摘要:

SummaryExperiments indicate the importance of three‐dimensional action during transition, while high‐Reynolds‐number‐flow theory indicates a multi‐structured type of analysis. In line with this, the three‐dimensional nonlinear unsteady triple‐deck problem is addressed here, for slower transition. High‐amplitude/high‐frequency properties show enhanced disturbance growth occurring downstream for single nonlinear oblique waves inclined at angles greater than tan−1√2 (≈54.7°) to the free stream, in certain interesting special cases. The three‐dimensional response there is very ‘spiky’ and possibly random, with sideband instabilities present. A second nonlinear stage, and then an Euler stage, are entered further downstream, although faster transition can go straight into these more nonlinear stages. More general cases are also considered. Sideband effects, sublayer bursting and secondary instabilities are discussed, along with the relation to experimental observations.

ISSN:0025-5793    

DOI:10.1112/S0025579300007178

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

摘要:

AbstractThe nonlinear interaction equations describing vortex‐Rayleigh wave interactions in highly curved boundary layers are derived. These equations describe a strongly nonlinear interaction between an inviscid wave system and a streamwise vortex. The coupling between the two structures is quite different from that found by Hall and Smith [13] in the absence of wall curvature. Here the vortex is forced over a finite region of the flow rather than in the critical layer associated with the wave system. When the interaction takes place the wave system remains locally neutral as it moves downstream and its self interaction drives a vortex field of the same magnitude as that driven by the wall curvature. This modification of the mean state then alters the wave properties and forces the wave amplitude to adjust itself in order that the wave frequency is constant. Solutions of the interaction equations are found for the initial stages of the interaction in the case when the wave amplitude is initially small. Our analysis suggests that finite amplitude disturbances can only exist when the vortex field is nonzero at the initial position where the interaction is stimulated.

ISSN:0025-5793    

DOI:10.1112/S002557930000718X

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

摘要:

AbstractDimension prints were developed in 1988 to distinguish between different fractal sets in Euclidean spaces having the same Hausdorff dimension but with very different geometric characteristics. In this paper we compute the dimension prints of some fractal sets, including generalized Cantor sets on the unit circleS1in ℝ2and the graphs of generalized Lebesgue functions, also in ℝ2. In this second case we show that the dimension print for the graphs of the Lebesgue functions can approach the maximal dimension print of a set of dimension 1. We study the dimension prints of Cartesian products of linear Borel sets and obtain the exact dimension print when each linear set has positive measure in its dimension and the dimension of the Cartesian product is the sum of the dimensions of the factors.

ISSN:0025-5793    

DOI:10.1112/S0025579300007191

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300007208

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S002557930000721X

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300007221

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300007233

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

摘要:

AbstractKreck and Stolz recently exhibited exotic structures on a family of seven dimensional homogeneous spaces which are quotients of the compact Lie groupSU3. We observe that there is an invariant obtainedviathe Pontrjagin–Thorn construction which detects these exotic structures in many cases.

ISSN:0025-5793    

DOI:10.1112/S0025579300007245

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove a result related to the Erdős‐Ginzburg‐Ziv theorem: Letpandqbe primes, α a positive integer, andm∈{pα,pαq}. Then for any sequence of integersc= {c1, c2,…, cn} there are at least(⌊12n⌋m)+(⌈12n⌉m)subsequences of lengthm, whose terms add up to 0 modulom(Theorem 8). We also show why it is unlikely that the result is true for anymnot of the formpαorpαq(Theorem 9).

ISSN:0025-5793    

DOI:10.1112/S0025579300007257

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY

摘要:

AbstractFor any fixed positive real number ε, any integerb≥2 and anydε{0, 1,…, b−1}, the set of Borel's simply normal numbers to basebin [0, 1] is partitioned into a countable number of sets in eight different ways according to the largest place and the number of places at which the proportiond's to that place in theb‐adic expansion of such a number exceeds or is not less thanb−1– ε, or is less than or does not exceedb−1– ε. For selected values ε, the Lebesgue measures of the sets in these decompositions are given explicitly.

ISSN:0025-5793    

DOI:10.1112/S0025579300007269

出版商:London Mathematical Society    

年代:1994

数据来源: WILEY