Hans Albert Einstein: Innovation and Compromise in Formulating Sediment Transport by Rivers Robert Ettema1 and Cornelia F. Mutel2 Abstract: This paper is written to mark the hundredth anniversary of the birth of Hans Albert Einstein ͑1904–1973͒. It casts his career as that of the archetypal researcher protagonist determined to master intellectually the way water flows and conveys alluvial sediment in rivers. In that effort, Einstein personified the mix of success and frustration experienced by many researchers who have attempted to formulate the complicated behavior of alluvial rivers in terms of mechanically based equations. His formulation of the relationship between rates of bed-sediment transport ͑especially bedload transport͒ and water flow comprised an innovative departure from the largely empirical approach that prevailed at the time. He introduced into that relationship the emerging fluid-mechanic concepts of turbulence and boundary layers, and concepts of probability theory. Inevitably the numerous complexities attending sediment transport mire formulation and prompt his use of several approximating compromises in order to make estimating bed-sediment transport practicable. His formula- tion nonetheless is a milestone in river engineering. DOI: 10.1061/͑ASCE͒0733-9429͑2004͒130:6͑477͒ CE Database subject headings: Sediment transport; Rivers; Alluvial streams; Fluid mechanics; Turbulence; Boundary layer. Introduction ally earned an undergraduate degree in civil engineering from the Swiss Federal Institute of Technology ͑ETH͒. Albert then encour- Hans Albert Einstein, born in May 1904, might have remained aged his son to come to Germany ͑where Albert was a professor one of countless civil engineers whose work, although locally at the University of Berlin͒. Albert facilitated this move by help- important, had little impact on the world as a whole. However, his ing him locate a job at the steel construction firm of August trenchant independence of spirit and famous father, Albert Ein- Klonne, in Dortmund, where Einstein worked as a structural en- stein, launched him into a productive career as a researcher and gineer focusing on bridge construction. However, by 1931 Albert educator fascinated with the mechanics of bed-sediment transport was becoming increasingly apprehensive about the growing Nazi and water flow in alluvial rivers. By virtue of the times in which power in Germany. Understanding well the threat posed to Jews, he lived ͑1904–1973͒, the trans-Atlantic span of his life, and his and concerned about his son’s safety, Albert encouraged a return name, Hans Albert Einstein’s ͑hereinafter called Einstein͒ career to Switzerland. Seven years later, Albert would again feel the forms a convenient course along which to view the advance of pressure to ensure his son’s safety, and would facilitate a second alluvial-river mechanics as an engineering science. This paper move ͑this time to the United States͒ and job change. Thus Ein- follows part of his career, viewing his efforts to understand and stein’s career was also marked by historic movements; each shift formulate two central issues in alluvial-river behavior: the rela- in its course was induced by a change in the political climate tionship between bed-sediment transport and water flow, and that linked with such movements. between flow depth and flow rate. This paper discusses how despite the politically encouraged Although Einstein lived most of his youth with his mother moves, or perhaps because of them, Einstein emerged as a leading Mileva, who had separated from Albert when Einstein was 10 expert in alluvial-river mechanics, his expertise being sought years old, his career was strongly marked by his father’s influ- around the world. The paper does so with scant inclusion of equa- ence. Family correspondence reveals that, though Albert first dis- tions. Practically every major textbook on alluvial-river mechan- suaded his son from entering civil engineering, he later fostered ics and sediment transport ͓e.g., the books by Einstein’s doctoral and partly directed that career. Until 1927, Einstein and his students Graf and Chien ͑Graf 1971; Chien and Wan 1999͔͒ mother resided in Zurich, where he attended school and eventu- present the main equations comprising Einstein’s formulations. For a broad technical assessment of Einstein’s contributions to 1IIHR-Hydroscience and Engineering, Dept. of Civil and alluvial-river mechanics, the writers defer to the useful synopsis Environmental Engineering, College of Engineering, The Univ. of Iowa, by Shen ͑1975͒, another of his doctoral students. The Proceedings Iowa City, IA. E-mail: [email protected] of a symposium, to honor Einstein on the occasion of his retire- 2IIHR-Hydroscience and Engineering, Dept. of Civil and ment, lists his publications and the graduate students with whom Environmental Engineering, College of Engineering, The Univ. of Iowa, he worked ͑Shen 1972͒. Iowa City, IA. E-mail: [email protected] A theme running through this paper is innovation and compro- Note. Discussion open until November 1, 2004. Separate discussions mise. Though springing innovatively from emerging concepts of must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing turbulent flow and probability theory, concepts that were becom- Editor. The manuscript for this paper was submitted for review and pos- ing well established in engineering only during the early decades sible publication on January 8, 2004; approved on February 6, 2004. This of the twentieth century, Einstein’s formulation of sediment trans- paper is part of the Journal of Hydraulic Engineering, Vol. 130, No. 6, port becomes beleaguered by confounding physical details and June 1, 2004. ©ASCE, ISSN 0733-9429/2004/6-477–487/$18.00. the natural variability of sediment and flow conditions in rivers. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 477 and supervising the construction of ETH’s impressive hydraulics laboratory with which to undertake it. A French engineer, Du Boys ͑1879͒, had done some simple flume experiments and proposed the first mechanistic formula for estimating bed sediment transport as bedload, the portion of bed sediment transport whereby bed particles move on or near the bed. A difficulty with his formula, though, was its basis on a misconceived notion of bed-particle movement. Du Boys had as- sumed that bed sediment moves as a series of superimposed shearing layers, and had arrived at a formula relating rate of bed- load transport as per unit width of channel to a critical flow con- dition beyond which flow mobilized bed sediment, and an excess of average shear stress exerted on the bed. Subsequent flume ex- periments showed the sliding layer view of bed-sediment move- Fig. 1. Alpine Rhine constrained to a single, straightened channel ment to be fallacious ͑e.g., Schoklitsch 1914; Gilbert 1914͒. Nev- just upstream of Lake Constance, Switzerland ertheless, the notion of a critical shear stress ͑or flow rate, flow depth͒ associated with bed-sediment transport was conceptually appealing. Consequently formulas similar to Du Boys’ were con- sidered best suited for estimating not only bedload transport but Inevitably, simplifying assumptions, empiricism, and other judi- also the total rate of bed-sediment transport; prior to the 1930s, it cious compromises are needed to prop formulation so that it is of was moot whether engineers actually distinguished between the practical engineering use. It is a theme common to many efforts in two transport terms. formulating sediment and water movement in alluvial rivers. Perhaps the most advanced at sizing alluvial channels were the British, who had sought an improved design method for irrigation canals dug through sandy terrain in parts of the Indian subconti- Beginnings: Meyer-Peter’s Flume nent and Egypt. The method, termed the Regime Method ͑e.g., Lacey 1929͒, relied almost entirely on empirical relationships to Professor Eugene Meyer-Peter of the Swiss Federal Institute of characterize channels under long-term equilibrium or ‘‘regime.’’ Technology ͑ETH͒ in Zurich needed to know how much sediment The Regime Method was still in development, and its applicabil- moved with water flowing along the Alpine Rhine, especially the ity to the Alpine Rhine with its gravel bed was uncertain. amount of coarser sediment, gravels and sands, that moved along The problems with the Alpine Rhine clearly showed that the the river’s bed. This need was to bring the young Einstein from few existing formulas were far from being dependable or useful. Germany, where he then worked, back to Switzerland, the country More understanding of fundamental processes was needed. Ac- of his birth. cordingly, Meyer-Peter implemented a comprehensive plan entail- In the late 1920s, the Swiss federal government and the local ing field measurements in the Alpine Rhine, as well as hydraulic cantonal government of St. Gallen, responding to concerns about modeling and flume experiments to be conducted in ETH’s new an alarming increase in the frequency with which the river hydraulics lab. flooded, had contracted Meyer-Peter to recommend an effective To recruit research assistants, Meyer-Peter placed an advertise- modification to the Alpine Rhine over a 20-km reach extending ment in a Zurich newspaper. The ad caught the attention of Mil- from the Alps to the head of Lake Constance. The river, which eva Einstein, and she contacted Albert. He had briefly thought and ͓͑ ͔ ͒ wends through the Swiss Alps to Lake Constance ͑Fig. 1͒, was written about aspects of river mechanics Albert Einstein 1926 , aggrading, and likely would break out of its leveed banks and appreciated the importance of Meyer-Peter’s work, and saw a disastrously flood its valley. Political considerations gave Meyer- promising, safer career opportunity for his and Mileva’s elder son. Peter’s work urgency, as the Alpine Rhine above Lake Constance In 1931 Einstein joined Meyer-Peter’s research effort and started formed an international border between Switzerland, Austria, and working toward the doctoral degree.