The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for s...The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow fluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numerically. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i.e., opposite to wave propagation) for a certain range of yield stress.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
基金The work was supported by CRCG Research Grant 10203302 awarded by the University of Hong Kong,and Grants HKU 7117/99E and HKU 7081/02E awarded by the Research Grants Council of the Hong Kong Special Administrative Region
文摘The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow fluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numerically. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i.e., opposite to wave propagation) for a certain range of yield stress.
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.
