Study Of Abrupt Transitions in Two-Dimensional Flows
A Singular Perturbation Approach
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Swirling and stratified flows demonstrate a complexbehaviour with rich spectrum of possible regimes andsudden changes in the pattern of flow. It is knownthat these flows may become sensitive to smallperturbation in boundary conditions and form aninternal jump-like transition from one flow patternto a different one a hydraulic jump in stratifiedand a vortex breakdown in swirling flows. Analysis ofthe motion equations for such flows revealssingularly perturbed nature of the problem; thisexplains the abruptness and sensitivity oftransitions. The book reviews the model flows,develops a theoretical...
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.
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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