The free-surface signature of unsteady, two-dimensional vortex flows (original) (raw)

1990, Journal of Fluid Mechanics

The interaction of two-dimensional vortex flows with a free surface is studied numerically using a combined vortex/boundary integral technique. The vorticity is modeled as point vortices, vortex sheets and finite area vortex regions. Two 3 problems are studied in considerable detail, the large amplitude Kelvin-Helmholtz instability of a submerged shear-layer and the head-on collision of a vortex pair with 5 the free surface. The surface deformation is controlled by a Froude number, based on the vortical motion, and the geometrical parameters describing the initial vortex con-3 figuration. Large Froude numbers generally lead to strong interactions for sufficiently shallow vortices. , o.. r 0 Statement A per telecon Dr. Edwin Rood Dt__ __ ONR/Code 1132 Arlington, VA 22217-5000 ---ilailiaa or_ i SAe-ia-3 Hogan, S. J. 1981. Some effects of surface tension on steep water waves. J. Fluid Mech. 110, 384-410. U Hong, S. W. 1987. Unsteady separated flow around a two-dimensional bluff 3 body near a free surface. Ph.D. Thesis. The University of Michigan. Kochin, N. E., Kibel, I. A., and Roze, N. V. 1964. Theoretical Hydrodynamics. Interscience, New York. 5 Krasny, R. 1986. Desingularization of periodic vortex sheet roll up. J. Comput. Phys. 65, 292-313. 31 U Krasny, R. 1988. Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123-155. 3 Lamb, H. 1945. Hydrodynamics. Dover Publication, New York, 738 pages. 5 Leonard, A. 1980. Vortex methods for flow simulation. J. Comput. Phys. 37, 289-335. I Longuet-Higgins, M. S. and Cokelet, E. D. 1976. The deformation of steep 3 surface waves on water. II. Growth of normal-mode instabilities. Proc. Roy. Soc. Lond. A 364, 1-28. U Lugt, H. J. 1981. Numerical modeling of vortex flows in ship hydrodynamics. 3 Atmospheric and Oceanic Physics 17, 709-714. Overman, E. A. and Zabusky, N. J. 1982. Coaxial scattering of Euler-equation translating V-states via contour dynamics. J. Fluid. Mech. 125, 187-202. 3 Peace, A. J. and Riley, N. 1983. A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409-426. Pozrikidis, C. and Higdon, J. J. L. 1985. Nonlinear Kelvin-Helmholtz instability 3 iof a finite vortex layer. J. Fluid Mech. 157, 225-263. 3 32 I T Pullin, D. I. 1982. Numerical studies of surface-tension effects in non-linear U Kelvin-Helmholtz and Rayleigh-Taylor instability. J. Fluid Mech. 119, 507-3 532. Saffman, P. G. 1979. The approach of a vortex pair to a plane surface in inviscid I fluid.