摘要:

An equation which expresses the behavior of the frequency spectrum for capillary waves occurring in horizontal gas–liquid flows is derived using a dynamic energy balance. This balance assumes that the energy source for these waves is nonlinear interactions between the dominant gravity–capillary waves and that, in the same manner as for single waves, the dissipation of energy is caused by viscosity. Experimental measurements for both water and a water–glycerin solution with a viscosity of 2 cP in an air flow are described well by the theory over a frequency range of 40–100 Hz.

ISSN:0031-9171    

DOI:10.1063/1.865482

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The Grassberger–Procaccia dimension is determined from pressure and temperature measurements in a pool of water agitated by steam injection. For this complex flow system, three distinct values of dimension ranging from ∼4.2 to ∼8.0 (corresponding to three different measurement locations) are obtained.

ISSN:0031-9171    

DOI:10.1063/1.865483

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A definition is given of corrugational stability for plane‐fronted shock waves. By using the theory of singular surfaces it is shown how one can obtain necessary conditions for corrugation stability. The theory is then applied to relativistic shock waves and yields a restriction on the state equation of a relativistic fluid in order for it to allow the existence of corrugationally stable shocks.

ISSN:0031-9171    

DOI:10.1063/1.865484

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A weakly nonlinear theory of Kelvin–Helmholtz instability for magnetic fluids is presented. The method used is that of multiple scales. The equations governing the evolution of the amplitude are derived when the differenceUbetween the velocities of the two fluids is less than or equal to the critical velocityUc. It is shown that for subcriticial values ofUthe wave train of constant amplitude is unstable against modulations whereas for the supercritical values the instability is governed by a nonlinear Klein–Gordon equation. From the latter equation, the various stability criteria are obtained.

ISSN:0031-9171    

DOI:10.1063/1.865485

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Simulations of nonlinear instability in a one‐dimensional Vlasov plasma with a relative electron‐ion drift velocity have been extended to parameter ranges more extensive than previously reported [Phys. Fluids28, 155 (1985)]. Linearly stable runs, withTe/Ti=1,mi/me=100, and a system length ofL=512&lgr;Dshow nonlinear hole instability. As in the case ofmi/me=4, andL=32&lgr;D, the hole depth, double‐layer potential structure, acceleration, and growth rate agree well with a theory of hole growth that results from momentum exchange from reflected particles. For a linearly unstable plasma (Te/Ti≫1), the fluctuations and their time evolution are related to the linearly stable case, but are somewhat more complex. A spatially intermittent distribution of ‘‘wavelike fluctuations’’ grows to large amplitude and then evolve into trapped ion phase‐space hole structures. The hole potentials are of ordere&fgr;/Te=1, as in the linearly stable (Te/Ti=1) runs, but becauseTe/Ti≫1, are of large amplitude (e&fgr;/Ti≫1) relative to the ions. The hole structure and dynamics agree well with the large‐amplitude extension of the smalle&fgr;/Tihole theory.

ISSN:0031-9171    

DOI:10.1063/1.865486

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The saturation mechanism for density and potential fluctuation spectra that evolve from linearly unstable electrostatic resistive interchange modes are investigated using particle simulations. Detailed comparisons of the nonlinear evolution, saturation levels, and resultant spectra between two‐ and three‐dimensional sheared magnetic field configurations are made. Significant differences appear. The single rational surface, quasilinear‐dominated evolution, fluctuation spectrum is adequately described using a density convection model. For the multiple rational surface case, the potential fluctuations are adequately represented by a balance between the nonlinearly modified source (curvature drive) and linear sink (parallel resistive field line diffusion). An accurate description of the density spectrum requires a mode coupling theory based on the two‐point density correlation evolution equation.

ISSN:0031-9171    

DOI:10.1063/1.865487

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A renormalized reduced magnetohydrodynamics turbulence theory based upon the direct‐interaction approximation is presented. Importantly, the statistical equations derived conserve energy. The equations also properly contain the effects of magnetic shear. For stationary and homogeneous turbulence in a uniform mean magnetic field, the direct‐interaction approximation naturally separates into two parts: a coherent part that can be interpreted in terms of a frequency‐ and wavenumber‐dependent turbulent resistivity and viscosity, and an incoherent nonlinear mode coupling source term. In a two‐dimensional isotropic spectrum that is narrow in wavelength (the spread in wavenumber of the energy containing modes is small compared to the mean wavenumber), the plasma response at nearby wavelengths is characterized by a turbulent resistivity that depends only on the kinetic energy of the fluctuations, while the turbulent viscosity is negligible in comparison. At much shorter wavelengths the turbulent resistivity and viscosity are identical and both depend on the total energy in the fluctuations including the magnetic energy.

ISSN:0031-9171    

DOI:10.1063/1.865488

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The general procedure for the kinetic analysis of low‐frequency electrostatic and electromagnetic modes in toroidal geometry is now well known. In the collisionless limit the relevant dynamics (e.g., trapped particles, resonances, etc.) can be treated appropriately. However, with the introduction of collisional effects, it is customary for tractability to employ model collision operators that do not rigorously satisfy all conservation properties of more exact collision operators. Insight into the essential required features of such operators can be gained by studying models with increasing levels of completeness for a simpler, unsheared slab geometry. The results presented here for this simpler geometry can provide guidance in choosing model collision operators for toroidal‐geometry kinetic calculations.

ISSN:0031-9171    

DOI:10.1063/1.865489

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes and typical tokamak parameters, parallel dynamics predominantly determine the growth rate when &bgr; is within ∼20%–40% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the magnetohydrodynamic (MHD) value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in the region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases.

ISSN:0031-9171    

DOI:10.1063/1.865490

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Using the concept of an anisotropic plasma as a working hypothesis, a stress tensor has been constructed that is determined by five independent coefficients. As an application the general expression for the dispersion relation is derived. Under certain limiting conditions it was found that the plasma mode &ohgr;2&egr;=(4&pgr;&eegr;&egr;e2)/m&egr;decays exponentially because of thec33coefficient, with a decay time &tgr;33=2&rgr;0/c33k2.

ISSN:0031-9171    

DOI:10.1063/1.865491

出版商:AIP    

年代:1986

数据来源: AIP