摘要:

This paper addresses the question of implications of the effects of fluid compressibility on the equations governing unsteady flows of power law fluids through a porous medium. A generalized Burgers equation is shown to arise in the flow description. Some self‐similar flows of practical interest are presented and discussed, from which the nonlinear effects associated with fluid compressibility are analyzed with regard to a better interpretation of transient pressure response in a well of non‐Newtonian displacing fluid te

ISSN:0022-2526    

DOI:10.1002/sapm19908211

年代:1990

数据来源: WILEY

摘要:

It is well known that the addition of surface‐tension effects to the classic Stokes model for water waves results in a countable infinity of values of the surface tension coefficient at which two traveling waves of differing wavelength travel at the same speed. In this paper the third‐harmonic resonance (interaction of a one‐crested wave with a three‐crested wave) with O(2) spatial symmetry is considered. Nayfeh analyzed the third‐harmonic resonance for traveling waves and found two classes of solutions. It is shown that there are in fact six classes of periodic solutions when the O(2) symmetry is acknowledged. The additional solutions are standing waves, mixed waves and secondary branches of “Z‐waves.” The normal form and symmetry group for each of the solution classes are developed, and the coefficients in the normal form are formally computed using a perturbation method. The physical aspects of the most unusual class of waves (three‐mode mixed waves) are illustrated by plotting the wave height as a function ofxfor di

ISSN:0022-2526    

DOI:10.1002/sapm199082113

年代:1990

数据来源: WILEY

摘要:

This paper presents analytical and numerical solutions of a new amplitude equation governing long waves on thin films. At lowest order in the long‐wave parameter, the equation is nondispersive and represents a balance between nonlinearity and cross‐stream diffusion. Numerical solutions tracing the temporal evolution of an initially localized disturbance indicate that the aforementioned diffusion partly mitigates the tendency of the wave to break. We have also obtained a closed‐form solution resembling an undular bore propagating in an oblique dire

ISSN:0022-2526    

DOI:10.1002/sapm199082137

年代:1990

数据来源: WILEY

摘要:

The centrifugal batch separation of an initially homogeneous mixture of particles and fluid is considered in containers of finite length for which end‐wall effects can be important. The “full” nonlinear theory can be reduced to the determination of an appropriate analytic function. Vortex‐line stretching due to suction into the Ekman layers counteracts the baroclinic generation of vorticity caused by the pressure and density

ISSN:0022-2526    

DOI:10.1002/sapm199082149

年代:1990

数据来源: WILEY

摘要:

A hyper‐rook domain of an elementxin the space (words of lengthnover alphabets withkelements) is a sphere with centerxand fixed radiusjin Hamming distance. The numberjdetermines the dimension of the hyper‐rook domain. The classical (and far from solved) problem of covering by rook domains (here considered as the 1‐dimensional case) is the problem of finding minimal coverings of by such spheres. Very few results are known in the literature for dimensions ≥ 2. We prove in this paper certain classes of inequalities based on coverings using matrices, which give upper and lower bounds for several cases of the problem for higher dim

ISSN:0022-2526    

DOI:10.1002/sapm199082159

年代:1990

数据来源: WILEY

摘要:

The present paper is concerned with the stationary needle crystal growth with arbitrary undercooling. We discuss two classes of asymptotic solutions: (1) the regular‐tip solutions; (2) the smooth‐root solutions. When the surface tension is nonzero, the regular‐tip solutions may not have smooth roots. Among the regular‐tip solutions, however, one can identify a “principal regular‐tip solution,” which has the best behavior in the far field and is physical

ISSN:0022-2526    

DOI:10.1002/sapm199082177

年代:1990

数据来源: WILEY