Theodor Meyer (July 1, 1882 – March 8, 1972) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

born in

Bad Bevensen Bad Bevensen (West Low German: ''Bemsen'') is a town in the north of the district Uelzen in Lower Saxony, Germany. It is situated to the east of the Lüneburg Heath (''Lüneburger Heide''). The Ilmenau river, a tributary of the Elbe, flows thro ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

. He was a protege of

Ludwig Prandtl Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German Fluid mechanics, fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlyin ...

and is credited as one of the pioneers in the establishment of the scientific discipline known today as

compressible flow Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressibility, compressible, flows are usually treated as being incompressible flow, incom ...

gas dynamics Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ...

.G. S. Settles, E. Krause, and H. Fütterer: Theodor Meyer – Lost pioneer of gas dynamics, ''

Progress in Aerospace Sciences ''Progress in Aerospace Sciences'' is a monthly peer-reviewed scientific journal covering all areas of aerospace and aerospace engineering. It covers all areas of aerospace and aerospace engineering, particularly with respect to new theoretical and ...

'' 45 (6–8), pp. 203–210, 2009.J. D. Anderson: ''Modern compressible flow: With historical perspective,'' New York:McGraw-Hill, 2003.

Biography

As a youth, Meyer studied

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

. He was privileged to learn from several of the great minds in these fields, including

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

Carl Runge Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist. He was co-developer and co-eponym of the Runge–Kutta method (), in the field of what is today known as numerical analysi ...

Hermann Minkowski Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, o ...

, and

. He and Prandtl made a great team, for Prandtl's intuitive and experimental approach to

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

has become legendary,J. C. Rotta: ''Die Aerodynamische Versuchsanstant in Göttingen: ein Werk Ludwig Prandtls,'' Göttingen:Vandenhoeck & Ruprecht, 1990. and Meyer complemented his advisor's strengths with a formidable mathematical talent. During the first decade of the 20th century, Meyer worked under Prandtl's guidance at the Georg-August University in

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, Germany on the theory of supersonic gas flows, then a brand-new field of study that we now call compressible flow or gas dynamics.H. W. Liepmann and A. Roshko: ''Elements of gasdynamics,'' New York:Wiley, 1957 (reprint available from Dover Publications). In particular, Meyer developed the theory for how gases traveling at

supersonic speed Supersonic speed is the speed of an object that exceeds the speed of sound (Mach number, Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater tha ...

slow down abruptly through

oblique shock An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the direction of incoming air. It occurs when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The ...

waves, and how they accelerate smoothly through what we now call a

Prandtl–Meyer expansion fan A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite numb ...

. Prandtl first showed images of such flows captured by

Schlieren photography Schlieren photography is a process for photographing fluid flow. Invented by the Germans, German physicist August Toepler in 1864 to study supersonic motion, it is widely used in aeronautical engineering to photograph the airflow, flow of air ar ...

,L. Prandtl: Neue Untersuchung über die strömende Bewegung der Gase und Dämpfe, ''Physicalische Zeitschrift'' 8 (1), pp. 23–30, 1907 then the underlying theory appeared in Meyer's Ph.D. dissertation,T. Meyer: ''Über zweidimensionale Bewegungsvorgänge in einem Gas, das mit Überschallgeschwindigkeit Strömt,'' Göttingen University, 1908, Ph.D. Dissertation. hence the present terminology for the

Prandtl–Meyer function In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1. The maximum angle through which a sonic ( ''M'' = 1) flow can be turned ar ...

and the Prandtl–Meyer expansion fan. Although the names of Prandtl and Meyer are now universally connected with fans of expansion or compression waves in high-speed gas flows, their leading role in the discovery of oblique-shock waves has been forgotten. Present-day textbooks on compressible flow and gas dynamics simply present the oblique shock theory without attribution. The last textbook to properly acknowledge Prandtl and Meyer for oblique-shock theory was apparently written in 1947.R. Sauer: ''Theoretical gasdynamics,'' Ann Arbor, MI:J. W. Edwards, 1947. Nonetheless, the Ph.D. dissertation of Theodor Meyer in 1908 is arguably one of the most influential in the entire field of

. Until recently, nothing was known about Theodor Meyer's life after he finished his Ph.D. research in 1908. We now know that he served as a junior officer in the German infantry during

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

. He was injured in trench warfare on the infamous Western Front, and he came into contact with

Fritz Haber Fritz Jakob Haber (; 9 December 1868 – 29 January 1934) was a German chemist who received the Nobel Prize in Chemistry in 1918 for his invention of the Haber process, a method used in industry to synthesize ammonia from nitrogen gas and hydrog ...

, later a Nobel Prizewinner and now known as the "father of chemical warfare." After the war, Meyer sought further employment in theoretical physics but could not find it in depression-era postwar Germany. Ludwig Prandtl was not financially able to hire him, but Meyer did design the

de Laval nozzle A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube which is pinched in the middle, with a rapid convergence and gradual divergence. It is used to accelerate a compressible fluid to supersonic speeds in the a ...

for a

supersonic wind tunnel A supersonic wind tunnel is a wind tunnel that produces supersonic speeds (1.2

that Prandtl wanted to build. Prandtl sought funding from the German military to build this advanced aerodynamic test facility, but he did not succeed. Meyer subsequently worked as an engineer and as a high-school teacher of math and physics. By the time of his death at almost age 90 in 1972, not even his family or his neighbors in

, Germany were aware of the formative role he had played, with Ludwig Prandtl, in the scientific discipline known as compressible flow or gas dynamics.

References

{{DEFAULTSORT:Meyer, Theodor 20th-century German physicists 1972 deaths 1882 births German fluid dynamicists