By Milton Van Dyke
Over four hundred appealing black-and-white images, gathered from world wide, illustrate the good range of fluid movement. Flows starting from creeping to hypersonic speeds, in either the laboratory and Nature, are saw at once, or made seen utilizing smoke, ink, bubbles, debris, shadographs, schlieren, interferometry, and different concepts. Succinct captions describe the fundamental gains of every movement.
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Extra info for Album of Fluid Motion
This notation is commonly called the Gibbs dyadic notation (Malvern 1969). The inner product of two vectors v and u is u v = v u = mvi. 3) 14 1. Background and overview Likewise, the inner product from the left (right) of vector v with the tensor T is v - T = v&jej (T-v = eiTijVj). Inner products involving tensors of second- or higher order are not commutative unless the tensors possess certain symmetry properties. 5) 0 otherwise. ', . , tor i ^ j . (1-2-6) Thus, for any vector v, v = I • v or Vi = SijVj.
Consider a function w(x,t) defined for t > 0 and —oo < x < oo. 7) where s is the transform parameter. Suppose that w(x, t) is integrable over any finite interval of t and \w(x, t)\ = O (ea+t) as t —• oo, where a+ is a real constant. 7) converges for Re(s) > a+ and it defines some function of s in that half plane. Furthermore, the integral can be differentiated with respect to s, and the derivative converges for Re(s) > a+. Thus, w(x,s) is an analytic function of the complex variable s in Re(s) > a+ forfixedx.
Other topical areas that are not yet fully developed are identified in the overview to follow or in the later chapters. 4-1 Basic elastodynamic solutions for a stationary crack In Chapter 2, the fundamental stationary crack problems of linear elastodynamics are analyzed. The two-dimensional configuration of a semi-infinite crack in an otherwise unbounded body is considered. The body is initially stress free and at rest. At time t = 0, equal and opposite spatially uniform tractions begin to act on the crack faces.