摘要:

The probability distribution, in space, of a passive scalar advected by a model, divergence‐free, velocity field is analytically calculated. It is found to have a logarithmic singularity at the origin and a quasi‐Gaussian decay away from it. The significance of this result for the general case of convection of passive scalars and the relation to a recent theory of Yakhot and Sinai [Phys. Rev. Lett.63, 1962 (1989)] are discussed.

ISSN:0899-8213    

DOI:10.1063/1.857578

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.

ISSN:0899-8213    

DOI:10.1063/1.857579

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

In order to study the rotational motion of a vortex ring or the locomotion of bacteria, which propel their cells by rotating their long curved filaments called flagella, the low‐Reynolds‐number flow resulting from the rotation of a torus is studied. The velocity field is obtained by distributing uniform rotlets along a circle with the rotlet directions tangent to the circle. It is found that the effect of curvature of this ring distribution of uniform rotlets is to displace this rotlet ring from the center of the cross section toward the outside of the torus in the normal direction. The net force exerted on the surrounding fluid by the rotational torus is zero. The net torque acting on the fluid is also zero.

ISSN:0899-8213    

DOI:10.1063/1.857580

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A water drop falling into a shallow pool of water can give rise to a splash that ejects droplet fragments high into the air. The height reached by the highest‐flying ejected droplet is greatest when the depth of the target liquid is equal to the radius of the hemispherical crater formed by the impact of the incident drop. This phenomenon, referred to here as the tuning of a splash, is still observed when liquids of very different viscosity and surface tension are substituted for water, but a thin sponge layer cemented over the floor of the pan all but destroys the tuning behavior. Cine images reveal a possible explanation for the tuning phenomenon based on a delay of the upward retraction of the collapsing crater.

ISSN:0899-8213    

DOI:10.1063/1.857581

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Numerical experiments of natural convection of a zero Prandtl (Pr) number fluid in 4×1×2 (length to height to width) and 4×1×1 rectangular cavities (with a free top surface) and enclosures (having a solid top surface) are performed. The cavities are referred to as R‐F (rigid‐free) while enclosures are referred to as R–R (rigid–rigid). The objective of this study is to establish the pattern of three‐dimensional convection and to determine the value of the critical Grashof number, Grcrit, at which the flow becomes time dependent. A three‐dimensional laminar flow model of a constant property fluid is used. The model equations are solved numerically by a finite volume method. The flow field is steady at relatively low Grashof number (Gr), and is represented by one cell, unlike the multicellular flow predicted by two‐dimensional studies. When Gr reaches Grcrit, the flow becomes oscillatory. Transition to time dependence is a function of the geometry and the type of top surface (rigid or free). The R–R flow is more stable than that of the R‐F case, for both widths considered (one and two). The width of cavity and/or enclosure has an important effect on transition to oscillatory convection, for it is found that reducing the width from two to one, leads to a much higher Grcrit, making the results of two‐dimensional numerical simulations completely inadequate.

ISSN:0899-8213    

DOI:10.1063/1.857582

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

It was shown by Rayleigh [Philos. Mag.14, 184 (1882)] that a conducting spherical drop becomes unstable when the net dimensionless charge on its surface,Qc, exceeds the value of 4(&pgr;)1/2 . More recently, Tsamopoulosetal. [Proc. R. Soc. London Ser. A401, 67 (1985)] have shown, both analytically and numerically, that at this point a transcritical bifurcation occurs. The finite element methodology that they employed is limited to cases where the drop shapes are not very deformed because of truncation problems with mesh representing the infinitely extending surrounding medium. This situation has now been rectified by employing the integral form of Laplace’s equation, which only requires discretization and solution on the surface of the drop. Thus a hybrid method results with the integral equations solved via boundary element techniques, while finite elements are still used for the remaining governing equations. Using this hybrid method, previous results have been reproduced much more accurately and efficiently. In addition, new solution families have been discovered. In particular, several shape families that are not symmetric about the equatorial plane were found to bifurcate from the families of two‐ and four‐lobed shapes. A disjoint family with saddle point shapes was found to extend to small values of charge. It corresponds to the Frankel–Metropolis family that is well known in nuclear physics(Cohenetal. [Ann. Phys.82, 557 (1974)]). All newly discovered solution families are linearly unstable.

ISSN:0899-8213    

DOI:10.1063/1.857583

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

In comparing their results with those of Mack, Wazzanetal. [Phys. Fluids27, 331 (1984)] found major differences regarding the effect of free‐stream Mach number on viscous instability. The present work shows that all past observations concerning stability behavior in the supersonic range based on Mack’s work are accurate to the level of approximation involved. More importantly, as a consequence of discussions with Mack (private communication) prompted by this dispute, this paper clarifies the fluid‐property assumptions made by him in his earlier calculations and demonstrates the sensitivity of stability calculations to the accuracy of the basic state.

ISSN:0899-8213    

DOI:10.1063/1.857584

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The linear stability of a steady stagnation flow over a cylindrical body is examined. Special consideration is given to the influence oscillatory modulation of the steady flow has on the bifurcation of three‐dimensional vortical disturbances from stability. It is shown that such modulations result in a fixed bifurcation point according to linear stability theory. The sensitivity of the bifurcation point to the time‐harmonic modulation and steady flow speed is considered in the analysis. It is shown that stagnation flow exhibits instability if unsteadiness is introduced into the basic state of the flow. Analytical results are compared to experimental data.

ISSN:0899-8213    

DOI:10.1063/1.857585

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A center manifold theory is used to determine all modes that contribute significantly to the leading‐order sideband stability of finite‐amplitude monochromatic waves. The classical multiscale theories based on the Ginzburg–Landau equation are extended away from near‐critical conditions and are shown to have omitted an important contribution from nonlinear interactions with low wave‐number modes. Stability bounds on stable monochromatic waves are reported for dispersive systems that extend the classical Eckhaus bound for nondispersive systems and the Lange–Newell and Benjamin–Feir stability conditions for monochromatic waves with critical wave numbers. These new stability bounds are verified numerically by computing the evolving spectrum of a model equation.

ISSN:0899-8213    

DOI:10.1063/1.857586

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The subharmonic instability of a two‐dimensional compressible boundary layer over an insulated flat plate is analyzed using the Floquet model. The resulting problem is solved numerically by using both finite differences and the computer codesuport. Results are presented for subsonic, transonic, and supersonic flows. For supersonic flows results for the first and second modes are presented. The effects of Mach number, spanwise wave number, amplitude of the primary wave, Reynolds number, and frequency are studied.

ISSN:0899-8213    

DOI:10.1063/1.857587

出版商:AIP    

年代:1990

数据来源: AIP