On the intense sensitivity to wall convergence of instability in a channel

• Published in: Physics of fluids (1994) Vol. 36; no. 10
• Main Authors: Kumar, Anup, Govindarajan, Rama
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.10.2024
• Subjects: Convergence; Flow stability; Fluid dynamics; Fluid flow; Laminar flow; Pipe flow; Reynolds number; Velocity distribution
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0227042

The classical Jeffery–Hamel flow at small wall convergence has received less attention than it should and is the subject here. While laminar flow through a plane channel displays only a parabolic velocity profile, for even small convergence angles, the Jeffery–Hamel equations display a variety of non-unique laminar flow solutions at a given Reynolds number. Three such solutions are shown to be stable at low Reynolds number and could possibly be attained in the experiment. Multiple critical layers can occur, and dissipation need not attain a maximum at the wall. In the one-lobed velocity profile, the critical Reynolds number for the first instability is known [K. Fujimura, J. Phys. Soc. Jpn. 51, 2000–2009 (1982); M. R. Jotkar and R. Govindarajan, Phys. Fluids 29, 064107 (2017)] to be an extremely sensitive function of the wall tilt angle, and we show that this is because the dominant balance in the critical layer is different from the traditional one in a plane channel. Finally, a direct analogy to divergent pipe flow is drawn.