摘要:

The dam breaking problem in terms of changing water levels behind and ahead of the dam, has been solved in the shallow water model. Here the effect of dam breaking on a symmetric downstream floating body is considered. A forced Duffing equation model, proposed by one of the authors, is used. The analysis has practical implications in terms of how far a marina should be situated from a large dam. Comparison with basin erosion, as caused by a water surface soliton, is instructive.

ISSN:0899-8213    

DOI:10.1063/1.858794

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxe´n law for the pressure moment of one spherical particle in a general low‐Reynolds‐number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Pe´clet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle‐phase pressure, used in two‐phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported.

ISSN:0899-8213    

DOI:10.1063/1.858795

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The motion of small, spherical noninteracting bubbles in two‐dimensional vortical flows by means of numerical simulations is investigated. After a discussion concerning the various bubble equations, bubble trajectories are calculated in a solid‐body vortex, where it is found that the bubble motion can be described in terms of the location where the bubbles accumulate, or equilibrium points, and the rate of entrapment into these equilibrium points. Of importance here is that the rate of entrapment into the vortex has an optimum value for some value of the inertia parameter, or inverse Stokes number. The bubble motion in a temporally evolving shear layer is investigated, where it is found that the solid‐body vortex model predicts the trends in the growth in concentration about the vortex center for the case without gravity. For the case with gravity, not all bubbles are captured by the vortex, and the percentage of bubbles captured increases with decreasing inertia parameter. Also discussed is how these factors affect the generation of the interface between regions seeded and not seeded with bubbles.

ISSN:0899-8213    

DOI:10.1063/1.858750

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A wavy free‐surface flow of a viscous film down a cylinder is considered. It is shown that if the cylinder radius is large, as compared to the film thickness, the long‐wave perturbation approach yields a rather simple evolution equation. This nonlinear equation is similar to the well‐known Benney equation of planar films, and becomes exactly the latter in the limit of infinite radius. Thus it is the annular‐case analog—which was missing in the literature—of the Benney equation. It is argued that under conditions implicitly implied in their derivation, the Benney‐type equations are not uniformly valid for large times. However, both the new and Benney equations are important heuristically—as sources of other, simpler, equations which, in certain domains of system parameters, are valid for all time. Also, the new equation of annular films is important as a qualitative model incorporating all significant physical factors.

ISSN:0899-8213    

DOI:10.1063/1.858895

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In homogeneous porous media, the analytical expression of the dispersion tensorD* can be calculated by the method of moments and by a multiple scale expansion; the symmetric component of this tensor is identical in both cases. Numerically,D* can be computed by two methods, namely theBequation and random walks. The porous media are modeled as being spatially periodic;D* is determined as a function of the Pe´clet number for four types of unit cells: deterministic, fractal, random, and reconstructed. A systematic comparison is made with existing numerical and experimental data. The long time behavior, and its Gaussian limit, is documented.

ISSN:0899-8213    

DOI:10.1063/1.858751

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

This work presents the results of numerical simulations of unsteady recirculating flows at high Reynolds number. The two geometries investigated are a two‐dimensional channel that incorporates a sudden expansion in the form of a single backward‐facing step and a two‐dimensional channel that incorporates a sudden expansion in the form of a double symmetrical backward‐facing step. The random vortex method (RVM) is used in this study. This grid‐free Lagrangian method solves the unsteady, incompressible Navier–Stokes equations and the continuity equation, with the appropriate physical boundary conditions, using a formulation in vorticity variables. In order to show the ability of the RVM an extensive set of numerical results is presented and compared with experimental results from the literature. In particular, the dissymmetrical behavior of the flow in the double expansion channel, as observed experimentally, is simulated accurately. Frequency analyses and autocorrelation analyses show that the flows are characterized by dominant frequencies and turbulent length scales that are function of the position inside the channels. Those frequencies and turbulent length scales are related to the dynamics of the flow fields.

ISSN:0899-8213    

DOI:10.1063/1.858752

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In this paper the linear stability of a fluid layer flowing down the inside and outside of a rotating vertical cylinder is investigated. To this end, two approximations are made: the small wave number approximation and the small Reynolds number approximation. In the former, only the radial destabilizing effect of surface tension is important and may be counteracted by the centrifugal force at a critical value. In the latter, the analysis integrates the azimuthal modes different fromm=0. It is shown that for flow outside the cylinder, the magnitude of centrifugal force and wave number may change the dominant mode of instability. For flow inside the cylinder, only the modem=0 may be unstable. These results generalize those of Boudourides and Davis [Z. Angew. Math. Phys.37, 597 (1986)] for swirling viscous flows.

ISSN:0899-8213    

DOI:10.1063/1.858753

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Rigorous analysis shows that the spin synchronous mode fluid motion inside a nutation fluid damper on board of a spinning satellite can be modeled as an incompressible, laminar pulsatile flow in a circular straight pipe. The pipe rotates with constant angular velocity &ohgr;_ about an axis perpendicular to its own axis. The distance between the rotation axis and the pipe axis is much greater thana, the pipe’s radius. The flow is driven by a three‐dimensional harmonic oscillation of the pipe wall with frequency &OHgr; and amplitudew’0, and is governed by three‐dimensionless parameters:R&OHgr;(=&OHgr;a2/&ngr;), &Dgr;(=&ohgr;/&OHgr;), andA( =w’0/&OHgr;a), where &ngr; is the kinematic viscosity of the fluid. Both the asymptotic analysis and the numerical calculation have been carried out forR&OHgr;=0.1–1000 and &Dgr;=0–2 underA≪1. It is found that the rotating effect increases the energy dissipation significantly in comparison with the result of the pulsatile straight pipe flow in an inertia frame (the previous theory for the nutation damper). For &Dgr;=1.5, the energy dissipation in a rotating pipe flow is 5.43 times that in a ‘‘stationary’’ pipe flow for largeR&OHgr;, which agrees with the previous experiment. A steady stream is induced by the convective effect for finite values ofA. Such steady motion is consisted of axial counter flows together with pairs of counter‐rotating vortices in the cross‐sectional plane.  

ISSN:0899-8213    

DOI:10.1063/1.858754

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The equations for three‐dimensional, time‐dependent convection in a gravitationally modulated fluid layer heated from below are solved numerically using the Galerkin method in space and a Crank–Nicolson scheme in time. Nonlinear solutions are obtained for the Prandtl number of air (0.71) and for two Rayleigh numbers above the value for onset of oscillatory convection. Multiples of the fundamental frequency of oscillatory convection were chosen in order to study the effects of possible resonances of the frequency of gravitational modulation. Modulation causes a transition from traveling wave convection, which persists in the unmodulated case, to standing wave convection and phase locking occurs for moderate values of the amplitude of the dimensionless gravitational modulation (scaled with the standard acceleration of gravity) in the range 0 to 3. For larger values of the modulation amplitude, frequency locking breaks down and chaotic time dependence occurs.

ISSN:0899-8213    

DOI:10.1063/1.858755

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The flow in the unobstructed space between a pair of disks corotating at high speed in a fixed cylindrical enclosure can be divided into five regions amenable to theoretical analysis [C. A. Schuler, Ph.D. Thesis, University of California at Berkeley (1990); C. A. Schuleretal., Phys. Fluids A2, 1760 (1990)]. One of these, region III in Fig. 2, is an axially‐aligned detached shear layer predicted by the analysis to be located atrIII/R2≊&Ggr;1/2and of thickness &dgr;III/R2≊(2 Re)−1/4, whereR2is the radius of the disks, Re is the Reynolds number based onR2and the tip speed of rotation of the disks (&ohgr;R2), and &Ggr; is an experimentally determined constant. Through viscous diffusion, the detached shear layer allows the transition that must take place between the bulk of the three‐dimensional flow in the interdisk space (region II) and the two‐dimensional flow in solid body rotation surrounding the hub that spins the disks (region IV). Present findings, based on flow visualization, confirm these hitherto untested theoretical expressions and reveal that beyond a critical value of the Reynolds number the detached shear layer oscillates in the cross‐stream (r‐z) plane of the flow. The unsteadiness appears to originate at the enclosure side wall where the disk Ekman layers collide as a result of being redirected from the radial into the axial direction. These observations agree with the direct numerical simulations of Schuler [Ph.D. Thesis, University of California at Berkeley (1990)] which also show that the onset of flow unsteadiness in the cross‐stream plane coincides with the appearance of an integer number of circumferentially‐periodic large‐scale flow structures with large component of axial vorticity, of the type found by Hide and Titman [J. Fluid Mech.29, 39 (1967)] in a similar flow configuration as of a critical value of the Reynolds number.

ISSN:0899-8213    

DOI:10.1063/1.858756

出版商:AIP    

年代:1993

数据来源: AIP