The displacement effect of a sphere in a two-dimensional shear flow

1956 ◽  
Vol 1 (2) ◽  
pp. 142-162 ◽  
Author(s):  
I. M. Hall
Keyword(s):  
Shear Flow ◽  
Three Dimensional ◽  
Pitot Tube ◽  
Experimental Result ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Dimensional Approach ◽  
Displacement Effect ◽  
First Approximation ◽  
Vortex Tubes

This paper contains a theoretical investigation of the displacement effect of a pitot tube in a shear flow. Viscosity is neglected throughout so that the vorticity field alone is considered.It is first shown that a two-dimensional approach does not produce a large enough displacement effect because it does not include the stretching of vortex tubes that takes place around a three-dimensional pitot tube. Then the three-dimensional problem is considered. A solution is obtained in the plane of symmetry for a sphere in a shear flow. This solution is found by making an assumption about the rate of stetching of vortex tubes perpendicular to the plane of symmetry and then considering the shear flow as a small perturbation of a uniform flow. A solution in the plane of symmetry is sufficient to obtain the displacement effect, which is found to be of the same order as the experimental result obtained by Young & Maas (1936) for a conventional pitot tube. The sphere may be considered to represent a conventional pitot tube (of slightly smaller diameter), so it is concluded that a large part of the displacement effect of a pitot tube may be accounted for without the inclusion of viscosity, i.e. by consideration of the vorticity field alone.To a first approximation, the vorticity in the plane of symmetry is found to depend only on the distance from the centre of the sphere.An outline of shear flows past some two-dimensional bodies is given in an appendix. The bodies considered are a circular cylinder and a two-dimensional ‘pitot-tube’ consisting of two parallel semi-infinite plates.

Shifting perspectives: method, media and the complex image

1998 ◽  
Vol 10 (1-3) ◽  
pp. 100-108 ◽  
Author(s):  
Alicia Colson ◽  
Ross Parry
Keyword(s):  
Image Processing ◽  
Three Dimensional ◽  
Geographical Location ◽  
Spatial Relationship ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Complex Image ◽  
Cultural Resonance

This article argues that the analysis of a threedimensional image demanded a three-dimensional approach. The authors realise that discussions of images and image processing inveterately conceptualise representation as being flat, static, and finite. The authors recognise the need for a fresh acuteness to three-dimensionality as a meaningful – although problematic – element of visual sources. Two dramatically different examples are used to expose the shortcomings of an ingrained two-dimensional approach and to facilitate a demonstration of how modern (digital) techniques could sanction new historical/anthropological perspectives on subjects that have become all too familiar. Each example could not be more different in their temporal and geographical location, their cultural resonance, and their historiography. However, in both these visual spectacles meaning is polysemic. It is dependent upon the viewer's spatial relationship to the artifice as well as the spirito-intellectual viewer within the community. The authors postulate that the multi- faceted and multi-layered arrangement of meaning in a complex image could be assessed by working beyond the limitations of the two-dimensional methodological paradigm and by using methods and media that accommodated this type of interconnectivity and representation.

A New Approach to Thin Aerofoil Theory

1951 ◽  
Vol 3 (3) ◽  
pp. 193-210 ◽  
Author(s):  
M.J. Lighthill
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Approximate Solutions ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
General Technique ◽  
New Approach ◽  
Flow Problems ◽  
Physical Problems ◽  
First Approximation

SummaryThe general technique for rendering approximate solutions to physical problems uniformly valid is here applied to the simplest form of the problem of correcting the theory of thin wings near a rounded leading edge. The flow investigated is two-dimensional, irrotational and incompressible, and therefore the results do not materially add to our already extensive knowledge of this subject, but the method, which is here satisfactorily checked against this knowledge, shows promise of extension to three-dimensional, and compressible, flow problems.The conclusion, in the problem studied here, is that the velocity field obtained by a straightforward expansion in powers of the disturbances, up to and including either the first or the second power, with coefficients functions of co-ordinates such that the leading edge is at the origin and the aerofoil chord is one of the axes, may be rendered a valid first approximation near the leading edge, as well as a valid first or second approximation away from it, if the whole field is shifted downstream parallel to the chord for a distance of half the leading edge radius of curvature ρL. It follows that the fluid speed on the aerofoil surface, as given on such a straightforward second approximation as a function of distance x along the chord, similarly is rendered uniformly valid (see equation (52)) if the part singular like x-1 is subtracted and the remainder is multiplied by .

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Instability of pressure-driven gas–liquid two-layer channel flows in two and three dimensions

2018 ◽  
Vol 849 ◽  
pp. 1-34 ◽  
Author(s):  
Lennon Ó Náraigh ◽  
Peter D. M. Spelt
Keyword(s):  
Flow Pattern ◽  
Linear Theory ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Channel Flows ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Flow Pattern Map

We study unstable waves in gas–liquid two-layer channel flows driven by a pressure gradient, under stable stratification, not assumed to be set in motion impulsively. The basis of the study is direct numerical simulation (DNS) of the two-phase Navier–Stokes equations in two and three dimensions for moderately large Reynolds numbers, accompanied by a theoretical description of the dynamics in the linear regime (Orr–Sommerfeld–Squire equations). The results are compared and contrasted across a range of density ratios $r=\unicode[STIX]{x1D70C}_{liquid}/\unicode[STIX]{x1D70C}_{gas}$. Linear theory indicates that the growth rate of small-amplitude interfacial disturbances generally decreases with increasing $r$; at the same time, the cutoff wavenumbers in both streamwise and spanwise directions increase, leading to an ever-increasing range of unstable wavenumbers, albeit with diminished growth rates. The analysis also demonstrates that the most dangerous mode is two-dimensional in all cases considered. The results of a comparison between the DNS and linear theory demonstrate a consistency between the two approaches: as such, the route to a three-dimensional flow pattern is direct in these cases, i.e. through the strong influence of the linear instability. We also characterize the nonlinear behaviour of the system, and we establish that the disturbance vorticity field in two-dimensional systems is consistent with a mechanism proposed previously by Hinch (J. Fluid Mech., vol. 144, 1984, p. 463) for weakly inertial flows. A flow-pattern map constructed from two-dimensional numerical simulations is used to describe the various flow regimes observed as a function of density ratio, Reynolds number and Weber number. Corresponding simulations in three dimensions confirm that the flow-pattern map can be used to infer the fate of the interface there also, and show strong three-dimensionality in cases that exhibit violent behaviour in two dimensions, or otherwise the development of behaviour that is nearly two-dimensional behaviour possibly with the formation of a capillary ridge. The three-dimensional vorticity field is also analysed, thereby demonstrating how streamwise vorticity arises from the growth of otherwise two-dimensional modes.

scholarly journals Definition and prevalence of severe and persistent mental illness

2000 ◽  
Vol 177 (2) ◽  
pp. 149-155 ◽  
Author(s):  
Mirella Ruggeri ◽  
Morven Leese ◽  
Graham Thornicroft ◽  
Giulia Bisoffi ◽  
Michele Tansella
Keyword(s):  
Mental Illness ◽  
Psychotic Disorders ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Prevalence Rates ◽  
Dimensional Approach ◽  
Persistent Mental Illness ◽  
Annual Prevalence ◽  
Catchment Areas ◽  
Service Contact

BackgroundThere is little consistency in how severe mental illness (SMI) is defined in practice, and no operational definitions.AimsTo test two operationalised definitions, based on the National Institute of Mental Health (1987) definition: the first uses three criteria (diagnosis of psychosis; duration of service contact ≥ 2 years; GAF score ≤ 50), the second only the last two.MethodAnnual prevalence rates of SMI in two European catchment areas for each criterion and the criteria combined were calculated.ResultsThe first definition produced rates of 2.55 and 1.34/1000 in London and Verona, respectively; the second permitted an additional 0.98/1000 non-psychotic disorders to be included in Verona.ConclusionsThe three-dimensional definition selects a small group of patients with SMI who have psychotic disorders. The two-dimensional approach allows estimates of SMI prevalence rates which include all forms of mental disorder.

Cilia Microtubule Deformation: A Preliminary Report

1976 ◽  
Vol 34 ◽  
pp. 80-81
Author(s):  
R. Redding
Keyword(s):  
Dimensional Analysis ◽  
Preliminary Report ◽  
Recent Literature ◽  
Three Dimensional ◽  
Curvilinear Relationship ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Cross Sectional

Various hypotheses for the mechanism of ciliar motility either purport or oppose the concept of microtubule contraction. Recent literature supporting the Sliding Microtubule Model has established that microtubule doublets move relative to one another during the process of bending. Satir (1968) concluded that there is no change of length in the doublets during bending of cilia. He based his conclusion upon: (1) circular relationships and (2) a two dimensional configuration of the microtubules. Accuracy of the circular relationships is dependent upon how close the approximation is to the true curvilinear relationship expressed by a ciliutn. Cross sectional rotation during bending may limit the validity of two dimensional analysis. This communication is a preliminary report on a new, three dimensional approach for determining the deformational characteristics of elongation or shortening of microtubules as they may be expressed in cilia.

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