The effect of interaction on the boundary layer induced by a convected rectilinear vortex

Abstract

The effect of interaction on the boundary layer induced by a convected rectilinear vortex is considered. Two schemes are employed in the numerical discretization of the edge interaction condition; the first, developed by Veldman (1981) is useful at larger Reynolds numbers but fails to capture the interactive phase of the motion for Reynolds numbers less than 8 × 104. A scheme devised by Napolitano, Werlé & Davis (1978) is employed at smaller Reynolds numbers and yields similar results to Veldman's scheme at higher Reynolds numbers, while exhibiting greater numerical stability during the interactive phase of the motion. The effect of interaction is found to be negligible during much of the motion, even for a strong vortex, but during the latter stages of the calculations, interaction appears to round off the top of the eddy and delays breakdown for all Reynolds numbers studied when compared with the non-interactive results of Doligalski & Walker (1984). In addition, in the latter stages of the calculations, and during the early stages of the interactive phase, a third eddy is formed with vorticity of the same sign as the main eddy spawned deep within the boundary layer. Such a tertiary eddy has been observed in the experimental work of Walker et al. (1987) in their study of the boundary layer induced by a vortex ring. During the interactive phase of the motion a streamwise lengthscale emerges whose length is approximately $O(Re^{-\frac{3}{11}})$, broadly in line with the analytical predictions of Elliott, Cowley & Smith (1983). A novel feature of the computations is the use of a pseudospectral method (Burggraf & Duck 1982) in the streamwise direction which requires no special coding in reversed-flow regions.