ISSN:0025-5793    

DOI:10.1112/S0025579300009724

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300009736

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300009748

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S002557930000975X

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

摘要:

SummaryThe temporal and spatial linear instability of Poiseuille flow through pipes of arbitrary cross‐section is discussed for large Reynolds numbers (R). For a pipe whose aspect ratio is finite, neutral stability (lower branch) is found to be governed by disturbance modes of large axial wavelength (of orderhR, wherehis a characteristic cross‐sectional dimension). By contrast, spatial instability for finite aspect ratios is governed by length scales betweenO(h) and O(hR). When the aspect ratio is increased toO(R1/7), however, these two characteristic length scales both becomeO(R1/7h) and a match with plane channel flow instability is achieved. Thus the general cross‐section produces temporal and spatial instability if the aspect ratio isO(R1/7). Further, in the flow in a rectangular pipe neutral stability (lower branch) exists for some finite aspect ratios, while for the flow in any non‐circular elliptical pipe spatial instability is possible. It is suggested that both temporal and spatial instability occur for a wide range of pipe cross‐sections of finite aspect ratio. Part 2 (Smith 1979a), which studies the upper branch neutral stability, confirms the importance of theO(hR) scale modes in neutral stability for finite aspect ratios.

ISSN:0025-5793    

DOI:10.1112/S0025579300009761

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

摘要:

SummaryA study complementary to Part 1 (Smith 1979) is made of the linear stability characteristics, at high Reynolds number (R), of Poiseuille How through tubes with closed cross‐sections. The first significant deviation of the upper branch of the neutral stability curve (Part 1 having described the lower bilanch) from that of plane Poiseuille flow arises when the aspect ratio is decreased from infinity toO(R1/11). The axial wavenumber α on the upper branch is thenO(R‐1/11). A further decrease of the aspect ratio, to a finite value, forces this α to fall sharply toO(R‐1). A similar phenomenon occurs for the lower branch (Part 1). Thus the two branches are likely to meet only when the aspect ratio becomes finite, with the neutrally stable disturbances then having very large axial length scales.

ISSN:0025-5793    

DOI:10.1112/S0025579300009773

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

摘要:

AbstractA higher‐order, double boundary‐layer theory is employed to investigate the mass transport velocity due to two‐dimensional standing waves in a system consisting of two semi‐infinite, homogeneous fluids of different densities and viscosities. For moderately large wave amplitudes, the leading correction to the tangential mass transport velocity near the interface is extremely significant and may typically contribute about 20% of the total velocity.

ISSN:0025-5793    

DOI:10.1112/S0025579300009785

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300009797

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300009803

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300009815

出版商:London Mathematical Society    

年代:1979

数据来源: WILEY