摘要:

Numerical experiments were performed to clarify apparent differences between experimental observations and a theoretical prediction of the secondary instability in plane Poiseuille flow. It is shown that subharmonic breakdown is unlikely in natural transition as a result of the initial growth of what we call the ‘‘minus’’ modes and consequent forcing of Orr–Sommerfeld modes present in the background noise. Subharmonic breakdown was achieved only when these minus modes were continuously suppressed.

ISSN:0899-8213    

DOI:10.1063/1.857374

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The mechanism of the reduction of nonlinearity recently observed in simulations of decaying isotropic turbulence by Kraichnan and Panda [Phys. Fluids31, 2395 (1988)] is investigated. It is shown that although the alignment of velocity and vorticity in physical space is not the sole source of the effect, it can enhance the effect significantly. Another source of the reduction seems to be a tendency of the Lamb vectorv×&ohgr; in Fourier space to align with the wave vectork. The ordering of the energy transfer is suggested to be a dynamically generic effect driving the reduction.

ISSN:0899-8213    

DOI:10.1063/1.857375

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no‐slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow‐independent slip‐length boundary condition. The trajectories of individual molecules in Poiseuille flow are examined, and it is also found that their average behavior is given by Taylor–Aris hydrodynamic dispersion. An immiscible two‐fluid system is simulated by a species‐dependent intermolecular interaction. A static meniscus is observed whose contact angle agrees with simple estimates and, when motion occurs, velocity‐dependent advancing and receding angles are observed. The local velocity field near a moving contact line shows a breakdown of the no‐slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan [AIChE J.23, 131 (1977)].

ISSN:0899-8213    

DOI:10.1063/1.857376

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Axisymmetric equilibrium shapes and stability of isolated charged drops are found by solving simultaneously the Young–Laplace equation for surface shape and the Laplace equation for the electric field. Families of two‐, three‐, and four‐lobed shapes that branch from the trunk family of spheres are treated systematically by means of the Galerkin/finite element method and a tessellation that deforms with the free surface. The results show that at the limit found by Rayleigh in 1882 the spherical family exchanges stability with a family of two‐lobed shapes, a transcritically bifurcating family, one arm of which proves to consist of stable shapes. The results are reinforced by those of approximating the stable drop shapes as oblate spheroids. Thus oblate drops carrying charge in excess of the Rayleigh limit ought to be seen in experiments, though none have yet been reported.

ISSN:0899-8213    

DOI:10.1063/1.857551

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A highly conducting charged drop that is surrounded by a fluid insulator of another density can be levitated by suitably applying a uniform electric field. Axisymmetric equilibrium shapes and stability of the levitated drop are found by solving simultaneously the augmented Young–Laplace equation for surface shape and the Laplace equation for the electric field, together with constraints of fixed drop volume, charge, and center of mass. The means are a method of subdomains, finite element basis functions, and Galerkin’s method of weighted residuals, all facilitated by a large‐scale computer. Shape families of fixed charge are treated systematically by first‐order continuation. Previous analyses by Abbasetal. in 1967 and Abbas and Latham in 1969, in which the shapes of levitated drops are approximated as spheroids, are corrected. The new analysis shows that drops charged to less than the Rayleigh limit lose shape stability at turning points, with respect to external field strength, and that the instability seen in experiments of Doyleetal. in 1964 and others is not a bifurcation to a family of two‐lobed shapes, but rather is a related imperfect bifurcation.

ISSN:0899-8213    

DOI:10.1063/1.857377

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The flow of a centrifugally separating mixture of particles (droplets) and fluid is considered, with emphasis on the azimuthal no‐slip requirement on the side wall of the cylindrical container. In the framework of the ‘‘mixture’’ averaged equations—when the Ekman numberE, particle Taylor number &bgr;, and relative density difference &egr; are small—a single partial differential nonhomogeneous parabolic equation is obtained for the angular velocity &ohgr;(r,t) (relative to the rotating vessel). Analytical and numerical solutions are presented for the dilute limit and for the more general case, respectively. It is shown that, during the separation process, &ohgr; develops a quasisteady boundary layer of thickness &dgr;(&lgr;/(&lgr;−1))1/2onr=1, only if &lgr;>1, where &dgr;=H1/2E1/4is the typical Stewartson layer scale, &lgr;=E1/2/&egr;&bgr;H, andHis the dimensionless height of the container. If &lgr;≤1, however, the side wall affects &ohgr; in an unsteady, diffusing viscous domain. Correspondingly significant variations in the axial flux are induced by the Ekman layers. Comparisons to numerical results (produced by a code discussed elsewhere) of the full two‐fluid equations display a favorable agreement.

ISSN:0899-8213    

DOI:10.1063/1.857378

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The equation governing the average rate of change of disturbance kinetic energy is evaluated for various wavenumbers at fixed values of Reynolds number, Weber number, and angle of inclination. The dominant energy production term is associated with the work done by the perturbation shear stress at the free surface. The mechanism of instability, however, is associated with a shift of perturbation vorticity relative to the surface displacement resulting from advection.

ISSN:0899-8213    

DOI:10.1063/1.857379

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The finite‐amplitude growth of finger convection at an interface of two uniform solutions is studied to determine the processes that govern the scale and amplitude of the convection, the growth of the fingering interface, and the transition of the convection to turbulence. A conceptual model of fingering processes is provided and details are studied by means of direct numerical simulation. The simulations obtain full finger convection and turbulence for ratios of viscosity to diffusivities in the range between 1 and 10. The study shows that the evolution of finger convection in its entirety is characterized by the scale and amplitude of the fastest growing finger mode. In the parameter range studied, the growth of the fingering interface is found to be controlled mostly by molecular diffusion. Convective flux divergence only plays a secondary role. The growth of the interface is shown to have the effect of increasing the horizontal scale of the convection while decreasing the buoyancy flux. However, the kinetic and potential energies remain statistically stationary for fully developed finger convection. Density inversion developed within finger convection is shown to play an important role in the breakup of finger structures into turbulence. The significance of ‘‘collective’’ instability in determining this transition is not substantiated by the simulation for the parameter values studied here.

ISSN:0899-8213    

DOI:10.1063/1.857380

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The onset of convective instability is investigated in a multicomponent fluid layer in which the density depends onNstratifying agencies with different diffusivities. The general equations required to determine the topology of the neutral curves and stability boundaries are given. We show that 1+2[(N−1)/2] (where [&agr;] is the integer part of &agr;) critical Rayleigh numbers are sometimes required to specify the linear stability criteria. This multivaluedness can be traced to the existence of disconnected neutral curves. The general theory is illustrated by a numerical example for the quintuply diffusive case (N=5).

ISSN:0899-8213    

DOI:10.1063/1.857381

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Spectral simulation is used to test the perturbation expansion of Davey [J. Fluid Mech.14, 336 (1962)] applied to two‐dimensional, streamwise‐oriented vortices in curved channel flow and rotating channel flow over a wide range of parameters. The power series dependence on Reynolds number implied by the perturbation expansion provides an excellent description of the amplitudes of all ten independent Fourier modes resolved in the numerical simulations. Weakly nonlinear analysis, associated with truncating the perturbation expansion, is developed for rotating channel vortices and compared to the full simulations. For both channel geometries, significant increases in the accuracy of weakly nonlinear theory occurs with increasing vortex wavenumber; this is explained by examining spatial energy spectra.

ISSN:0899-8213    

DOI:10.1063/1.857382

出版商:AIP    

年代:1989

数据来源: AIP