Study Of Abrupt Transitions in Two-Dimensional Flows

Swirling and stratified flows demonstrate a complex§behaviour with rich spectrum of possible regimes and§sudden changes in the pattern of flow. It is known§that these flows may become sensitive to small§perturbation in boundary conditions and form an§internal jump-like transition from one flow pattern§to a different one a hydraulic jump in stratified§and a vortex breakdown in swirling flows. Analysis of§the motion equations for such flows reveals§singularly perturbed nature of the problem; this§explains the abruptness and sensitivity of§transitions. The book reviews the model flows,§develops a theoretical framework for handling the§singularity at the point of transition, and provide a§procedure for finding the transition point. A§generalisation of the Tikhonov s boundary function§method is developed to study the problem. This§approach is illustrated by calculating of parameters§of an internal hydraulic jump for a model stratified§fluid flow. The book is aimed for graduate students§and professionals in fluid mechanics and applied§mathematics.