摘要:

A particle simulation is used to test the hypothesis that the small, low phase velocity part of the antenna spectrum used in lower‐hybrid current drive experiments is important in bridging the gap between the velocity of the bulk of the electron distribution and the phase velocity of the major part of the spectrum. A simulation with the small, low phase velocity part of the spectrum numerically removed showed a strong quenching of the current compared to a simulation with the full spectrum, consistent with the hypothesis.

ISSN:0031-9171    

DOI:10.1063/1.865451

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Effective equations for nonlinear wave propagation in a bubbly liquid are derived by the method of homogenization for the case where the volume fraction of the gas is finite. The analysis is valid when the ratio of the mean interbubble distance to wavelength is small. The effective equations are coupled with a canonical (cell) problem on the microscopic scale. The dominant mode of oscillation of a bubble is volume preserving and asymmetric with finite amplitude. The cell problem and the averaging in the effective equations can be simplified by the method of matched asymptotics for the case of small volume fraction. The cell problem can be further simplified by using the small gas‐to‐liquid density ratio. Approximate solutions are then constructed to the cell problem. These are coupled to the effective equations on the macroscopic scale to form a closed system. The solutions of this system are analyzed in the linear and weakly nonlinear regime.

ISSN:0031-9171    

DOI:10.1063/1.865452

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The generation of gravity‐capillary waves (ripples) by a flap‐type wavemaker is examined theoretically and experimentally. Qualitative agreement is found in the trapped wave region; measured amplitudes exceed those predicted by the linear theory and the data extend further from the wavemaker. The air–water–aluminum contact line on the paddle face appears to cause a phase shift away from the paddle in the measured results. Excellent agreement is found with the linear dispersion relation for the progressive waves when the water is scrupulously cleaned of ions and organics, and filtered of minute particles. The presence of minute particles (only) necessitates introduction of the notion of ‘‘dynamic’’ surface tension which is about 30% lower than the measured static value. When particles are removed the dynamic and static values of surface tension are equivalent. The amplitudes of the progressive waves agree well with theory when the product of the wavenumber and water depth does not exceed seven, and the inviscid theory is modified to account for decay by viscosity. Agreement requires the assumption of a ‘‘fully contaminated’’ surface even when the water is particle filtered. Otherwise, the viscous decay is about twice that predicted by the fully contaminated surface model. Longitudinal instabilities of the progessive waves are observed when the product of wavenumber and water depth exceeds about seven. These instabilities appear to be modeled well by the nonlinear Schro¨dinger equation. Transverse instabilities are also observed in the data over the full range of wave frequencies investigated.

ISSN:0031-9171    

DOI:10.1063/1.865453

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The simplest experiments for flows in porous pipes occur when either the pressure or the pressure gradient outside the pipe is constant. Several classes of analytical solutions corresponding to some of these flows are presented.

ISSN:0031-9171    

DOI:10.1063/1.865454

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Two concentric corrugated cylinders are separated by a viscous fluid. When the inner cylinder is rotated, unsteady and steady torque and forces may be generated. Assuming low Reynolds numbers and small amplitude corrugations, the Navier–Stokes equations are solved by perturbations to second order. The torque and forces are dependent on the gap width, the amplitude of corrugations, and especially the number of waves of the corrugations.

ISSN:0031-9171    

DOI:10.1063/1.865455

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A local similarity solution to the viscous‐gravity jet valid for large Reynolds number flows is given. The jet is divided into an inner core where axial gradients are small relative to the outer annular region. A similarity transformation is found for the outer region, reducing the resulting differential equations to a two‐point boundary value problem. This solution is matched to the inner solution through the boundary conditions. This approach effectively eliminates the mathematical difficulties associated with the unknown free surface and the stress singularity at the exit.

ISSN:0031-9171    

DOI:10.1063/1.865456

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The rotating flow of a separating mixture of particles and fluid in a finite straight axisymmetric container is considered. The analysis employs the ‘‘mixture’’ (‘‘diffusion’’) model under the assumptions that the Ekman numberE, the particle Taylor number &bgr;, and the relative density difference &egr; are small, and the volume fraction &agr; possesses initially a slight ‘‘stratification’’ aroundA0. It is shown that the Ekman layers on the endplates may considerably affect the azimuthal motion of the inviscid core via a spin‐up mechanism that has a relative importance reflected by &lgr;=E1/2/&egr;&bgr;H(His the dimensionless height of the container). When &lgr;≪1 a considerable retrograde motion, proportional to &egr;A0/&bgr;, shows up in agreement with previous infinitely ‘‘long cylinder’’ (i.e., endcaps neglected) solutions; this motion is substantially reduced when &lgr;∼1 and diminishes for &lgr;≫1. On the other hand, the radial motion in the core is insignificantly influenced by the Ekman layers; therefore, the main separation process is properly represented by the long cylinder solutions for a wide range ofH. In addition, it is shown that an initial radial stratification may induce a similar axial variation of &agr; in the Ekman layers.

ISSN:0031-9171    

DOI:10.1063/1.865457

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

An analytical solution predicting the behavior of particles in the presence of both gravitational and rotational fields is obtained at the limit of quasisteady creeping flow. The experiments performed in the present work using fluid particles, as well as the experiments already reported on solid particles, agree satisfactorily with the theory.

ISSN:0031-9171    

DOI:10.1063/1.865458

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The stability of finite amplitude, two‐dimensional solitary waves of permanent form in water of uniform depth with respect to two‐dimensional infinitesimal disturbances is investigated. It is numerically confirmed that the recent analytical results obtained by Saffman (submitted to J. Fluid Mech.) for the ‘‘superharmonic’’ instability of periodic waves hold also in the case of solitary waves.

ISSN:0031-9171    

DOI:10.1063/1.865459

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A Lagrangian form of the KdV equation (LKdV) is given which governs the evolution of nonlinear shallow water waves. Wave motion described by this equation in the context of the inverse scattering transform (IST) is discussed. For a single soliton it is shown that LKdV allows for an orthogonal decomposition of the particle motion into a kink (tanh) soliton in the horizontal and a pulse (sech2) soliton in the vertical. Generalizations to the orthogonal decomposition ofN‐soliton motion and to motion with periodic boundary conditions are also discussed. Implications of this approach on experimental measurements and on other integrable (soliton) systems are briefly explored.

ISSN:0031-9171    

DOI:10.1063/1.865460

出版商:AIP    

年代:1986

数据来源: AIP