AbstractThe purpose of this collaborative research was to reflect on one client's experience of using writing therapy during brief workplace counselling. The client/co‐researcher used expressive and creative writing between counselling sessions, the benefits of which are reported. A brief review of the literature on writing therapy is provided. The focus of the study is on investigating the process of writing therapy from the client's point of view. The epistemological assumptions and research methods are influenced by narrative inquiry. Feminist values inform both the therapeutic practice and research.
Therapists’ experiences of relational depth: A qualitative interview study
Authors: Cooper Mick 
Published: April 2006

AbstractThe aim of this study was to explore therapists’ experiences of meeting their clients at a level of ‘relational depth’. This was defined as a feeling of profound contact and engagement with another, in which the therapists experienced high levels of empathy, acceptance and transparency towards their clients, and experienced their clients as acknowledging their empathy and acceptance in a genuine way. Participants were primarily experienced person‐centred therapists, five of whom were female and three of whom were male. Data was gathered through the use of qualitative, unstructured interviews within the broader framework of a person‐centred and phenomenological methodology. All interviewees described experiencing moments of relational depth with their clients, and substantial commonalities emerged in their descriptions. These included heightened feelings of empathy, acceptance and receptivity towards their clients; powerful feelings of immersion in the therapeutic work; increased perceptual clarity; and greater levels of awareness, aliveness and satisfaction. At these times, the therapists also experienced their clients as highly transparent; articulating core concerns and issues; and reciprocating the therapist's acknowledgement of them in a flowing, bi‐directional encounter. These findings are discussed in relation to recent research on ‘presence’ and ‘flow’ and it is proposed that relational depth can be conceptualised as a form of ‘co‐presence’ or a co‐experiencing of the person‐centred ‘core conditions’. Limitations of the study and areas for further research are discussed.
A general theory of almost convex functions
Authors: Dilworth S. , Howard Ralph , Roberts James 
Published: April 2006

Let

Δ
m

=
{
(

t
0

,
…
,

t
m

)
∈

R

m
+
1

:

t
i

≥
0
,

∑

i
=
0

m

t
i

=
1
}

\Delta _m=\{(t_0,\dots , t_m)\in \mathbf {R}^{m+1}: t_i\ge 0, \sum _{i=0}^mt_i=1\}

be the standard

m
m

-dimensional simplex and let

∅
≠
S
⊂

⋃

m
=
1

∞

Δ
m

\varnothing \ne S\subset \bigcup _{m=1}^\infty \Delta _m

. Then a function

h
:
C
→

R

h\colon C\to \mathbf {R}

with domain a convex set in a real vector space is

S
S

-almost convex iff for all

(

t
0

,
…
,

t
m

)
∈
S

(t_0,\dots , t_m)\in S

and

x
0

,
…
,

x
m

∈
C

x_0,\dots , x_m\in C

the inequality
\[

h
(

t
0

x
0

+
⋯
+

t
m

x
m

)
≤
1
+

t
0

h
(

x
0

)
+
⋯
+

t
m

h
(

x
m

)

h(t_0x_0+\dots +t_mx_m)\le 1+ t_0h(x_0)+\cdots +t_mh(x_m)

\]
holds. A detailed study of the properties of

S
S

-almost convex functions is made. If

S
S

contains at least one point that is not a vertex, then an extremal

S
S

-almost convex function

E
S

:

Δ
n

→

R

E_S\colon \Delta _n\to \mathbf {R}

is constructed with the properties that it vanishes on the vertices of

Δ
n

\Delta _n

and if

h
:

Δ
n

→

R

h\colon \Delta _n\to \mathbf {R}

is any bounded

S
S

-almost convex function with

h
(

e
k

)
≤
0

h(e_k)\le 0

on the vertices of

Δ
n

\Delta _n

, then

h
(
x
)
≤

E
S

(
x
)

h(x)\le E_S(x)

for all

x
∈

Δ
n

x\in \Delta _n

. In the special case

S
=
{
(
1

/

(
m
+
1
)
,
…
,
1

/

(
m
+
1
)
)
}

S=\{(1/(m+1),\dotsc , 1/(m+1))\}

, the barycenter of

Δ
m

\Delta _m

, very explicit formulas are given for

E
S

E_S

and

κ
S

(
n
)
=

sup

x
∈

Δ
n

E
S

(
x
)

\kappa _S(n)=\sup _{x\in \Delta _n}E_S(x)

. These are of interest, as

E
S

E_S

and

κ
S

(
n
)

\kappa _S(n)

are extremal in various geometric and analytic inequalities and theorems.
A Study of the psychological effects of facial deformity in children
Authors: LANSDOWN RICHARD , POLAK LETTEKE 
Published: April 2006

SUMMARY
Anecdotal reports of the psychological effects of facial deformity suggest that the area around the mouth is of crucial importance. In the first of two studies, children‐ in London and Amsterdam ranked drawings of facially deformed children; their ordering was consistent, with a hare lip or protruding teeth being the most commonly rejected.A second study followed up 24 children aged about 8 years who had had a hare lip repair. The results did not confirm the hypothesis that such children differ from their non‐handicapped peers in overt behaviour in school.