Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth

Scattering of water waves by a sphere in a two-layer fluid, where the upper layer has an ice-cover modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves - the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave scattering by a submerged sphere placed in either of the layers. The exciting forces for vertical and horizontal directions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero, the numerical results for the exciting forces for the problem with free surface are recovered as particular cases. (C) 2011 Elsevier Ltd. All rights reserved.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

Studies on n=2 Aurivillius phases: structure of the series Bi3-xLaxTiNbO9 (0 <= x <= 1)

The crystal structures of the solid solutions of Bi3-xLaxTiNbO9 (0 less than or equal to x less than or equal to 1) have been analyzed by powder X-ray diffraction with supporting evidence from selected area electron diffraction (SAD). The structure of the starting member (x = 0) is verified to be in the orthorhombic space group A2(1) am while the end member (x = 1) is determined to crystallize in the centrosymmetric orthorhombic space group Pmcb. The structure of x = 1 phase is solved by ab initio powder diffraction. The intermediate compositions belong to the space group A2(1) am as confirmed by Rietveld refinements. Rietveld refinements on all the compositions reveal that the La3+ ion is disordered only in the A site and not in the [Bi2O2](2+) layer. The tilt in the Ti/NbO6 octahedra decreases with increasing x. (C) 2003 Elsevier B.V. All rights reserved.

Thermal characterization of microheaters from the dynamic response

Thermal characterization of surface-micromachined microheaters is carried out from their dynamic response to electrothermal excitations. An electrical equivalent circuit model is developed for the thermo-mechanical system. The mechanical parameters are extracted from the frequency response obtained using a laser Doppler vibrometer. The resonant frequencies of the microheaters are measured and compared with FEM simulations. The thermal time constants are obtained from the electrical equivalent model by fitting the model response to the measured frequency response. Microheaters with an active area of 140 µm × 140 µm have been realized on two different layers (poly-1 and poly-2) with two different air gaps (2 µm and 2.75 µm). The effective time constants, combining thermal and mechanical responses, are in the range of 0.13–0.22 ms for heaters on the poly-1 layer and 1.9 µs–0.15 ms for microheaters on the poly-2 layer. The thermal time constants of the microheaters are in the range of a few microseconds, thus making them suitable for sensor applications that need a faster thermal response.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

ChemInform Abstract: Synthesis of Anion-Deficient Layered Perovskites, ACa2Nb3-xMxO10-x (A: Rb, Cs; M: Al, Fe), Exhibiting Ion-Exchange and Intercalation. Evidence for the Formation of Layered Brownmillerites, ACa2Nb2AlO9 (A: Cs, H)

Anion-deficient layered perovskite oxides of the formula, ACa2Nb3-xMxO10-x (A = Rb, Cs; M = Al, Fe) for 0 < x less-than-or-equal-to 1.0, possessing tetragonal structures similar to the parent ACa2Nb3O10, have been synthesized. The interlayer A cations in these materials are readily exchanged with protons in aqueous HNO3 to give the protonated derivatives, HCa2Nb3-xMxO10-x; the latter are solid Bronsted acids intercalating a number of organic amines including aniline (pK(a) = 4.63). The distribution of acid sites in the interlayer region of HCa2Nb2MO9 inferred from n-alkylamine intercalation suggests that oxygen vacancies and Nb/M atoms are disordered in the ACa2Nb2MO9 samples prepared at 1100-1200-degrees-C. Annealing a disordered sample of CsCa2Nb2AlO9 for a long time at lower temperatures tends to order the Nb/Al atoms and oxygen vacancies to produce octahedral (NbO6/2)-tetrahedral (AlO4/2)-octahedral (NbO6/2) layer sequence reminiscent of the brownmillerite structure.

Peristaltic transport of two immiscible viscous fluids in a circular tube

Peristaltic motion of two immiscible viscous incompressible fluids in a circular tube is studied in pumping and copumping ranges under long-wavelength and low-Reynolds-number assumptions. The effect of the peripheral-layer viscosity on the time-averaged flux and the mechanical efficiency is studied. The formation and growth of the trapping zone in the core and the peripheral layer are explained. It is observed that the bolus volume in the peripheral layer increases with an increase in the viscosity ratio. The limits of the time-averaged flux (Q) over bar for trapping in the core are obtained. The trapping observed in the peripheral layer decreases in size with an increase in (Q) over bar but never disappears. The development of the complete trapping of the core fluid by the peripheral-layer fluid with an increase in the time-averaged flux is demonstrated. The effect of peripheral-layer viscosity on the reflux layer is investigated. It is also observed that the reflux occurs in the entire pumping range for all viscosity ratios and it is absent in the entire range of copumping.

Dynamics of the Indian-Ocean oxygen minimum zones

In the Indian Ocean, mid-depth oxygen minimum zones (OMZs) occur in the Arabian Sea and the Bay of Bengal. The lower part of the Arabian-Sea OMZ (ASOMZ; below 400 m) intensifies northward across the basin; in contrast, its upper part (above 400 m) is located in the central/eastern basin, well east of the most productive regions along the western boundary. The Bay-of-Bengal OMZ (BBOMZ), although strong, is weaker than the ASOMZ. To investigate the processes that maintain the Indian-Ocean OMZs, we obtain a suite of solutions to a coupled biological/physical model. Its physical component is a variable-density, 6 1/2-layer model, in which each layer corresponds to a distinct dynamical regime or water-mass type. Its biological component has six compartments: nutrients, phytoplankton, zooplankton, two size classes of detritus, and oxygen. Because the model grid is non-eddy resolving (0.5 degrees), the biological model also includes a parameterization of enhanced mixing based on the eddy kinetic energy derived from satellite observations. To explore further the impact of local processes on OMZs, we also obtain analytic solutions to a one-dimensional, simplified version of the biological model. Our control run is able to simulate basic features of the oxygen, nutrient, and phytoplankton fields throughout the Indian Ocean. The model OMZs result from a balance, or lack thereof, between a sink of oxygen by remineralization and subsurface oxygen sources due primarily to northward spreading of oxygenated water from the Southern Hemisphere, with a contribution from Persian-Gulf water in the northern Arabian Sea. The northward intensification of the lower ASOMZ results mostly from horizontal mixing since advection is weak in its depth range. The eastward shift of the upper ASOMZ is due primarily to enhanced advection and vertical eddy mixing in the western Arabian Sea, which spread oxygenated waters both horizontally and vertically. Advection carries small detritus from the western boundary into the central/eastern Arabian Sea, where it provides an additional source of remineralization that drives the ASOMZ to suboxic levels. The model BBOMZ is weaker than the ASOMZ because the Bay lacks a remote source of detritus from the western boundary. Although detritus has a prominent annual cycle, the model OMZs do not because there is not enough time for significant remineralization to occur.

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.

The harmonic torsional oscillations of a thin disk submerged in a fluid with a surfactant surface layer

A formulation in terms of a Fredholm integral equation of the first kind is given for the axisymmetric problem of a disk oscillating harmonically in a viscous fluid whose surface is contaminated with a surfactant film. The equation of the first kind is converted to a pair of coupled integral equations of the second kind, which are solved numerically. The resistive torque on the disk is evaluated and surface velocity profiles are computed for varying values of the ratio of the coefficient of surface shear viscosity to the coefficient of viscosity of the substrate fluid, and the depth of the disk below the surface.

A note on the slow rotation of a disc in a bounded fluid with a surfactant surface layer

A method involving eigenfunction expansion and collocation is employed to solve the axisymmetric problem of a slowly and steadily rotating circular disc in a fluid of finite extent whose surface is covered with a surfactant film. The present method (originally described by Wang (Acta Mech. 94, 97, 1992)) is observed to produce results of practical importance associated with the problem more quickly and more easily than the one used earlier by Shail and Gooden (Int. J. Multiphase Flow 7, 245, 1992). (C) 1994 Academic Press, Inc.

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

In this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid-porous system is modelled by a coupled two-dimensional Navier-Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.