ISSN:0025-5793    

DOI:10.1112/S0025579300012882

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

摘要:

AbstractGörtler vortices are thought to be the cause of transition in many fluid flows of practical importance. In this paper a review of the different stages of vortex growth is given. In the linear regime nonparallel effects completely govern this growth and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Gortler vortices are given; in particular vortices induced by free‐stream perturbations impinging on the leading edge of the wall are considered. It is found that the most dangerous mode of this type can be isolated and its neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices ofO(l) wavelengths are given and compared with experimental observations. The agreement between theory and experiment is shown to be excellent up to the point where unsteady effects become important. For small wavelength vortices the nonlinear regime is of particular interest since a strongly nonlinear theory can be developed there. Here the vortices can be large enough to drive the mean state which then adjusts itself to make all modes neutral. The breakdown of this nonlinear state into a three‐dimensional time dependent flow is also discussed.

ISSN:0025-5793    

DOI:10.1112/S0025579300012894

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012900

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012912

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012924

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012936

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012948

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

摘要:

AbstractLetAn(a, b)={(xi) ∈ Rn:∑i=1n−1xi2⩽a2,|xn|⩽b}.It is proved that for suitableaandb,n≥7, one can haveVn(An) =Vn(Bn) andVn−1(H∩An)

ISSN:0025-5793    

DOI:10.1112/S002557930001295X

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012961

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012973

出版商:London Mathematical Society    

年代:1990

数据来源: WILEY