摘要:

The evolution of material lines and surfaces is important in mixing involving fast reactions between fluids. It is shown that direct numerical tracking of the interface presents formidable computational problems in even the simplest chaotic flows because of storage requirements. The results indicate the need for a building block approach for the analysis of mixing problems involving chaotic flows.

ISSN:0031-9171    

DOI:10.1063/1.866449

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The bifurcations to two‐dimensional unsteady behavior of a large amplitude equilibrium shear wave train in two‐dimensional Poiseuille flow are studied by direct simulation of the time evolution of the full Navier–Stokes equations. It is found that the wave train becomes unstable at Re∼5600, and sheds a limit cycle which, at higher Re, seems to undergo further transitions to more complex behaviors. It is shown that the site of the original bifurcation is in the neighborhood of the walls and that it shows some characteristics suggestive of the burst generation mechanism in the boundary layer.

ISSN:0031-9171    

DOI:10.1063/1.866450

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A local analysis has been made about a point at the free surface of an incompressible viscous fluid flow at steady state by means of series expansions of the Navier–Stokes equations. Dividing streamlines, curvature effects, and the role of vorticity have been studied. A single dividing streamline is always perpendicular to the free surface. This means, in particular, that all steady vortices with one end of their axes attached to a free surface are perpendicular to it. Double dividing streamlines of two‐dimensional viscous fluid flows at a free surface always have an angle of 90° between them, whereas double dividing streamlines of inviscid irrotational motion on a free or solid surface are separated by an angle of 60°. For an interface between two immiscible viscous fluids a novel ‘‘refraction law’’ for dividing streamlines has been derived.

ISSN:0031-9171    

DOI:10.1063/1.866451

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Energy spectrum equations for homogeneous axisymmetric turbulence are formulated using the eddy‐damped quasinormal Markovian (EDQNM) approximation. The equations, which consist of two spectrum functions of the two variablesk(the magnitude of the wavevectork) and &mgr; (the cosine of the angle betweenkand the direction of axisymmetry), are computed directly, without any reduction, under initial conditions for different degrees of anisotropy. In this paper, the results for cases of medium anisotropic and nearly two‐dimensional initial conditions are reported. A remarkable result was that in the nearly two‐dimensional case, some characteristic properties of two‐dimensional isotropic turbulence, such as inverse energy cascades, are observed. Also, particular attention is paid to the effects of pressure‐strain correlation and inertial energy transfer on the return of anisotropic turbulence to isotropy.

ISSN:0031-9171    

DOI:10.1063/1.866452

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Since Bird [Phys. Fluids6, 1518 (1963)] first proposed the idea of direct simulation Monte Carlo (DSMC) techniques in order to model rarefied gas flows, a concern has been that his method does not provide a solution to the Boltzmann equation. Several simulation schemes have now been developed and, in a review of these methods, Nanbu [J. Phys. Soc. Jpn.52, 3382 (1983)] showed that only his method [J. Phys. Soc. Jpn.49, 2042 (1980)] gave a true solution to the Boltzmann equation. However, Nanbu’s simulation method is also the most computationally expensive scheme and in his review paper he recommended the use of the Bird technique for complicated engineering problems. Nanbu’s method also suffers from the apparent disadvantage that momentum and energy are not conserved at each collision. With the advent of the supercomputer the relative expense of the methods will inevitably be of lesser importance so that the testing of the Nanbu method in an engineering context is desirable. A detailed study of the implementation and performance of the Bird and Nanbu simulation schemes has therefore been carried out with reference to the expansion of a gas into vacuum. The results reported herein show, however, that in addition to increased computational overheads, the Nanbu method suffers from further defects that make its implementation more difficult. It is concluded that the Nanbu method is generally less flexible than that of Bird and that greater care must be exercised if meaningful results are to be obtained using the Nanbu approach.

ISSN:0031-9171    

DOI:10.1063/1.866402

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

An approximate method for estimating the strength of the overtaking wave developed by Chisnell and the present author [J. Fluid Mech.120, 523 (1982)] is applied to the motion of a strong shock wave in a medium with exponentially varying density. The strength of the overtaking wave is calculated for various values of &ggr;, the ratio of specific heats. There is a significant improvement in the accuracy of the propagation parameter for most values of &ggr;.

ISSN:0031-9171    

DOI:10.1063/1.866403

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Linear waves superimposed on an arbitrary basic state in ideal magnetohydrodynamics (MHD) are studied by an asymptotic expansion valid for short wavelengths. It has not been necessary to introduce any assumption beyond the usual regularity assumptions on the arbitrarily given solution which represents the basic state in this paper; it may even be time dependent. The theory also allows for a gravitational potential; it may therefore be applied both in astrophysics and in problems related to thermonuclear fusion. The linearized equations for the perturbations of the basic state are found in the form of a symmetric hyperbolic system. This symmetric hyperbolic system is shown to possess characteristics of nonuniform multiplicity, which implies that waves of different types may interact. In particular, it is shown that mass, Alfve´n, and slow magnetoacoustic waves will persistently interact in the exceptional case where the local wavenumber vector is perpendicular to the magnetic field. The equations describing this interaction are found in the form of a weakly coupled hyperbolic system. This weakly coupled hyperbolic system is studied in a number of special cases and detailed analytic results are obtained for some such cases. The results show that the interaction of the waves may be one of the major causes of instability of the basic state. It seems beyond doubt that the interacting waves contain the physically relevant parts of the waves, which often are referred to as ballooning modes, including Suydam and Mercier modes.

ISSN:0031-9171    

DOI:10.1063/1.866404

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A simple graphic method of solving the Vlasov–Poisson system associated with nonlinear eigenvalue conditions for arbitrary potential structures is presented. A general analytic formulation for nonmonotonic double layers is presented and illustrated with some particular closed form solutions. This class of double layers satisfies the time stationary Vlasov–Poisson system while requiring a Sagdeev potential, which is a double‐valued function of the physical potential. It follows that any distribution function having a density representation as any integer or noninteger power series of potential can never satisfy the nonmonotonic double‐layer boundary conditions. A Korteweg–de Vries‐like equation is found showing a relationship among the speed of the nonmonotonic double layer, its scale length, and its degree of asymmetry.

ISSN:0031-9171    

DOI:10.1063/1.866405

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The relativistic equations of motion are analyzed for charged particles in a magnetized plasma and externally imposed electromagnetic fields (&ohgr;,k), which have wave vectorskthat are at arbitrary angles. The particle energy is obtained from a set of nonlinear differential equations, as a function of time, initial conditions, and cyclotron harmonic numbers. For a given cyclotron resonance, the energy oscillates in time within the limits of a potential well; stochastic acceleration occurs if the widths of different Hamiltonian potentials overlap. The net energy gain for a given harmonic increase with the angle of propagation, and decreases as the magnitude of the wave magnetic field increases. Potential applications of these results to the acceleration of ionsopheric electrons are presented.

ISSN:0031-9171    

DOI:10.1063/1.866406

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Based on a hydrodynamic Maxwell formalism of a weakly inhomogeneous magnetized plasma, a mode–mode coupling eikonal relation is derived. Finite wavelength and arbitrary polarization of a monochromatic driver pump have been taken into account as well as longitudinal and transverse components of the self‐consistent plasma electric field. A weak turbulence theory method is used to solve the resulting inhomogeneous Volterra‐type integral equation in tensorial form, i.e., an expansion of hydrodynamic quantities over the resultant electric field (driver pump and self‐consistent field) up to the third order. The eikonal coupling relation thus obtained is discussed for the case of longitudinal and transverse interactions.

ISSN:0031-9171    

DOI:10.1063/1.866407

出版商:AIP    

年代:1987

数据来源: AIP