Trailing vortices in a free-surface flow

The free-surface effect on two-dimensional flow structures, especially on the trailing vortices, is investigated numerically in this paper. The solution procedure employs a higher-order semi-implicit projection method. The numerical results have been compared with experimental data on wave elevation disturbed by a submerged translating hydrofoil with a positive angle of attack. The schematic computations reveal some interesting and unique characteristics of the trailing-vortex development in a laminar flow beneath a free surface. Based on the computational data, an empirical Strouhal-Reynolds-Froude number relationship is proposed for the purely laminar vortex shedding in a free-surface flow. Moreover, the numerical findings also indicate that the presence of a free surface accelerates the Strouhal vortex frequency, yet delays not only the onset of a large-scale Karman instability but also the occurrence of transitional behaviors. The shedding frequency downshifts drastically or even becomes discontinuous when the secondary vortex grows on the suction side. A metastable transition frequency emerges at the same time and becomes distinct with increasing Reynolds number. The variation of the vortex-shedding Strouhal number with respect to both Reynolds and Froude numbers is obtained. The power spectra of the trailing wake consist of harmonics of the vortex-shedding and transition frequencies (mf(s),nf(t)), as well as their combinations (mf(s)+/-nf(t)). (C) 2002 American Institute of Physics.