Accurate prediction of the motion of a body moving around another one in anunbounded fluid and determination of the hydrodynamic interaction between them are important in thecoastal and offshore engineering. For two-d...Accurate prediction of the motion of a body moving around another one in anunbounded fluid and determination of the hydrodynamic interaction between them are important in thecoastal and offshore engineering. For two-dimensional cases, most of the previous studies werefocused on the interaction between circular cylinders without considering the non-circularsituation. To break through the limitation of ''circular'' bodies, in the present paper the boundaryperturbation method was employed to investigate the motion of a slightly distorted circular cylinderaround a circular one. An approximate complex velocity potential in terms of double infinite seriesexpanded at two singular points was derived using the method of continued fractions. Thehydrodynamic interaction between two cylinders was computed by solving the dynamical equations ofmotion. In a relative coordinate system moving with the uniform stream, the kinetic energy of thefluid was expressed as a function of fifteen added masses. Approximate analytical solutions of addedmasses in the series form were obtained and applied to determine the trajectories of the slightlydistorted circular cylinder around a fixed circular one. Numerical results show that the presence ofthe circular cylinder affects the planar motion of the slightly distorted circular cylinder and theinitial configuration of the slightly distorted circular cylinder has a decisive influence on thedevelopment of its rotational motion.展开更多
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-...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.展开更多
文摘Accurate prediction of the motion of a body moving around another one in anunbounded fluid and determination of the hydrodynamic interaction between them are important in thecoastal and offshore engineering. For two-dimensional cases, most of the previous studies werefocused on the interaction between circular cylinders without considering the non-circularsituation. To break through the limitation of ''circular'' bodies, in the present paper the boundaryperturbation method was employed to investigate the motion of a slightly distorted circular cylinderaround a circular one. An approximate complex velocity potential in terms of double infinite seriesexpanded at two singular points was derived using the method of continued fractions. Thehydrodynamic interaction between two cylinders was computed by solving the dynamical equations ofmotion. In a relative coordinate system moving with the uniform stream, the kinetic energy of thefluid was expressed as a function of fifteen added masses. Approximate analytical solutions of addedmasses in the series form were obtained and applied to determine the trajectories of the slightlydistorted circular cylinder around a fixed circular one. Numerical results show that the presence ofthe circular cylinder affects the planar motion of the slightly distorted circular cylinder and theinitial configuration of the slightly distorted circular cylinder has a decisive influence on thedevelopment of its rotational motion.
文摘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.
