Fluid Dynamics
Part 2: Asymptotic Problems of Fluid Dynamics
The book is the second part in a series which describes fluid dynamics. The book introduces asymptotic methods, and their applications to fluid dynamics. It first discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The book then considers supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. It also discusses the second-order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are discussed in detail. The book concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered: the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stoke’s paradox. The book shows that this paradox can be resolved using the formalism of matched asymptotic expansions.
Part 2: Asymptotic Problems of Fluid Dynamics
The book is the second part in a series which describes fluid dynamics. The book introduces asymptotic methods, and their applications to fluid dynamics. It first discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The book then considers supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. It also discusses the second-order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are discussed in detail. The book concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered: the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stoke’s paradox. The book shows that this paradox can be resolved using the formalism of matched asymptotic expansions.
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