Introduction

In the early decades of the 20th century Göttingen was the center for mathematics. The foundations were laid by Carl Friedrich Gauss (1777–1855) who from 1808 was head of the observatory and professor for astronomy at the Georg August University (founded in 1737). At the turn of the 20th century, the well-known mathematician Felix Klein (1849–1925), who joined the University in 1886, established a research center and brought leading scientists to Göttingen. In 1895 David Hilbert (1862–1943) became Chair of Mathematics and in 1902 Hermann Minkowski (1864–1909) joined the mathematics department. At that time, pure and applied mathematics pursued diverging paths, and mathematicians at Technical Universities were met with distrust from their engineering colleagues with regard to their ability to satisfy their practical needs (Hensel, 1989). Klein was particularly eager to demonstrate the power of mathematics in applied fields (Prandtl, 1926b; Manegold, 1970). In 1905 he established an Institute for Applied Mathematics and Mechanics in Göttingen by bringing the young Ludwig Prandtl (1875–1953) and the more senior Carl Runge (1856–1927), both from the nearby Hanover. A picture of Prandtl at his water tunnel around 1935 is shown in Figure 2.1.

Prandtl had studied mechanical engineering at the Technische Hochschule (TH, Technical University) in Munich in the late 1890s. In his studies he was deeply influenced by August Föppl (1854–1924), whose textbooks on technical mechanics became legendary.

To supplement the foregoing chapters, we offer below a table listing some key developments in turbulence research over the period covered by this book, i.e. roughly up to mid-1970s. Later developments involving massive computations, low-dimensional dynamics, the renormalization group, turbulence control, modern instrumentation, and so on, are not included; nor do we include such closely related areas as turbulent thermal convection, combustion, wave turbulence, or the vast field of applications in geophysics, astrophysics and plasma physics. Moreover, the table is ‘internal’ to the subject, in that we make no attempt to relate the events to developments in other scientific fields or to the wider historical context. Despite these limitations, it is our hope that the table, necessarily subjective to some extent, will provide a useful point of reference for the reader. We thank the authors of this book for their comments on the table, especially Professor R. Narasimha for the inspiration he provided.

Opening remarks

Taylor's reputation

The obituary of G.I. Taylor (7 March 1886–27 June 1975), written by Sir Brian Pippard1 in 1975, begins thus: “Sir Geoffrey Ingram Taylor, who died at the age of 89, was one of the great scientists of our time and perhaps the last representative of that school of thought that includes Kelvin, Maxwell and Rayleigh, who were physicists, applied mathematicians and engineers – the distinction is irrelevant because their skill knew no such boundaries. Between 1909 and 1973 he published voluminously, and in a lifetime devoted to research left his mark on every subject he touched and on every one of his colleagues … his outgoing manner and complete lack of pomposity conveyed, as no formal exposition could have done, the enthusiasm and intuitive understanding that informed all his work.” These words, taken together with Pippard's closing sentence, “To his many friends he was an inspiration, at once a profound thinker and, it seemed, a truly happy man”, summarize the essential G.I. Taylor. Goldstein (1969) had this to say: “By the end of the first half-century there was a stronger and more widespread element of physics in thought and research on fluid mechanics than in the first twenty or thirty years, and this is much more so now. Several factors and several research workers contributed to this, but the greatest influence has been the example of G.I. Taylor.”

Introduction

Satish Dhawan was born on 25 September 1920 in Srinagar, Kashmir, the home town of his mother Lakshmi. His father, Devidayal, was from the North Western Frontier Province; both parents came from professional families, full of doctors, lawyers and academics – Devidayal retired as a respected judge of the High Court in Lahore, now in Pakistan. Satish's education began under private tutors at home, as his father kept getting transferred in his early career from one town to another in the North West (Kipling country to Indo-British readers). He completed his Indian education at the University of Punjab in Lahore with an unusual combination of degrees: BA in physics and mathematics (1938), MA in English literature (1941) and BE (Hons.) in mechanical engineering (1945). In 1946 he sailed to the USA on a government scholarship, and obtained an MS in aeronautical engineering from the University of Minnesota the following year. (The summer of 1947 saw much turmoil in the subcontinent preceding its imminent partition, and Satish's parents reluctantly left Lahore for India – never to return – a week before the formal end of colonial rule.) In the USA Satish moved to the California Institute of Technology where, with Hans W. Liepmann as his adviser, he obtained the degree of Aeronautical Engineer in 1949 and a PhD in aeronautics and mathematics in 1951. Dhawan made a strong impression, scientifically and otherwise, on everybody he came in contact with at Caltech.