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.

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