摘要:

Experiments are described which suggest that the first wavy instability of fluidized beds is convective in nature. In particular, this instability is shown to be sensitive to a harmonic forcing localized at the bottom of the bed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869002

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A method for computing Laplace and Stokes interactions amongNspherical particles arbitrarily placed in a unit cell of a periodic array is described. The method is based on an algorithm by Greengard and Rokhlin [J. Comput. Phys.73, 325 (1987)] for rapidly summing the Laplace interactions among particles by organizing the particles into a number of different groups of varying sizes. The far‐field induced by each group of particles is expressed by a multipole expansion technique into an equivalent field with its singularities at the center of the group. The resulting computational effort increases only linearly withN. The method is applied to a number of problems in suspension mechanics with the goal of assessing the efficiency and the potential usefulness of the method in studying dynamics of large systems. It is shown that reasonably accurate results for the interaction forces are obtained in most cases even with relatively low‐order multipole expansions. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869003

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A method based upon Taylor dispersion theory is used to determine the shear‐induced diffusion coefficient in concentrated suspensions. The experiments are performed in a cylindrical Couette device with a suspension consisting of polystyrene spheres in a density‐matched solution of glycerin and water. A sequence of several hundred transit times for a single tagged sphere to complete successive orbits within the device is measured. The data are analyzed to compute the azimuthal Taylor dispersion coefficient from which the coefficient of shear‐induced diffusivity is obtained. In our experiments the particle Reynolds numbers areO(10−1). The experimental results are compared to the existing measurements of the shear‐induced diffusion coefficient obtained at lower particle Reynolds numbers and based upon short‐time data. We find a shear‐enhanced diffusion coefficientD⊥/&ggr;˙a2=O(0.1) for a volume fraction of &fgr;≊0.25; this is comparable to existing results from previous low particle Reynolds number studies (R<10−3). ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869004

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The properties and computation of Stokes flow due to a periodic array of point forces exerted in the interior of a fluid‐filled cylindrical tube with an arbitrary cross‐sectional shape are discussed. It is shown that the relationship between the pressure drop and the axial flow rate occurring when the point forces have a component parallel to the generators can be deduced immediately from a knowledge of the velocity profile corresponding to unidirectional pressure‐driven flow. A boundary‐integral method for computing the associated Green’s function of Stokes flow is developed and implemented in a numerical procedure that exploits the cylindrical boundary geometry to improve the accuracy of the results and efficiency of the computations. Streamline patterns of the flow within tubes with circular, elliptical, and nearly square shapes are presented and discussed with reference to flow reversal. In the limit as the separation between the point forces becomes increasingly larger than the typical size of the cross section of the tube, we recover the flow due to a solitary point force, and the numerical result are in agreement with those derived by previous authors for the particular case of a tube with a circular cross‐sectional shape. The flow due to the point forces is then coupled with the boundary integral representation to develop asymptotic expansions for the surface stress, force, torque, and higher moments of the traction exerted on a small suspended particle that belongs to a periodic array. Each particle may translate and rotate while the ambient fluid undergoes pressure‐driven flow. The coefficients of the asymptotic expansion are related to the non‐singular part of the Green’s function and its spatial derivatives, evaluated at the location of the point force. These quantities are computed and plotted for several cross‐sectional shapes. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869005

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Theexactwithinpotentialflowintegral equation approach of Evans and Ford [Proc. R. Soc. London Ser. A452, 373 (1996)] for thenormalsolitary wave, is here generalized to 2‐layer, ‘‘internal’’ solitary waves. This differs in its mathematical form from other exact integral equation methods based on the complex velocity potential. For both ‘‘rigidlid’’ (i.e., flat toplayer surface) and ‘‘free‐surface’’ boundary conditions, a set of coupled non‐linear integral equations are derived by an application of Green’s theorem. For each point on the layer interface(s), these describe functional constraints on the profiles and interface fluid velocity moduli; theexactprofiles and velocities being those forms that satisfy these constraints atallsuch interface points. Using suitable parametric representations of the profiles and interface velocity moduli as functions of horizontal distance,x, and utilizingtailoredquadraturemethods [Int. J. Comput. Math. B6, 219 (1977)], numerical solutions were obtained by the Newton–Raphson method that are highly accurate even atlargeamplitudes. For ‘‘rigid lid’’ boundary conditions, internal wave solutions are presented for layer density and depth ratios typical ofoceanicinternal wave phenomena as found in the Earth’s marginal seas. Their various properties, i.e., mass, momentum, energy, circulation, phase and fluid velocities, streamline profiles, internal pressures, etc., are evaluated and compared, where possible, with observed properties of such phenomena as reported, for example, from the Andaman Sea. The nature of the limiting (or ‘‘maximum’’) internal wave is investigated asymptotically and argued to be consistent with two ‘‘surge’’ regions separating the outskirts flow from a wide mid‐section region of uniform ‘‘conjugateflow’’ as advocated by Turner and Vanden‐Broeck [Phys. Fluids31, 286 (1988)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869006

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The time‐dependent motion of fluid in a circular tank with a radial barrier as a result of an increase in angular velocity of the tank is investigated. The length of the barrier is considered as the main experimental parameter. The flow field immediately after the increase in angular velocity is calculated analytically. Experiments have been performed with a tank placed on a rotating table. Quantitative results for the time‐dependent flow were obtained by the tracking of small particles floating at the free surface of the fluid. The flow appears to be characterized by separation from the end of the barrier and the subsequent formation of a stable vortex pattern. The trajectory of the vortex that is shed from the end of the barrier is determined with dye visualization, and compared with analytical results from a point‐vortex model. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869007

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A theory is developed to describe the generation of edge waves on a uniform beach by a wave‐maker. The theory is based on the linear shallow‐water equations. The wave‐maker is a vertical plate spanning between the shoreline and the paddle axis offshore, and oscillates periodically in the alongshore direction. It is found theoretically that only propagating modes exist; the evanescent modes are always accompanied by incoming waves from offshore and are not permissible in this case. For each propagation mode the cross‐shore variation is described by the Laguerre polynomial with an exponentially decaying amplitude. Laboratory experiments are performed and experimental data are compared with theoretical solutions. Since the viscous damping is ignored in the theory, the wave amplitudes for the experimental data are usually lower than the theoretical predictions. However, the cross‐shore variations of the wave form are predicted well by the theory. Furthermore, from both theoretical and experimental data, it is shown that wave fields are dominated by the Stokes edge‐wave mode in the low frequency range,f<0.5 Hz. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869008

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Three different sets of shallow water equations, representing different levels of approximation are considered. The numerical solutions of these different equations for flow past bottom topography in several different flow regimes are compared. For several cases the full Euler solutions are computed as a reference, allowing the assessment of the relative accuracies of the different approximations. Further, the differences between the dispersive shallow water (DSW) solutions and those of the highly simplified, hyperbolic shallow water (SW) equations is studied as a guide to determining what level of approximation is required for a particular flow. First, the Green‐Naghdi (GN) equations are derived as a vertically‐integrated rational approximation of the Euler equations, and then the generalized Boussinesq (gB) equations are obtained under the further assumption of weak nonlinearity. A series of calculations, each assuming different values of a set of parameters—undisturbed upstream Froude number, and the height and width of the obstacle, are then presented and discussed. In almost all regions of the parameter space, the SW and DSW theories yield different results; it is only when the flows are entirely subcritical or entirely supercritical and when the obstacles are very wide compared to the depth of the fluid that the SW and DSW theories are in qualitative and quantitative agreement. It is also found that while the gB solutions are accurate only for small bottom topographies (less than 20% of the undisturbed fluid depth), the GN solutions are accurate for much larger topographies (up to 65% of the undisturbed fluid depth). The limitation of the gB approximation to small topographies is primarily due to the generation of large amplitude upstream propagating solitary waves at transcritical Froude numbers, and is consistent with previous analysis. The GN approximation, which makes no assumptions about the size of the nonlinearity, is thus verified to be a better system to use in cases where the bottom topographies are large or when the bottom topographies are moderate but the flow transcritical. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869009

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

As basilisk lizards (Basiliscusbasiliscus) and shore birds run along the water surface they support their body weight by slapping and stroking into the water with their feet. The foot motions exploit the hydrodynamic forces of low‐speed water entry. To determine the forces that are produced during water entry at low speeds, we measured directly the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1–80). Also, we measured the period during which the air cavity behind the disk remains open to atmospheric air. We found that the force impulse produced during the impact phase is due to the acceleration of the virtual mass of fluid associated with a disk at the water surface. A dimensionless virtual massM, defined asM=mvirtual/(4/3)&pgr;&rgr;r3, has a value near 1/&pgr; for disks. After impact, as penetration depth of the disk increases, the drag force can rise by as much as 76% even though the downward velocity is steady. However, a dimensionless force which includes the contribution from hydrostatic pressure [CD*=Drag(t)/(&rgr;Sgh(t)+0.5&rgr;Su2)] takes a constant value near 0.7 regardless of disk size, speed, or cavity depth. Over the entire range of disk sizes and velocities, the period between impact and cavity closure,Tseal, can be described by a single value of dimensionless time, &tgr;=Tseal(g/r)0.5, near 2.3. We con‐ clude that the fundamental phenomena associated with the low‐speed water entry of a disk can be characterized by three dimensionless numbers (M,CD*, and &tgr;). ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869010

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

It is known that two‐dimensional vortices are subject to generic three‐dimensional instabilities. This phenomenon is located near the core of vortices and depends on the eccentricity of their streamlines. In this paper we are concerned with the modification of this instability when stretching is applied to such vortices. We describe this instability by linearizing the Navier–Stokes equations around a basic state, which is an exact time‐dependent solution. The complete system for the perturbations is reduced to a single equation for the perturbed velocity along the vortex span. In the limit of weak stretching, a perturbation theory can be performed and leads to a WKBJ approximation for the solution. This procedure demonstrates that a small amount of stretching is able to prevent the appearance of three‐dimensional instabilities for vortices with a low enough eccentricity. Since most vortices are slightly elliptical in turbulent flows, the above computations are expected to cover a wide range of experimental cases. In particular, it is tentatively argued that this mechanism may explain recent experimental observations [Phys. Fluids7, 630 (1995)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868982

出版商:AIP    

年代:1996

数据来源: AIP