摘要:

The three‐dimensional linear instability of Kirchhoff’s elliptic vortex in an inviscid incompressible fluid is investigated numerically. Any elliptic vortex is shown to be unstable to an infinite number of short‐wave bending modes, with azimuthal wave numberm=1. In the limit of small ellipticity, the axial wave number of each unstable mode approaches the value obtained by the asymptotic theory of Vladimirov and Il’in, indicating that the instability is caused by a resonance phenomena. As the ellipticity increases, the bandwidth broadens and neighboring bands overlap each other. The maximum growth rate of each mode, except for that of the longest one, agrees fairly with that of the elliptical instability modified by the influence of a Coriolis force. The growth rate of these three‐dimensional modes are larger than those of the two‐dimensional modes when ellipticity is smaller than a certain value. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868719

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A hydrodynamic boundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868767

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The manner in which the Navier–Stokes equations of fluid mechanics break down under conditions of low‐density, hypersonic flow is investigated numerically. This is performed through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. Both normal shock waves and bow shocks formed by flow over a sphere are considered for argon and nitrogen. It is found that a Knudsen number based on local flow conditions and gradients is a convenient and accurate criterion for indicating breakdown of the continuum flow equations. Failure of the Navier–Stokes equations in hypersonic transitional flows occurs both in the shock front and in the region immediately adjacent to the body surface. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868720

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The hydrodynamic instability of a deflagration wave propagating with finite Mach number has been investigated. This paper deals with a wave front of deflagration as a surface of hydrodynamic discontinuity, and considers the pressure change through the wave front. The instability of the deflagration wave with respect to infinitesimal fluctuations is analyzed, and the relation between growth rates of fluctuations and their wave numbers (dispersion relation) is obtained. The obtained dispersion relation is consistent with the Darrieus–Landau solution when the Mach number is sufficiently small. Increased value of the Mach number causes larger pressure differences, and causes high growth rates compared with the results of Darrieus and Landau. Therefore, one should take account of the pressure change in the stability analysis of the deflagration wave propagating with considerably fast velocity. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868721

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Recent experiments by Diezetal. [Phys. Fluids A4, 1148 (1992)] have shown that converging flow of a very viscous liquid over a rigid horizontal surface, near the time of convergence, approximates a certain self‐similar solution to the nonlinear diffusion equation governing the flow. This Brief Communication presents a rigorous mathematical theory of the flow considered by Diezetal., which justifies their observations. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868722

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

When a thread or column of liquid breaks, a growing blob of liquid forms on the broken ends of the thread as surface tension pulls the ends back toward the rest of the thread. Asymptotic expansions of the shape of the blob and of the flow in it are constructed. Similar expansions are found for the cylindrical blob at the edge of a broken film or sheet of liquid. These results supplement previous calculations of the mass and velocity of the blob. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868723

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Flow visualization and velocity measurements are performed in order to investigate the unsteady nature of vortex breakdown location over a delta wing. The results indicate that the fluctuations of vortex breakdown location occur at much lower frequencies than the frequency of the hydrodynamic instability of the flow in the wake of the vortex breakdown. It is suggested that the helical mode instability does not influence the unsteady nature of breakdown location. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868724

出版商:AIP    

年代:1995

数据来源: AIP