Free-surface flow phenomena ahead of a two-dimensional body in a viscous fluid
The zero tangential-stress condition generates vorticity at a curved free surface, viscosity diffuses the vorticity into the fluid to form a boundary layer, and convective transport downstream leads to a thickening of the boundary layer. It is believed that this free-surface boundary layer is responsible for the origin of the vortices that have been observed ahead of a body in motion. This study first analyzes the flow near a free surface to examine the occurrence of a stagnation point which, in turn, explains the origin of the bow vortices. The free-surface boundary-layer equations are then derived from an order-of-magnitude analysis and an integral method for their solution is presented. The potential flow ahead of several bodies is calculated and the resulting free-surface shapes and velocity fields are used to estimate the momentum thickness of the boundary layer. A numerical method for the solution of the full, unsteady, two-dimensional Navier-Stokes equations with the exact boundary conditions at the free surface is then presented. Special treatments for the application of the exact boundary conditions at the free surface are discussed in detail.
- Research Organization:
- Iowa Univ., Iowa City (USA)
- OSTI ID:
- 7029695
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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