UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID

BRIEFINTRODUCTIONOFTHEPAPER :　Inthefirstpartofthisthesis ,thefundamentalsolutionsforthesingularStokesandOseenflowsinanun boundedfluidarederivedinauniversalformwhichinvolvestheHamiltonian ,Hessian ,andLaplacianoperators ,andelementaryfunctions .Inthesecondpart,theinteractionofunsteadylow Reynolds numberflowswithafreesurfaceisinvestigatedanalytically .Thedisturbedflows ,generatedbysubmergedbodiesmovingverticallydownwardsawayfromthesurfaceofthefluid ,aregovernedbytheunsteadyStokeseq…

UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID

The interaction of laminar flows with free surface waves generated by submerged bodies in an incompressible viscous fluid of infinite depth is investigated analytically. The analysis is based on the linearized Navier-Stokes equations for disturbed flows. The kinematic and dynamic boundary conditions are linearized for the small-amplitude free-surface waves, and the initial values of the flow are taken to be those of the steady state cases. The submerged bodies are mathematically represented by fundamental singularities of viscous flows. The asymptotic representations for unsteady free-surface waves produced by the Stokeslets and Oseenlets are derived analytically. It is found that the unsteady waves generated by a body consist of steady-state and transient responses. As time tends to infinity, the transient waves vanish due to the presence of a viscous decay factor. Thus, an ultimate steady state can be attained.