Roll-up of a viscous vortex sheet
Journal
Journal of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an
Journal Volume
14
Journal Issue
5
Pages
507-517
Date Issued
1991
Author(s)
Abstract
Abstract The vortex sheet roll‐up for a viscous fluid flow under an initially periodic perturbation is studied by using a core‐spreading vortex method [2]. The viscous term, usually neglected in prior studies, is considered in the present study. In order to avoid the singularity at the center of point vortices, a convolution decomposition procedure is applied to form the vortex blobs. When calculating the stream function and the velocity field, the computations for the vortex method are usually time‐consuming due to the involvement of a large number of vortex blobs. This is improved by employing an efficient algorithm based on multipole expansions [6] to perform far‐field calculations. With the help of the fast algorithm, the time complexity of the one‐step calculation is directly proportional to the number of vortex blobs. Numerical results show that the roll‐up of a vortex sheet with the viscous effect is slower than that of an inviscid vortex sheet. During the roll‐up of the vortex sheet, the spread and the flatness of the vorticity distribution are also studied by calculating the second moments and the fourth moments, respectively. Both results indicate the roll‐up of an inviscid vortex sheet is stretched slightly longer than that of a viscous vortex sheet.
Type
journal article