摘要:

Supersonic free jets issuing from rectangular orifices have been observed by using a laser‐induced fluorescence technique. Anisotropy of expansion in two directions, the orifice length (z) and width (y), apparently occurs in the jet structure at a large pressure ratio (between reservoir and vacuum chambers); the jet spreads in theydirection whereas it converges in thezdirection. This effect is enhanced by interaction of lateral shocks from both ends of the orifice when a small aspect ratio orifice is used. Under a flow condition whereby the shocks reflect normally on the axis, the jet becomes very thin in thezdirection.

ISSN:0031-9171    

DOI:10.1063/1.866516

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

It is shown that an external electron current gradient in a nonuniform magnetized plasma can drive a purely growing instability involving coupled convective cells and magnetostatic modes. Accounting for the mode coupling, it is demonstrated that the quasistationary state of the unstable flute modes can lead to a spatially ordered dipolar vortex structure. The latter could alter the transport properties and it may also be responsible for a relaxed state in a force‐free magnetized plasma.

ISSN:0031-9171    

DOI:10.1063/1.866204

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Observations made in various batch and continuously operated inclined settlers are reported. The systems considered are the so‐called ‘‘low aspect ratio’’ devices in which the width of the vessel is large enough such that the presence of the enclosing walls does not affect the dynamic phenomena. The principal aim of these experiments was to test the predictions of the recent theoretical papers of Shaqfeh and Acrivos [Phys. Fluids29, 3935 (1986);30, 960 (1987)] concerning the laminar base state convective flow and accompanying instability wave growth under conditions in which inertial effects play an important role. The observations confirm that the theory predicts various characteristics of the laminar flow both quantitatively and qualitatively and that, within the range of experimental conditions, the more recent linear stability theory qualitatively describes the salient features of the instability wave growth in these systems.

ISSN:0031-9171    

DOI:10.1063/1.866205

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

In an earlier paper, Maxey and Corrsin [J. Atmos. Sci.43, 1112 (1986)] studied the motion of small aerosol particles settling under gravity through an infinite, periodic, cellular flow field subject to the effects of a Stokes drag force and inertia of the particles. Particle inertia was shown to have an important influence on the motion: No permanent suspension in the flow occurred, particles generally settled more rapidly than in still fluid, and the particle paths merged into isolated asymptotic trajectories. This study is continued for particles that are not necessarily much denser than the surrounding fluid but vary in density. Two basic responses are identified: an aerosol response for particles denser than the fluid, similar to that mentioned, and a bubble response for particles less dense. For both, particle accumulation is still a recurring feature. Results of numerical simulations are discussed, together with the stability of equilibrium points and the role of particle or fluid inertia.

ISSN:0031-9171    

DOI:10.1063/1.866206

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A brief description of a numerical technique suitable for solving axisymmetric, unsteady free‐boundary problems in fluid mechanics is presented. The technique is based on a finite‐difference solution of the equations of motion on a moving orthogonal curvilinear coordinate system, which is constructed numerically and adjusted to fit the boundary shape at any time. The initial value problem is solved using a fully implicit first‐order backward time differencing scheme in order to insure numerical stability. As an example of application, the unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers is considered in the range of 0.1≤R≤100. The computation shows that the bubble extends indefinitely if the Weber number is larger than a critical value (W>Wc). Furthermore, it is shown that a bubble may not achieve a stable steady state even at subcritical values of Weber number if the initial shape is sufficiently different from the steady shape. Finally, potential‐flow solutions as an approximation forR→∞ have also been obtained. These show that an initially deformed bubble undergoes oscillatory motion ifW<Wc, with a frequency of oscillation (based on the surface tension time scale) that decreases as Weber number increases and equals zero at the critical Weber number beyond which steady solutions could not be obtained in the earlier numerical work of Ryskin and Leal [J. Fluid Mech.148, 37 (1984)]. This clearly indicates that the point of nonconvergence of the steady‐state numerical problem is, in fact, a limit point in the branch of steady‐state solutions.

ISSN:0031-9171    

DOI:10.1063/1.866207

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Stability boundaries separating different states of bimodal convection in a box of saturated porous material with impermeable bounding faces are determined. Two opposing vertical end walls are always insulated, while the thermal conditions on the other set of opposing vertical side walls range from insulated to perfectly conducting, as measured by the Biot number based on box height. The temperature difference between the hot lower plate and the cooler upper plate provides the mechanism for instability. The eigenvalue problem for the critical Rayleigh number is solved numerically over a range of box sizes and side‐wall heat transfer conditions. For small values of the distanceH2between conducting side walls, agreement with previous asymptotic analysis is obtained. New results for boxes with planform dimensions both comparable to the box height show the existence of isolated regions rich in bimodal structure. These islands are separated by broad regions having modal properties identical to those found for conducting side walls in the limitH2→0. The numerical results forO(1) box dimensions continue to exhibit the stabilizing effect of side‐wall heat transfer as previously observed for thin slabs.

ISSN:0031-9171    

DOI:10.1063/1.866208

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The problem of the hydrodynamic stability of a plane dielectric liquid layer subjected to unipolar injection and rotation examined here is in many ways analogous to that of rotating horizontal fluid layer heated from below. In both situations instability is likely to arise as steady or oscillatory convection depending on the values of only two parameters. The critical conditions for which instability sets in as a steady convection are determined as functions of both the Taylor number and the level of injection. Because of the mathematical complexity of the problem, the onset of convection as overstability is determined only for the particular case of weak injection. In this case, an analytical treatment is carried out that allows discrimination of regions of steady and oscillatory convective instability.

ISSN:0031-9171    

DOI:10.1063/1.866209

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The steady thermocapillary convection in an axisymmetric liquid bridge in the absence of gravitational forces is considered. The relative change in the surface tension is assumed to be very small, i.e., the appropriate capillary number is much less than 1. A detailed analysis of the flow field is carried out for cylindrical bridges. The field equations are simplified by neglecting convective effects (Marangoni numberM=0, Reynolds number Re=0). The effects of the bridge aspect ratio, differential heating of the side walls, and arbitrary heating of the free surface are analyzed numerically. The results show that flow patterns consisting of one, two, three, or more columns of vortices, or of their superposition, may exist in the liquid, depending on the type of heating. Decrease of the aspect ratio (long bridges) results in an emergence of the core zones of almost parallel flow. Increase of the aspect ratio (short bridges) leads to the emergence of several layers of vortices, with the strength of each layer decreasing approximately exponentially with the distance from the surface. It is noted that an asymptotic flow pattern around the interface emerges rapidly with the decrease of the length of the bridge.

ISSN:0031-9171    

DOI:10.1063/1.866210

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Surface deformation and capillary instability of nonisothermal liquid bridges have been analyzed. The results show that the maximum size of the bridge is limited by the capillary instability. When the length of the bridge increases, a nonstationary surface deformation may occur before the capillary instability sets in, and it may lead to an earlier breakup of the bridge. Detailed calculations have been carried out for cylindrical bridges. It has been found that such bridges bulge at the cold end and constrict at the hot end. An asymptotic form of surface deformation has been identified in the case of very short bridges.

ISSN:0031-9171    

DOI:10.1063/1.866211

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A two‐layer inviscid incompressible fluid system of intermediate depth is considered. A multiple‐scales perturbation technique is applied to the basic equations and boundary conditions for a two‐layer fluid system to derive a system of weakly nonlinear partial integrodifferential equations governing the resonant interaction between a surface gravity wave packet and an internal gravity wave at an intermediate depth, providing a bridge between the existing shallow and deep fluid theories. The convolution integral term in these equations accounts for the dispersion in the lower‐layer fluid. An iterative fast Fourier transform scheme is developed to find solitary wave solutions to this system of equations. The overtaking collision of two pairs of solitary waves, simulated using a spectral method, is found to be inelastic. It is found that the amplitude of the solitary waves changes slightly after the collision. The phase shifts these solitary waves undergo was calculated numerically.

ISSN:0031-9171    

DOI:10.1063/1.866212

出版商:AIP    

年代:1987

数据来源: AIP