Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, February 9, 2007 - 04:00

Location:

Gilkey 113

Guest Speaker:

Institution:

OSU Department of Civil Engineering

Abstract:

Within the basis of continuum hypothesis, the jump condition of conservation equation is derived. At a material boundary such as air-water interface, the jump condition of conservation of mass yields the kinematic free-surface boundary condition, the jump condition of conservation of linear momentum yields the dynamic free-surface boundary condition. The no-slip boundary condition arises at a material boundary as a consequence of the jump condition for mechanical-energy conservation; note that the no-slip condition is usually an assumed condition, but our analysis demonstrates that it is a necessary condition for the mechanical energy consideration at the interface. A constant magnitude of pressure along the free surface is often imposed in traditional water-wave problems for irrotational fluid motions. If this condition is imposed, the resulting potential-flow solution demands the fictitious energy input from the surroundings, i.e., air, through the free surface. Under a more rigorous free-surface condition such as vanishing stresses on the interface, irrotational flow cannot exist at the free surface and must form a boundary layer In a real-fluid environment, flows in general must be vortical at the free surface. Because of this observation, the jump condition of vorticity equation is examined. It is found that vorticity normal to the interface and vorticity bending caused by the interface curvature play important roles in determination free-surface vortex motions.