Drag on a circular cylinder oscillating in an elastico-viscous fluid

Résumé On calcule la force agissant sur un cylindre soumis à de petites oscillations latérales dans une masse infinie de fluide élastique et visqueux. On trouve que l'élasticité dans le liquide a pour effet de réduire à la fois la masse virtuelle du cylindre et la grandeur de la force d'amortissement agissant sur le cylindre.     

Drag on a sphere oscillating in an elastico-viscous fluid

Résumé On montre que la force agissant sur une sphère qui vibre autour d'une position moyenne dans une étendue infinie de liquide élastique et visqueux se compose de deux parties. L'une est en phase avec l'accélération et se produit parce que si la sphère se déplace le liquide se déplace nécessairement lui-même. L'autre s'oppose toujours au mouvement de la sphère et agit ainsi comme une force amortissante ne se trouvant pas en phase avec l'accélération. On trouve que pour toutes les valeurs de la fréquence, la résistance totae sur la sphère est beaucoup plus faible dans ce liquide que dans le liquide Newtonien correspondant.     

Flow past an elliptic cylinder

A theoretical investigation of the unsteady two-dimensional flow of a viscous, incompressible fluid normal to a thin elliptic cylinder is described. The cylinder, which is started impulsively from rest in an open field, continues to move with uniform velocity for the remainder of the problem. Using a vorticity-streamfunction formulation of the full Navier-Stokes equations, transformation techniques are employed to find the initial flow. Strategies which employ boundary layer theory and series expansions of the flow variables to find flow solutions for small values of time are outlined.     

Linear flow induced in fluid particle suspension by an infinite differentially rotating disk

The steady, axisymmetric laminar flow of a homogeneous incompressible fluid with suspended particles occupying the half-infinite space over a differentially rotating rigid plane boundary is analyzed in this paper. The effect of suspended particles is described by two parametersf and τ. The mass concentration parameterf is a measure of the concentration of suspended dust particles. The interaction parameter τ is a measure of the rate at which the velocity of dust particles adjusts to changes in the fluid velocity and depends upon the size of the individual particles. Due to Ekman suction, the particle density remains no longer a constant in the boundary layer but varies with the axial coordinate ξ. Flow characteristics and density variations are studied as functions off, τ and ξ. Possible limiting cases for τ≪1 and τ≫1 which correspond to the case of fine dust and coarse dust respectively are derived and discussed.     

The Fredholm index of a second order elliptic system on an infinite cylinder

This paper investigates the Fredholmness of a second order elliptic system on an infinite cylinder in various weighted or non-weighted Sobolev spaces, assuming homogeneous Dirichlet boundary conditions and suitable asymptotic behavior of the coefficients. It is shown that the index coincides with the spectral flow of an associated parametrized family of elliptic systems on the cross-section of the cylinder. Dependence or independence of the index upon the functional setting is discussed along with their impact on spectral invariance and elliptic regularity.      

Short-time dynamics of an elliptic cylinder moving in a viscous incompressible free-surface flow

The joint motion of a viscous incompressible fluid and a completely submerged elliptic cylinder is analyzed at short times. The cylinder is assumed to start from rest and move horizontally at a constant acceleration. A feature of the problem is that, at high accelerations, the fluid becomes detached from the cylinder surface and a cavity is formed. The problem is generalized to an elliptic cylinder floating on the surface of a viscous fluid.     

Unsteady flow of an elastico-viscous fluid past a circular cylinder

Résumé Une solution numérique est obtenue pour l'écoulement initial d'un fluid élastique et visqueux autour d'un cylindre circulaire, à nombres de Reynolds 40 et 100. On emploi la méthode d'integration numérique de l'équation de tourbillon.     

Boundary layer growth on a circular cylinder in a semi-infinite fluid

In this paper we study the problem of the boundary layer growth on a circular cylinder in a planar stagnation flow by the method of inner and outer expansions at small times and for finite but large Reynolds numbers. The emphasis is on the influence of the plane wall on the boundary layer detachment from the cylinder and the interaction between the cylinder and the flow. Certain correlations between some of the basic parameters are shown graphically.

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Zusammenfassung In dieser Arbeit wird das Anwachsen der Grenzschicht um einen kreisrunden Zylinder in einer ebenen Staupunktströmung behandelt. Verwendet wird die Methode der inneren und äußeren Entwicklung für große Reynoldssche Zahlen und kurze Zeiten. Betont wird der Einfluß einer ebenen Grenzplatte auf die Ablösung der Grenzschicht, und der gegenseitige Einfluß von Zylinder und Strömung. Gewisse Abhängigkeiten zwischen den Hauptparametern des Problems wurden auch graphisch dargestellt.

     

Slow rotation of a sphere in a slightly viscoelastic fluid contained in an infinite cylinder

Zusammenfassung In den letzten Jahren haben viskoelastische Strömungen an Bedeutung gewonnen. Wegen des nichtlinearen Charakters dieser Probleme ist es notwendig, vereinfachende Verfahren zu verwenden.Langlois undRivlin haben eine Anzahl solcher Aufgaben mit besonderen mathematischen Verfahren gelöst. In der klassischen Dynamik viskoser Flüssigkeiten ist das Problem der langsamen Bewegung einer Kugel in einem unendlichen Kreiszylinder durchBrenner undSonshine behandelt worden. In der vorliegenden Arbeit wird die Aufgabe verallgemeinert und die durch eine rotierende Kugel erzeugte Strömung einer schwach viskoelastischen Flüssigkeit in einem unendlichen Kreiszylinder untersucht. Die Bewegung wird so langsam vorausgesetzt, dass Trägheitsglieder vernachlässigbar sind. Das Geschwindigkeits- und das Druckfeld werden analytisch untersucht; ferner wird ein anschauliches Beispiel durchgerechnet und die Strömung im Bilde dargestellt.     

Inverse coefficient problems for elliptic equations in a cylinder: I

We study sufficient conditions for the unique solvability of the inverse coefficient problem. We obtain various global sufficient conditions in the form of constraints on the signs of the given functions and their derivatives. As a corollary, we consider statements of inverse coefficient problems with overdetermination on the boundary, where the Dirichlet conditions are supplemented with the vanishing condition for the normal derivative on part of the boundary.     

Some existence results for quasilinear elliptic equations in a finite cylinder

We study the existence of solutionsu in the finite cylinderS _a=(?a, a)×ω of the quasilinear elliptic equation $$\sum\limits_{i,j = 1}^n {a_{i,j} (x)\partial _{i,j} u + f(x,u,\nabla u) = 0} $$ with Dirichlet boundary condition on flat parts of σS _a and Neumann condition on the curved parts. In this paper, we focus on the technicality caused by the “corners” ofS _a. We prove the existence of such solutions provided that suitable sub and super solutions are known and under the condition that the coefficientsa _1,i,i#1 vanish on the corners. We also prove a more general result in ?².     

Inverse coefficient problems for elliptic equations in a cylinder: II

We study sufficient conditions for the unique solvability of the inverse coefficient problem. We obtain various global sufficient conditions in the form of constraints on the signs of the given functions and their derivatives. As a corollary, we consider statements of inverse coefficient problems with overdetermination on the boundary, where the Dirichlet conditions are supplemented with the vanishing condition for the normal derivative on part of the boundary. We prove sufficient conditions for the existence of a solution in this case.     

Circular oscillations of a cylinder in a viscous fluid

Summary The steady streaming velocity induced by the circular motion of a cylinder of elliptic cross-section in a viscous fluid is considered. The amplitude of this circular motion is supposed small compared with a typical diameter of the cylinder, which maintains a fixed orientation throughout the motion. Outside the Stokes shear-wave layer Reynolds stresses contribute to the induced steady streaming. The outer flow is calculated in the case of large streaming Reynolds numbers for two particular cylinders.

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Zusammenfassung Es wird die stationäre Strömung untersucht, die durch die kreisförmige Bewegung eines Zylinders mit elliptischem Querschnitt in einer zähen Flüssigkeit induziert wird. Die Amplitude dieser Kreisbewegung wird als klein angenommen gegenüber den Halbachsen der Ellipse, deren Orientierung während der Bewegung unverändert bleibt. Ausserhalb der Stokes-Schicht tragen die Reynolds-Spannungen zur Induzierten stationären Strömung bei. Die äussere Strömung wird im Falle von grossen Reynolds-Zahlen der Strömung für zwei besondere Zylinder berechnet.

     

Pointwise velocity error estimates for an elliptic fluid jet

Summary Pointwise estimates are obtained for the perturbation velocity to a novel theory of fluid jet behaviour based on Cosserat continuum mechanics. The method employed is one of weighted energy.

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Sommario In questo lavoro si determinano stime puntuali per il campo perturbato di velocità relativo ad una nuova teoria di getto fluido. Tale teoria è basata sul modello della meccanica dei continui di tipo Cosserat. Il metodo impiegato è quello dell'energia pesata.

     

Optimal control of a cylinder rotating in a viscous fluid

Under consideration is the axisymmetric problem of optimal boundary control of a mechanical system consisting of two coaxial cylinders and an incompressible viscous fluid filling the region between them. The control parameter is the angular velocity of the outer cylinder. The goal is to stop the interior cylinder at a prescribed time with minimal energy expense. We prove that the problem is uniquely solvable and obtain the optimality system.     

Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluid

We consider an integrable Hamiltonian system describing the motion of a circular cylinder and a vortex filament in an ideal fluid. We construct bifurcation diagrams and bifurcation complexes for the case in which the integral manifold is compact and for various topological structures of the symplectic leaf. The types of motions corresponding to the bifurcation curves and their stability are discussed.     

Controlling chaos in a fluid flow past a movable cylinder

The model of a two-dimensional fluid flow past a cylinder is a relatively simple problem with a strong impact in many applied fields, such as aerodynamics or chemical sciences, although most of the involved physical mechanisms are not yet well known. This paper analyzes the fluid flow past a cylinder in a laminar regime with Reynolds number, Re, around 200, where two vortices appear behind the cylinder, by using an appropriate time-dependent stream function and applying non-linear dynamics techniques. The goal of the paper is to analyze under which circumstances the chaoticity in the wake of the cylinder might be modified, or even suppressed. And this has been achieved with the help of some indicators of the complexity of the trajectories for the cases of a rotating cylinder and an oscillating cylinder.