Asymptotic theory of flow attachment for a viscous incompressible fluid

A study is made of the two-dimensional laminar flow of a viscous incompressible fluid in the neighborhood of the point of attachment of the flow to a solid surface. The case of large Reynolds numbers is considered. It is assumed that the dimensions of the separation region are of the same order of magnitude as the characteristic dimension of the body around which the flow takes place. The asymptotic theory of such flow is constructed by applying the method of matched asymptotic expansions to the analysis of the Navier-Stokes equations. It is shown that in the neighborhood of the attachment point the flow is locally inviscid and can be described by the complete system of Euler equations. A solution to the corresponding boundary-value problem is constructed numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 63–71, November–December, 1980.     

Propagation of wave packets in the boundary layer on a curved surface

The development of wave packets excited in a boundary layer by means of a local deformation of the surface in the longitudinal-transverse interaction regime is considered. A solution of the linearized system of equations of interaction theory is constructed using a Laplace transformation with respect to time and a Fourier transformation with respect to the space variables. Two problems are separately examined. In the first, the disturbances are induced by a surface deformation sinusoidal in the transverse direction. It is shown that the center of the wave packet with the greatest oscillation amplitude moves in a direction opposite to that of the flow in the boundary layer. At the same time the wave packet expands, so that in the course of time any fixed point will enter the region of growing oscillations. In the second problem the source of the disturbances is isolated. In this case the wave packet acquires a horseshoe shape. Expanding, it carries the disturbances away from the source in all directions, including upstream relative to the flow in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 59–68, March–April, 1990.     

Nonlinear equation for amplitude of Tollmien-Schlichting waves in a boundary layer

The nonlinear evolution of a Tollmien-Schlichting wave is analyzed with allowance for the flow being nonparallel in a boundary layer. In contrast to the early work of Zel'man [19], strict allowance is made for the fact that the extent to which the flow is nonparallel is not independent of the Reynolds number — the departure from parallel flow in a boundary layer is small only at large Reynolds numbers. Therefore, an asymptotic theory of Tollmien-Schlichting waves is constructed under the assumption that the Reynolds number tends to infinity.     

Harmonized protocol and certified reference material for the determination of extractable contents of phosphorus in freshwater sediments--a synthesis of recent works.

An analytical protocol for the determination of the extractable phosphorus contents in freshwater sediments has been harmonized through interlaboratory studies in the frame of the Standards Measurements and Testing Program of the European Commission. A homogeneous and stable sediment reference material has been prepared and certified on the basis of this protocol named SMT protocol, and will be available in spring of 2001. The SMT protocol, together with the reference material, are useful tools in the field of water management, especially at a time when quality assurance and data comparability are of paramount importance in laboratory analysis. The knowledge of the bioavailable forms of phosphorus is important not only for sediments but also for sludge and soils. Therefore, the SMT protocol could be extended to these materials and new CRMs could be prepared. The SMT protocol was used in a study of a reservoir, which allowed to calculate the P stock, therefore helping to predict the restoration delay of the lake. The paper describes the protocol and the CRM, and gives a brief outline of the case study.     

Cherenkov interaction of vortices with a free surface

The interaction of vortex filaments in an ideal incompressible fluid with the free surface of the latter is investigated in the canonical formalism. A Hamiltonian formulation of the equations of motion is given in terms of both canonical and noncanonical Poisson brackets. The relationship between these two approaches is analyzed. The Lagrangian of the system and the Poisson brackets are obtained in terms of vortex lines, making it possible to study the dynamics of thin vortex filaments with allowance for finite thickness of the filaments. For two-dimensional flows exact equations of motion describing the interaction of point vortices and surface waves are derived by transformation to conformal variables. Asymptotic steady-state solutions are found for a vortex moving at a velocity lower than the minimum phase velocity of surface waves. It is found that discrete coupled states of surface waves above a vortex are possible by virtue of the inhomogeneous Doppler effect. At velocities higher than the minimum phase velocity the buoyant rise of a vortex as a result of Cherenkov radiation is described in the semiclassical limit. The instability of a vortex filament against three-dimensional kink perturbations due to interaction with the “image” vortex is demonstrated. Zh. éksp. Teor. Fiz. 115, 894–919 (March 1999)     

Ball milling: An effective technique for the preparation of exfoliated clay filled unsaturated polyester toughened epoxy nanocomposite

This paper investigates the possibility of improving the mechanical and thermal properties of epoxy and unsaturated polyester toughened epoxy resins through the dispersion of octadecyl ammonium ion-exchanged montmorillonite (organoclay) through exfoliated mechanism. The nanocomposites prepared are characterized for their structural change and studied for their crystallite size, mechanical, thermal and water absorption (hydrophilicity) properties. The mechanical data indicates significant improvement in the flexural and tensile properties over the neat epoxy and UP-epoxy matrix according to the percentage content of organoclay. The thermal behavior too shows noticeable enhancement in glass transition temperature T _g and high thermal stability. Hydrophilicity of all the composites decreases irrespective of the concentration of organoclay on the epoxy and UP-epoxy matrices. The homogeneous morphology of epoxy and UP toughened epoxy nanocomposite hybrid systems is ascertained using scanning electron microscope (SEM). X-ray results point out that the cetyl ammonium modified clay filled composites exhibited the exfoliated structure.