The problem of the diffusion of two counter-rotating vortices of equal strength is studied numerically and analytically. Asymptotic expansions are derived for the limiting behavior of the solution for small times, for small Reynolds numbers, and for large times. The results are used to more fully understand the drift and decay of the vortex system. Thus it is shown that different measures for the position of the vortex system used by previous authors may give significantly different values for the drift velocity of the vortices. The expansion for small Reynolds number shows that these differences remain even in the Stokes limit Re-40, in which the vorticity system becomes symmetric about the line connecting the vortex centers. But surprisingly, the large time expansion shows that for large times all drift velocities become identical. Moreover, this universal velocity is different from the average velocity in each half plane although it equals the velocity of the centers of vorticity of those planes. The small time expansion shows that increasing Reynolds number makes the vortices more symmetric. This tends to reduce the differences between the drift velocities. The small time expansion describes the numerical solution well as long as the vortices remain small compared to their spacing. The numerical results show that the Stokes solution describes various flow quantities fairly well for Reynolds numbers up to 600 based on the circulation; however, nonzero Reynolds number reduces the decay of the circulation of the vortices even on a diffusive time scale. C 1995 American Institute of Physics.
Boundary-layer separation can be prevented or delayed by sucking part of the boundary layer into the surface, but in a straightforward application the required hydraulics entail significant penalties in terms of weight and cost. By means of computational techniques, this paper explores the possibility of autogenous suction, in which the local pressure differences that lead to separation drive the suction used to prevent it. The chosen examples include steady and unsteady laminar flows around leading edges of thin airfoils. No fundamental theoretical limit to autogenous suction was found in the range of angles of attack that could be studied, but rapidly increasing suction volumes suggest that practical application will become increasingly difficult for more severe adverse pressure gradients.
This paper describes the adaptation of a master's degree program so that the degree can be obtained by taking all the courses over the Internet. The degree program is Master of Science in Mechanical Engineering at the FAMU-FSU College of Engineering. A distinguishing feature of the adaptation is that it attempts to approximate the live classroom experience as closely as possible. This paper reviews, near the end of the first semester in which the required M.S. core classes have been offered live over the web, our motivation and experiences. Despite some minor drawbacks, the program is judged successful and will be made available to all eligible students worldwide starting Fall 2000.
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