摘要:

The structure of the vorticity field in the viscous wall layer of a turbulent channel is studied by examining the results of a fully resolved direct numerical simulation. It is shown that this region is dominated by intense three‐dimensional shear layers in which the dominant vorticity component is spanwise. The advection and reproduction processes of these structures are examined and shown to be consistent with the classical generation mechanism fortwo‐dimensionalTollmien–Schlichting waves. This process is fundamentally different from the usually accepted mechanism involving hairpin vortices.

ISSN:0031-9171    

DOI:10.1063/1.866721

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Previous works have used the fluctuation–dissipation theorem to evaluate the diffusion coefficient for particles in a turbulent flow which differs from the commonly accepted value. This calculation is reexamined and it is concluded that fluctuation–dissipation expressing energy equipartition is inappropriate for hydrodynamic turbulence.

ISSN:0031-9171    

DOI:10.1063/1.866722

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A new amplitude equation governing the velocity evolution of ion‐acoustic waves in a collisionless plasma is derived:Vtt+(V2)xt=[(1−V2)Vx]x+&bgr;Vxxtt. From this equation the existence of a critical amplitude threshold is immediately deduced, which leads to a double layer and above which solitary waves cannot exist. Above this threshold shock waves form and density undergoes explosive growth. Multidimensional waves and waves due to the magnetic drift are also considered.

ISSN:0031-9171    

DOI:10.1063/1.866723

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The motion in a half‐space of a viscous fluid governed by the Stokes flow equations and driven by the instantaneous velocity on the boundary is considered. It is demonstrated that the flow field can be represented as an integral of the boundary velocity distribution, and the simple kernel function is derived. Previously it was thought necessary for the flow to be represented as an integral of the force distribution on the boundary; the velocity distribution was then related to the force distribution through an integral equation, which was solved numerically. Expressions for the stress field in terms of the velocity distribution on the boundary are also determined, and some technical difficulties involving the convergence of the integrals are discussed.

ISSN:0031-9171    

DOI:10.1063/1.866724

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Experiments were performed in order to delineate the conditions under which small metal and plastic spheres rebound, as opposed to stick, when dropped upon a smooth quartz surface overlaid with a thin layer of a viscous fluid. The parameters that were varied include the fluid layer thickness and viscosity, and the ball size, density, and elastic properties. The minimum drop height that allowed the ball to rebound out of the fluid layer was determined. The results are in very good agreement with the recent elastohydrodynamic theory of Davisetal. [J. Fluid Mech.163, 479 (1986)]. Additional experiments were performed for which the quartz surface was made artificially rough by adhering fine glass spheres to it. For these experiments, the resistance to rebound caused by the fluid layer was significantly reduced, in close agreement with the recent theory for rough surfaces developed by Davis [Phys. Chem. Hydro.9, 41 (1987)].

ISSN:0031-9171    

DOI:10.1063/1.866725

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The nonlinear behavior of viscous fingering in miscible displacements is studied. A Fourier spectral method is used as the basic scheme for numerical simulation. In its simplest formulation, the problem can be reduced to two algebraic equations for flow quantities and a first‐order ordinary differential equation in time for the concentration. There are two parameters, the Peclet number (Pe) and mobility ratio (M), that determine the stability characteristics. The result shows that at short times, both the growth rate and the wavelength of fingers are in good agreement with predictions from our previous linear stability theory. However, as the time goes on, the nonlinear behavior of fingers becomes important. There are always a few dominant fingers that spread and shield the growth of other fingers. The spreading and shielding effects are caused by a spanwise secondary instability, and are aided by the transverse dispersion. It is shown that once a finger becomes large enough, the concentration gradient of its front becomes steep as a result of stretching caused by the cross‐flow, in turn causing the tip of the finger to become unstable and split. The splitting phenomenon in miscible displacement is studied by the authors for the first time. A study of the averaged one‐dimensional axial concentration profile is also presented, which indicates that the mixing length grows linearly in time, and that effective one‐dimensional models cannot describe the nonlinear fingering.

ISSN:0031-9171    

DOI:10.1063/1.866726

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

While the extended Stokes series (ESS) solution for the laminar pressure drop in coiled pipes predicts that the friction ratio (the ratio of pressure drop in the coiled pipe to that in the straight pipe of the same flow rate) varies asymptotically as one‐fourth power of the Dean number, the existing experimental data largely support a square‐root variation; previous boundary layer analyses also predict a square‐root variation. The subject of this paper is an examination of this paradox. A detailed review shows that the existing set of experimental data can be grouped into various categories depending on the precise flow conditions. It is shown that none of the existing data satisfies the proper experimental conditions required by the ESS method. New experiments reveal that the pressure drop demanded by the ESS solution can actually be observed if they are expressly designed to satisfy the conditions demanded by the ESS solution. The implication is that the domains of initial conditions appropriate to the boundary layer and ESS solutions are quite different.

ISSN:0031-9171    

DOI:10.1063/1.866727

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The development of complex velocity fields in curved ducts from an initially parabolic profile is studied using a three‐dimensional numerical model of theparabolizedNavier–Stokesequations. The velocity profiles are influenced strongly by a geometrical parameterRc(the radius of curvature) and a dynamic parameter Dn (Dean number, Re/(Rc)1/2). ForRc< 10 and Dn up to 200, the velocity fields develop into the previously observed two‐ and four‐cell solutions that areaxiallyinvariantand symmetric about the midplane. ForRc=100 and Dn>125 oscillatory solutions develop which areperiodicin the axial direction, but areasymmetricabout the midplane. Increasing the Dean number over a narrow range results in a significant increase in the frequency of such oscillations. Grid sensitivity tests indicate that such oscillations are not a numerical artifact. Development of oscillatory solutions isdelayedwithdecreasingradius of curvature. Thus forRc=10, axially invariant two‐dimensional solutions that retain the symmetry about the midplane could be obtained for Dn as high as 300. This trend is consistent with one of the earliest observations by Taylor [Proc. R. Soc. London Ser. A.124, 243 (1929)] that steady,symmetriclaminar flows can be observed over a larger range of Dean number intightlycoiled tubes. However, when an asymmetric perturbation is imposed at the inlet, oscillatory solutions develop even for lowRc, indicating that symmetric two‐dimensional solutions are not stable to asymmetric perturbations, as indicated by Winters [K. W. Winters and R. C. G. Brindley (private communication)]. Numerical results are also presented for flow through curved ducts with periodic step changes in curvature.

ISSN:0031-9171    

DOI:10.1063/1.866728

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self‐similar form are solved numerically by a finite‐difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start‐up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.

ISSN:0031-9171    

DOI:10.1063/1.867005

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Enhancement of the diffusive transport of impurities by two‐dimensional, time‐independent Rayleigh–Be´nard convection is studied experimentally. Two impurities are used: a molecular dye (methylene blue) and a particulate impurity (latex spheres). The convective flow is characterized by laser Doppler velocimetry, and the transport is monitored by optical absorption techniques. It is found that the transport can be modeled as a diffusive process on long space and time scales, with an effective diffusion coefficientD* whose absolute magnitude and variation with the velocity amplitudeWof the flow are in good agreement with recent theoretical predictions. The enhancement factorD*/Dscales with the Peclet number approximately as Pe1/2≡(Wd/&pgr;D)1/2, whereDis the diffusion coefficient anddthe layer depth. Several subtle problems that complicate the study of transport phenomena in cellular hydrodynamic flows are discussed.

ISSN:0031-9171    

DOI:10.1063/1.866729

出版商:AIP    

年代:1988

数据来源: AIP