Interaction of laminar far wake with a free surface

Wave disturbances caused by the uniform translatory motion of a submerged body on or beneath the free surface of a viscous fluid are investigated analytically. The submerged body is idealized as an Oseenlet or an Oseen doublet, and exact solutions in closed integral forms are obtained. Based on these exact solutions, asymptotic representations of the wave amplitude for large Reynolds numbers based on the deep-water wavelength at large distances downstream of the body are derived. The results obtained show explicitly the effect of the laminar wake on the amplitude and the phase of the surface waves thus created. ©1996 American Institute of Physics.published_or_final_versio

A separated vortex ring underlies the flight of the dandelion

Wind-dispersed plants have evolved ingenious ways to lift their seeds1,2. The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that helps to keep their seeds aloft. This passive flight mechanism is highly effective, enabling seed dispersal over formidable distances3,4; however, the physics underpinning pappus-mediated flight remains unresolved. Here we visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus. We hypothesized that the circular disk-like geometry and the porosity of the pappus are the key design features that enable the formation of the separated vortex ring. The porosity gradient was surveyed using microfabricated disks, and a disk with a similar porosity was found to be able to recapitulate the flow behaviour of the pappus. The porosity of the dandelion pappus appears to be tuned precisely to stabilize the vortex, while maximizing aerodynamic loading and minimizing material requirements. The discovery of the separated vortex ring provides evidence of the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures

Hydrodynamic interaction between a prolate spheroid and a sphere

The planar motion of a prolate spheroid around a sphere is investigated. Two sets of transformations of harmonics between the spherical co-ordinates and the prolate spheroidal ones are derived in terms of special functions. These transformations are employed to obtain the velocity potential for the two-body system of a moving prolate spheroid around a sphere by using the successive potential method, which is an extension of the sphere theorem. From the velocity potential, exact analytical expressions of added masses are thus obtained and adopted to determine the hydrodynamic interaction between these two bodies. The dynamical behaviour of the two-body system is discussed numerically for some typical situations. Numerical results demonstrate that the presence of a second body has an effect on the planar motion of the prolate spheroid, and the three-dimensional effect is feebler than that of two-dimensional bodies. Copyright © 2005 John Wiley & Sons, Ltd.link_to_subscribed_fulltex

Application of homotopy analysis method in nonlinear oscillations

In this paper, we apply a new analytical technique for nonlinear problems, namely the Homotopy Analysis Method (Liao 1992a), to give two-period formulas for oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. These two formulas are uniformly valid for any possible amplitudes of oscillation. Four examples are given to illustrate the validity of the two formulas. This paper also demonstrates the general validity and the great potential of the Homotopy Analysis Method

Interfacial waves due to a singularity in a system of two semi-infinite fluids

The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system of two semi-infinite immiscible fluids of different densities are investigated analytically. The two fluids are assumed to be incompressible and homogenous. There are three systems to be considered: one with two inviscid fluids, one with an upper viscous and a lower inviscid fluid, and one with an upper inviscid and a lower viscous fluid. The Laplace equation is taken as the governing equation for inviscid flows while the steady Oseen equations are taken for viscous flows. The kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity immersed above or beneath the interface is modeled as a simple source in the inviscid fluid while as an Oseenlet in the viscous fluid. Based on the integral solutions for the interfacial waves, the asymptotic representations of wave profiles in the far field are explicitly derived by means of Lighthill's two-stage scheme. An analytical solution is presented for the density ratio at which the maximum wave amplitude occurs. The effects of density ratio, immersion depth, and viscosity on wave patterns are analytically expressed. It is found that the wavelength of interfacial waves is elongated in comparison with that of free-surface waves in a single fluid.published_or_final_versio

Analytical study of porous wave absorber

Linear potential theory is applied to the analysis of wave reflection from a composite porous wave absorber that lies on a solid foundation with a seaward slope. By adopting the mathematical model of wave-induced flow in a porous medium, the interaction between water waves and a porous wave absorber is investigated. An extended linear refraction-diffraction model for surface waves is applied to the sloping region in front of the porous absorber. Using the eigenfunction expansions and the finite-difference method, an analytical study is undertaken to predict the wave reflection from such a composite porous absorber. The reflection behavior is discussed for several wave conditions, and the functional efficiency of this absorber is evaluated. It is noted that the present numerical results agree very well with the experimental results available in the literature

A Fourier-Chebyshev collocation method for the mass transport in a layer of power-law fluid mud

A Fourier-Chebyshev collocation spectral method is employed in this work to compute the Lagrangian drift or mass transport due to periodic surface pressure loading in a thin layer of non-Newtonian fluid mud, which is modeled as a power-law fluid. Because of the non-Newtonian rheology, these problems are nonlinear and must be solved numerically. On assuming that the solutions are of the same permanent waveform as the pressure loading, the governing equations are made time-independent by referring to a horizontal axis that moves at the same speed as the wave. The solutions are periodic in the horizontal direction, but are non-periodic in the vertical direction, and the computational domain is therefore discretized according to the Fourier-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix. In order to incorporate the boundary conditions, the matrix diagonalization technique is used to solve the matrix equation, and all the definite integrals in the vertical direction based on the collocation points are performed by the modified Clenshaw-Curtis quadrature rule. The developed method is applied to compute the first- and second-order motion of the mud. The comparison between the numerical results and the analytical solution in the Newtonian limit shows the good accuracy of the spectral method. © 2005 Elsevier B.V. All rights reserved.link_to_subscribed_fulltex

Spectral method applied to mass transport due to standing waves in water over non-newtonian mud

In this work, the mass transport due to a surface standing wave forcing in a water-mud system, in which the upper layer is clear water and the lower layer is a shear-thinning power-law non-Newtonian fluid, is investigated by the Fourier-Chebyshev collocation spectral method in space and the 4th-order finite-difference scheme in time discretization. An iteration-by-subdomain technique is introduced to tackle the interface in the two-layer system and an artificial diffusion term is added to stabilize the convective term and counterbalance the negative diffusion introduced by the Fourier scheme. Copyright © 2006 by The International Society of Offshore and Polar Engineers.link_to_subscribed_fulltex