On internal fluid dynamics

Motivated by a range of applications (biomedical, industrial, engineering, environmental) this contribution is focussed on a mathematical study of (a) constriction/distortion and (b) branching in a vessel or network of vessels containing fluid flow. The central interest addressed is in medium-to-high Reynolds numbers where asymptotic approaches and matching yield much insight. The main reasoning, order arguments and scaling factors within various parts of the vessels are presented. Theory and corresponding analysis are described for aspect (a) in symmetric and nonsymmetric cases and aspect (b) over short or long length scales with or without viscous–inviscid interactions, where attention is given to side-branching, large networks, viscous wall layers, flow reversal, eddies and upstream influence. Three-dimensional effects for (a) and (b) are also investigated. A final discussion includes suggestions of future project topics.