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Taking into account bending resistance and fluidity of the membrane, we calculate deformation of a vesicle of the lipid-bilayer membrane in a linear shear flow. Here it is assumed that the vesicle is spherical when the system is at rest and that the deformation is small because the flow is weak in comparison with the bending rigidity of the membrane. Our result includes Taylor's standard result on the drop in a linear shear flow as an exceptional case.

Using the Navier-Stokes equations of the vorticity-stream function form in body-fitted orthogonal coordinates, the flow past a flat plate at various angles of incidence has been numerically investigated for Reynolds number up to 30. By treating the singularity at the tip analytically, in that the near-tip behavior is expanded in powers of the local variables and matched to the outer finite-difference solution, the calculation procedure can be made very accurate, robust and efficient. It is shown that the singular behavior of the vorticity and pressure are well captured, and the analytic pressure distribution around the tip enables one to calculate the forces acting on the plate accurately. The results are seen to be in good agreement with those reported earlier for the flow past a normal flat plate. The flow pattern at other angles of incidence is discussed, and a detailed flow map along with the drag and lift coefficients with respect to the angle of incidence and Re is presented.

The coupled effects of thermal convection and solidification of a Single-component liquid in a porous medium are investigated. A rigorous two-parameter perturbation analysis is used to determine the effects on both the stability of the basic state of heat conduction and the stability of finite-amplitude convection. The analysis shows that due to the kinematic conditions at the solid/liquid interface, hexagons having upflow in the center are stable near the onset of convection. For sufficiently supercritical Rayleigh numbers, however, rolls are the only stable mode. The transition from hexagons to rolls is characterized by a hysteresis loop. Moreover, the transition is shown to be controlled by one particular critical value of the convection amplitude. This generic property holds for non-Boussinesq convection in bulk liquid-layers too.

Some specific features, primarily observed by smoke visualization, are described for a vortex ring interaction with a thin bluff body in the shape of a circular cylinder. Secondary vortices were found to be induced by boundary layer separation from the cylinder surface when the vortex ring travelled across it, and played a crucial role in the subsequent flowfield. The main vortex ring itself underwent distortion and moved like an elliptical ring. The ratio of the cylinder diameter to the core diameter of the vortex ring was found to be an essential parameter which governs the vortex motion after crossing the circular cylinder. In particular, the velocity of the vortex ring decreased as the ratio increased from 0.0063 to 0.25, but then increased as the ratio increased from 0.25 to 0.38. Increasing the ratio above 0.38 resulted in the velocity again decreasing after crossing the cylinder

Free convection boundary layer over a semi-infinite flat plate with a uniform surface heat flux which is inclined at a small angle to the horizontal is discussed. When the plate is inclined at a positive angle, series solutions, one valid near the leading edge and the other at large distances from it, are obtained. Very accurate numerical results are determined by using an implicit finite-difference scheme known as keller box method in the region where neither series is adequate. For negatively inclined plate, a series solution valid near the leading edge is again obtained and the same numerical method is employed to solve the full boundary layer equations to extend the solution downstream, past the point at which the boundary layer separates from the plate. Eigenvalues and their corresponding eigenfunctions which are associated with large distances from the leading edge have been sought and it has been found that their contribution up to third-order correction is identically zero. Numerical results have been determined for a wide range of values of the Prandtl number Pr but the results are only presented for Pr = 0.72 (air).

Turbulent entrainment laws obtained experimentally for an annular two-layer stratified flow are predicted theoretically using the mixing model recently developed by Mory (1991). This paper shows how the salinity spectra measured by Chai and Kit (1991) can be utilized by the model equations to predict the power of the entrainment law for a flow in an annulus with or without a velocity shear across the density interface. The predicted values are found to be very close to the measured ones.