Aerodynamics: Theories of fluid dynamics.
(Aérodynamique: Théories de la dynamique des fluides.)

*(French)*Zbl 0744.76008
Collection La Chevêche. Toulouse: Cepadues-Editions. 544 p. (1989).

This is a treatise on fluid dynamics, written from the aeronautical engineer’s point of view and intended for use as a reference book by advanced students, engineers, and researchers. The emphasis is on the derivation and manipulation of the equations of motion for various types of large and infinite Reynolds number flows around obstacles.

In the first chapter, the general partial differential equations of motion are presented, the elements of dimensional analysis are outlined, flows are classified by Mach and Reynolds numbers, and perfect (inviscid) fluids are introduced together with the thermodynamical background. The second chapter discusses stationary flows of inviscid incompressible fluids in more detail, plane flows are studied with complex variables methods, and three-dimensional stationary flows are treated with special emphasis on flows near wing tips and around slender bodies. Chapter three deals with inviscid compressible fluids, starting with a discussion of isentropic flows, moving on to a brief treatment of shock waves, and studying transonic two-dimensional flows in greater detail by the method of characteristics, the hodograph transform, and by linearizing the equation for the velocity potential in different regimes. A short fourth chapter studies instationary compressible inviscid flows. In chapter five, stationary viscous flows are treated, the main emphasis being on a discussion of the boundary layer, followed by a short section on Stokes flow around spheres and cylinders. Several appendices list formulae from vector calculus and give the (compressible) Navier Stokes equations in various coordinate systems. The bibliography lists ten titles, all monographies on engineering mathematics, theoretical mechanics, or aerodynamics.

The book is organized well and has a useful index. The mathematical techniques that are employed in this book include only classical tools such as conformal mappings, the method of characteristics, and elements of classical potential theory. Readers will look in vain for more modern concepts such as weak solutions or function spaces and will find only passing references to numerical methods. On the other hand, most of the approximations, representations, expansions, etc. that have been developed in the engineering literature in this area are presented in this book.

In the first chapter, the general partial differential equations of motion are presented, the elements of dimensional analysis are outlined, flows are classified by Mach and Reynolds numbers, and perfect (inviscid) fluids are introduced together with the thermodynamical background. The second chapter discusses stationary flows of inviscid incompressible fluids in more detail, plane flows are studied with complex variables methods, and three-dimensional stationary flows are treated with special emphasis on flows near wing tips and around slender bodies. Chapter three deals with inviscid compressible fluids, starting with a discussion of isentropic flows, moving on to a brief treatment of shock waves, and studying transonic two-dimensional flows in greater detail by the method of characteristics, the hodograph transform, and by linearizing the equation for the velocity potential in different regimes. A short fourth chapter studies instationary compressible inviscid flows. In chapter five, stationary viscous flows are treated, the main emphasis being on a discussion of the boundary layer, followed by a short section on Stokes flow around spheres and cylinders. Several appendices list formulae from vector calculus and give the (compressible) Navier Stokes equations in various coordinate systems. The bibliography lists ten titles, all monographies on engineering mathematics, theoretical mechanics, or aerodynamics.

The book is organized well and has a useful index. The mathematical techniques that are employed in this book include only classical tools such as conformal mappings, the method of characteristics, and elements of classical potential theory. Readers will look in vain for more modern concepts such as weak solutions or function spaces and will find only passing references to numerical methods. On the other hand, most of the approximations, representations, expansions, etc. that have been developed in the engineering literature in this area are presented in this book.

Reviewer: H.Engler (Bonn)

##### MSC:

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

76Bxx | Incompressible inviscid fluids |

76B47 | Vortex flows for incompressible inviscid fluids |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

76L05 | Shock waves and blast waves in fluid mechanics |