Two-dimensional Stokes flow in a semicircle

Постpоено точное pешение задачи о двумеpном течении Стокса в полукpуге, вызванное pавномеpным движением кpуговой или пpямолинейной гpаницы. Пpиведены контуpные линии тока и типичное pаспpеделение скоpости.Побудовано точний pозв'язок задачi пpо двовимipну течiю Стокса у напiвкpузi, яка зумовлена piвномipним pухом кpугової або пpямолiнiйної гpаницi. Наведенi контуpнi лiнiї тока та типовий pозподiл швидкостi.The exact analytical solution for the two-dimensional Stokes flow in a semicircle due to uniformly moving circular or straight boundary is obtained. The contour streamline pattern and a typical velocity distribution are shown

Stirring by blinking rotlets in a bounded Stokes flow

A blinking rotlet model is used for the analysis of stirring in a Stokes flow in a rectangular domain. After the two-dimensional biharmonic equation is solved analytically, the associated velocity field of a pair of blinking rotlets positioned symmetrically on the y -axis, is used studying the stirring qualities of this blinking rotlet model. Contour kinematic simulations are performed in order to obtain information about the chaotic behaviour of a blob of passive tracer material put in this flow field

Singularities Motion Equations in 2-Dimensional Ideal Hydrodynamics of Incompressible Fluid

In this paper, we have obtained motion equations for a wide class of one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them, are well known as point vortices. More complicated singularities correspond to vorticity point dipoles. It has been proved that point multipoles of a higher order (quadrupoles and more) are not the exact solutions of two-dimensional ideal hydrodynamics. The motion equations for a system of interacting point vortices and point dipoles have been obtained. It is shown that these equations are Hamiltonian ones and have three motion integrals in involution. It means the complete integrability of two-particle system, which has a point vortex and a point dipole.Comment: 9 page

The effect of the thermal reduction on the kinetics of low-temperature ⁴He sorption and the structural characteristics of graphene oxide

The kinetics of the sorption and the subsequent desorption of ⁴He by the starting graphite oxide (GtO) and the thermally reduced graphene oxide samples (TRGO, T reduction = 200, 300, 500, 700 and 900 °C) have been investigated in the temperature interval 1.5–20 K. The effect of the annealing temperature on the structural characteristics of the samples was examined by the x-ray diffraction (XRD) technique. On lowering the temperature from 20 to 11–12 K, the time of ⁴He sorption increased for all the samples, which is typically observed under the condition of thermally activated diffusion. Below 5 K the characteristic times of ⁴He sorption by the GtO and TRGO-200 samples were only weakly dependent on temperature, suggesting the dominance of the tunnel mechanism. In the same region (T < 5 K) the characteristic times of the TRGOs reduced at higher temperatures (300, 500, 700 and 900 °C) were growing with lowering temperature, presumably due to the defects generated in the carbon planes on removing the oxygen functional groups (oFGs). The estimates of the activation energy ( Ea) of ⁴He diffusion show that in the TRGO-200 sample the Ea value is 2.9 times lower as compared to the parent GtO, which is accounted for by GtO exfoliation due to evaporation of the water intercalated in the interlayer space of carbon. The nonmonotonic dependences Ea( T) for the GtO samples treated above 200 °C are determined by a competition between two processes—the recovery of the graphite carbon structure, which increases the activation energy, and the generation of defects, which decreases the activation energy by opening additional surface areas and ways for sorption. The dependence of the activation energy on T reduction correlates well with the contents of the crystalline phase in GtO varying with a rise of the annealing temperature

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow

Vortex merger near a topographic slope in a homogeneous rotating fluid

This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.PostprintPeer reviewe

Bending of an elastic rectangular clamped plate : exact versus 'engineering' solutions

This paper addresses the fascinating long history of the classical problem of bending of a thin rectangular elastic plate with clamped edges by uniform pressure. Among various mathematical and engineering approaches, a method of superposition proposed by Lamé (1852, 1859) and Mathieu (1881, 1890) and developed by the mathematician Koialovich (1902) and engineers Boobnoff (1902, 1914), Hencky (1913) and Inglis (1925) appears to be very useful for the analysis of distribution of stresses and deflection inside a plate. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm

Periodic points for two-dimensional Stokes flow in a rectangular cavity

The locations of periodic points for Stokes flow in a rectangular cavity is studied. Discontinuous and sinusoidal corotating periodic motions of the top and bottom walls are considered. An effective algorithm for one-dimensional search based on the use of symmetry conditions of the flow is proposed for both cases. It permits one to find and classify all periodic points of low-order periodicity. Specific features of the bifurcation diagrams are noticed. Two typical examples of flow with the dye blob situated around an elliptic or a hyperbolic periodic point show a striking difference in mixing properties