摘要:

A novel technique is presented for estimating the various transport quantities in two‐phase materials of random structure by extending, in an approximate manner, the effective continuum description of such systems. The method is then applied to three representative examples and is found to give results in excellent agreement with those obtained from exact calculations.

ISSN:0031-9171    

DOI:10.1063/1.866018

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The baroclinic quasigeostrophic equations describe the essential dynamics of large‐scale, low‐frequency atmospheric ocean flow. A nonlinear stability theorem is given based on a convexity argument of Arnold [Am. Math. Soc. Transl.19, 267 (1969)], complementing a linear analysis by Blumen [J. Atmos. Sci.25, 929 (1968)]. Anaprioriestimate bounding the growth of perturbation is derived.

ISSN:0031-9171    

DOI:10.1063/1.865953

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A Hamiltonian formulation using a noncanonical Poisson bracket is presented for the nonlinear dynamics of baroclinic quasigeostrophic fluid flow. Nonlinear integral invariants for the system are found to be in the kernel of the noncanonical Poisson bracket. A novel feature of this formulation is that dynamical boundary conditions are generated from the constrained energy Hamiltonian, via the noncanonical Poisson bracket.

ISSN:0031-9171    

DOI:10.1063/1.865956

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

At high altitudes, the condition in the shock layer near the stagnation point deviates significantly from thermal equilibrium. This condition is comparable to that in a relatively strong shock wave. The shock layer is, therefore, a Knudsen layer. Together with the strong shock wave preceding the shock layer, the hypersonic flow problem near a stagnation point is that of a triple Knudsen layer.

ISSN:0031-9171    

DOI:10.1063/1.865958

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The thermal equilibrium correlation properties of a magnetically confined pure electron plasma (McPEP) are related to those of a one‐component plasma (OCP). TheN‐particle spatial distribution &rgr;sand the Helmholtz free energyFare evaluated for the McPEP toO(&lgr;2d/a2), where &lgr;dis the thermal de Broglie wavelength andais an interparticle spacing. The electron gyromotion is allowed to be fully quantized while the guiding center motion is quasiclassical. The distribution &rgr;sis shown to be identical to that of a classical OCP with a slightly modified potential. ToO(&lgr;2d/a2) this modification does not affect that part ofFwhich caused by correlations, as long as certain requirements concerning the size of the plasma are met. This theory is motivated by a current series of experiments that involve the cooling of a magnetically confined pure electron plasma to the cryogenic temperature range.

ISSN:0031-9171    

DOI:10.1063/1.865987

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The Stokes flow of a Newtonian fluid is calculated inside a porous medium that is spatially periodic, the unit cell being a fractal named a Sierpinski carpet. Complete results are given for the longitudinal permeability. A scaling argument and complete numerical calculations provide two exponents of the power law that differ by only 2% when the construction stage is large; in this limit, the scaling argument provides the same result as the classical Carman equation. The agreement between these two results may be fortuitous and thus has to be considered with caution. Various comments and extensions to three‐dimensional media such as the Menger sponge are also presented.

ISSN:0031-9171    

DOI:10.1063/1.865971

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Unique wavenumbers are calculated for axisymmetric Rayleigh–Be´nard convection as a function of the Rayleigh number (R) up to the second critical value for several different Prandtl numbers. The analysis assumes slightly bent rolls (large radius of curvature) and that there exists a horizontal pressure gradient strong enough to force the net mean flow induced by curvature to be zero. The assumptions are satisfied for axisymmetric convection in a large aspect ratio cylinder (however, this may not be the only case). Manneville and Piquemal [Phys. Rev. A28, 1774 (1983)] found the initial slope of the selected wavenumber with respect to Rayleigh number (using an analytic solution valid for small amplitude solutions) and our calculations agree with theirs. This initial slope is sensitive to the Prandtl number (P), but at moderate to largeRthe selected wavenumber is approximately independent ofPwhenP>3. For smallerPlarger wavenumbers are found, but this does not contradict any available experimental evidence.

ISSN:0031-9171    

DOI:10.1063/1.865980

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The head‐on collision between two modified Korteweg–de Vries (MKdV) solitary waves is investigated where cubic and quadratic nonlinearities balance dispersion. These waves propagate at the interface of an inviscid two‐fluid system where the ratio of the fluids densities is comparable to the square of the ratio of depths. The third‐order perturbation solution is obtained and it is found that the collision is inelastic because of a dispersive wave train generated behind each emergent solitary wave.

ISSN:0031-9171    

DOI:10.1063/1.865944

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The transport equations for the Reynolds stresses are closed by modeling the turbulence and mean‐strain parts of the pressure‐strain‐rate correlation. The model constants are determined from simple relationships deduced from measurements in rectilinear and longitudinally curved shear flows. It is found that the effects of complex strain fields are more correctly predicted when the influence of the mean‐strain part is reduced from levels indicated by rapid distortion theory, and the turbulence part is adjusted to conform approximately with the measured rates of return to isotropy. The case of the swirling jet is used to illustrate the improved performance of the model.

ISSN:0031-9171    

DOI:10.1063/1.865951

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Lyapunov stability of relativistic ideal fluid and plasma equilibria is studied analytically using the energy‐Casimir method. Two‐ and three‐dimensional relativistic equilibria in a fixed bounded domain are investigated within the framework of the macroscopic multifluid plasma model. Linearized Lyapunov stability conditions and stability norms are given, accounting for warm‐plasma effects as well as relativistic and electromagnetic effects. The resulting Lyapunov stability conditions are compared to spectral stability analyses for relativistic cold plasmas in various examples and special cases, including (1) non‐neutral electron flow in a planar diode and (2) circularly symmetric plasma flow enclosed in a coaxial waveguide. These linearized stability results can be extended readily to nonlinear Lyapunov stability conditions for finite‐amplitude perturbations by employing standard convexity arguments for the Lyapunov functions given here. The relativistic stability conditions are shown to reduce either to their nonrelativistic counterparts or to trivial identities in the nonrelativistic limit.

ISSN:0031-9171    

DOI:10.1063/1.865952

出版商:AIP    

年代:1986

数据来源: AIP