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Bifurcations in Flow Patterns - Some Applications of the Qualitative Theory of Differential Equations in Fluid Dynamics (Hardcover, 1991 ed.)
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Bifurcations in Flow Patterns - Some Applications of the Qualitative Theory of Differential Equations in Fluid Dynamics (Hardcover, 1991 ed.)
Series: Nonlinear Topics in the Mathematical Sciences, 2
Expected to ship within 12 - 17 working days
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The main idea of the present study is to demonstrate that the
qualitative theory of diffe rential equations, when applied to
problems in fluid-and gasdynamics, will contribute to the
understanding of qualitative aspects of fluid flows, in particular
those concerned with geometrical properties of flow fields such as
shape and stability of its streamline patterns. It is obvious that
insight into the qualitative structure of flow fields is of great
importance and appears as an ultimate aim of flow research.
Qualitative insight fashions our know ledge and serves as a good
guide for further quantitative investigations. Moreover, quali
tative information can become very useful, especially when it is
applied in close corres pondence with numerical methods, in order
to interpret and value numerical results. A qualitative analysis
may be crucial for the investigation of the flow in the
neighbourhood of singularities where a numerical method is not
reliable anymore due to discretisation er rors being unacceptable.
Up till now, familiar research methods -frequently based on
rigorous analyses, careful nu merical procedures and sophisticated
experimental techniques -have increased considera bly our
qualitative knowledge of flows, albeit that the information is
often obtained indirectly by a process of a careful but cumbersome
examination of quantitative data. In the past decade, new methods
are under development that yield the qualitative infor mation more
directly. These methods, make use of the knowledge available in the
qualitative theory of differen tial equations and in the theory of
bifurcations."
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