Date of Award

Spring 2000

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical Engineering

First Advisor

N. Aubry

Second Advisor

Demetrius T. Papageorgiou

Third Advisor

Anthony D. Rosato

Fourth Advisor

Pushpendra Singh

Fifth Advisor

Chao Zhu


The interaction between a submerged vortex pair with a deformable free-surface in a viscous, incompressible fluid is directly simulated and the flow is thoroughly analyzed. This is a time-dependent nonlinear free-surface problem which we solve numerically by integrating the two-dimensional Navier-Stokes equations and using boundary-fitted coordinates capable of handling large free-surface deformations. In particular, the numerical simulation of the flow at relatively high Reynolds numbers (Re = 500,1000, 2000 ) and relatively high Froude numbers (Fr = 1. 125, Fr = 2.0) is investigated and analyzed for the first time. Details are given regarding the space-time deformation of the free-surface, the path of the primary vortices, the formation of strong free-surface vorticity and kinetic energy, and the generation of turbulence in the flow. In particular, the turbulence characteristics have been explored at Reynolds number Re =1000. In this flow, we identified a thin free-surface layer characterized by very fast variations of the turbulence intensity, the kinetic energy dissipation and velocity fluctuations. The turbulence intensity reaches a maximum at the level of the center of the primary vortex, and then decreases significantly as the free-surface is approached. This decay is due to a very large increase of the turbulent kinetic energy dissipation at the free surface and the formation of large vorticity peaks at the free-surface. Contrarily to previous findings, there is no redistribution of the turbulence intensity at the free-surface, that is a large increase of the horizontal velocity fluctuation at the expense of the vertical velocity fluctuation. Instead, the horizontal velocity fluctuation is smaller than the vertical velocity fluctuation. This is due to the fact.that our Froude number is elatively large and that the free-surface undergoes large (particularly vertical) deformations, as permitted by our numerical scheme, as the primary vortices approach the free-surface.