摘要:

Waves in parallel shear flows are found to have different characteristics depending on whether nonlinear or viscous effects dominate near the critical layer. In this paper a nonlinear theory is developed which gives rise to a class of disturbances not found in the classical viscous theory. It is suggested that the modes found from such an analysis may be of importance in the breakdown of laminar flow due to free stream disturbances.

ISSN:0022-2526    

DOI:10.1002/sapm1969483181

年代:1969

数据来源: WILEY

摘要:

By expanding the displacement and stress components together with the axial length scale in terms of a small thin shell parameter, three asymptotic shell theories are obtained which incorporate thickness effects in a systematic way. The expansions are made in the equations of linear three‐dimensional elasticity. These theories are used to examine the problem of longitudinal wave propagation in a shell of infinite lengt

ISSN:0022-2526    

DOI:10.1002/sapm1969483205

年代:1969

数据来源: WILEY

摘要:

The stability of certain steady flows in a rotating system with rigid bottom and free top surfaces is investigated. The simplest flow states having the essential spatial variations of steady responses of a rotating fluid system to differential heating in the horizontal are studied, that is, those with a constant gradient temperature distribution with both horizontal and vertical components, and the accompanying Coriolis‐balanced constant velocity shear (thermal wind). Ekman boundary layers and intermediate boundary layers are encountered in a systematic asymptotic analysis in two small parameters, the Ekman number and an inverse Richardson number. The resulting neutral stability curves indicate the possibility of instabilities above the inviscid stability criterion due to Eady, for some mean flow configurations. The estimate of the critical Taylor number is numerically close to the values obtained in the most nearly applicable experiment

ISSN:0022-2526    

DOI:10.1002/sapm1969483227

年代:1969

数据来源: WILEY

摘要:

For a one dimensional lattice model with long range exponential interaction the problem of deriving the thermodynamic properties of the system reduces to the problem of determining the spectrum of a differential equation for a one dimensional anharmonic oscillator with potentialαx2+ βγx4whereγis the inverse of the range of the interaction andαis a function of temperature which is positive at high temperatures and negative at low temperatures. It is proved that at low temperatures,α<0, and in the limitγ→ 0, (corresponding to an infinitely long range interaction) the spectrum becomes asymptotically degenerate. The relation of degeneracy to the occurrence of a phase transition is discussed and the generalization to higher dimensions is mentioned

ISSN:0022-2526    

DOI:10.1002/sapm1969483257

年代:1969

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1969483265

年代:1969

数据来源: WILEY

摘要:

The maximum numberN(n) of scalar functions of wavevector needed to represent the general cumulant of ordernof isotropic turbulence is determined. In addition to reproducing the known results thatN(2) = 1,N(3) = 2, it is shown thatN(4) = 4,N(5) = 4,N(6) = 9, etc.

ISSN:0022-2526    

DOI:10.1002/sapm1969483275

年代:1969

数据来源: WILEY

摘要:

It is proved thatλ2≤ (1 + 4/N)λ1whereλ1≤λ2≤ ··· are the eigenvalues of theN‐dimensional Laplace operator in a domainDwith vanishing boundary conditions. This extends theN= 2 case of Payne, Pólya and Weinberger and the result is independent

ISSN:0022-2526    

DOI:10.1002/sapm1969483281

年代:1969

数据来源: WILEY