Question: What German engineer who pioneered the development of rigorous systematic mathematical analyses which he used for underlying the science of aerodynamics, which have come to form the basis of the applied science of aeronautical engineering, also developed the Mixing length model in the early 20th century?

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History of ecology: Ecology is a new science and considered as an important branch of biological science, having only become prominent during the second half of the 20th century.  Ecological thought is derivative of established currents in philosophy, particularly from ethics and politics.  Its history stems all the way back to the 4th century.  One of the first ecologists whose writings survive may have been Aristotle or perhaps his student, Theophrastus, both of whom had interest in many species of animals and plants.  Theophrastus described interrelationships between animals and their environment as early as the 4th century BC.  Ecology developed substantially in the 18th and 19th century.  It began with Carl Linnaeus and his work with the economy of nature.  Soon after came Alexander von Humboldt and his work with botanical geography.  Alfred Russel Wallace and Karl Möbius then contributed with the notion of biocoenosis.  Eugenius Warming’s work with ecological plant geography led to the founding of ecology as a discipline.  Charles Darwin’s work also contributed to the science of ecology, and Darwin is often attributed with progressing the discipline more than anyone else in its young history.  Ecological thought expanded even more in the early 20th century.  Major contributions included: Eduard Suess’ and Vladimir Vernadsky’s work with the biosphere, Arthur Tansley’s ecosystem, Charles Elton's "Animal Ecology", and Henry Cowles ecological succession.  Ecology influenced the social sciences and humanities.  Human ecology began in the early 20th century and it recognized humans as an ecological factor.  Later James Lovelock advanced views on earth as a macro-organism with the Gaia hypothesis.  Conservation stemmed from the science of ecology.  Important figures and movements include Shelford and the ESA, National Environmental Policy act, George Perkins Marsh, Theodore Roosevelt, Stephen A. Forbes, and post-Dust Bowl conservation.  Later in the 20th century world governments collaborated on man’s effects on the biosphere and Earth’s environment.

Mixing length model: In fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a newtonian fluid boundary layer by means of an eddy viscosity.  The model was developed by Ludwig Prandtl in the early 20th century.  Prandtl himself had reservations about the model, describing it as, "only a rough approximation,"

What Engineers Know and How They Know It: What Engineers Know and How they Know It: Analytical Studies from Aeronautical History (The Johns Hopkins University Press, 1990) (ISBN  ) is a historical reflection on engineering practice in US aeronautics from 1908 to 1953 written by an accomplished practitioner and instructor.  This period represents the dawn of aviation which was fraught with uncertainties and numerous paths to many possible worlds.  The book captures two main conclusions from this period.  The first order conclusion of this book is about "what engineers know."  Five case studies from the history of aeronautical engineering are used to argue engineering often demands its "own" scientific discoveries.  Thus, engineering should be understood as a knowledge-generating activity that includes applied science but is not limited to applied science.  The second order conclusion of this book pertains to "how engineers know" by using the same case studies to reveal patterns in the nature of all engineering.  These patterns form an “epistemology” of engineering that may point the way to an “engineering method” as something distinct from scientific method.  Walter Vincenti ends the work with a general "variation-selection model" for understanding the direction of technological innovation in human history.  The book is filled with numerous additional observations and stories told by a practitioner and instructor.  This may be why Dr. Michael A. Jackson, author of "Structured Design" and "Problem Frames", once concluded a keynote address to engineers with the statement, "Read Vincenti's book.  Read it carefully.  Read it one hundred times."

Engineering apprentice: An engineering apprenticeship in the United Kingdom is an apprenticeship in mechanical engineering or electrical engineering or aeronautical engineering to train craftsmen, technicians, senior technicians, Incorporated Engineers and Chartered Engineer for vocational oriented work and professional practice.  Chartered Engineers are usually formed through a university degree programme at the Masters Engineering level and may undertake a short form of post graduate apprenticeship.  A typical example is the apprenticeships formerly available at the BTH and EEC at Rugby in England.  Subjects covered included mathematics, engineering sciences, limits and fits, metallurgy, foundry technology, engineering drawing, design, materials science for engineering materials, metalworking by hand, operating machine tools, and basic features of engineering design.  Also refer to apprenticeship and the UK and German section.  Elite technical apprenticeships (4-6 years long) have been a decades long tradition at UK companies such as BAE Systems, Rolls-Royce Holdings, Bombardier Aerospace (Short Brothers), and Babcock International.

Yakut scripts: There have been three major Yakut writing systems in use since the early 20th century.  The first systematic alphabet was developed by Semyon Novgorodov, and was based on the International Phonetic Alphabet.  Novgorodov's alphabet was developed in 1917, and continued in use until 1929.  In addition to the characters shown below, Novogorodov also introduced four letters to represent the diphthongs found in Yakut: /ɯa͡/ – ꭠ, /ie͡/ – ꭡ, /uo͡/ – ꭣ, and /yø͡/ – w. Vowel and consonant length was indicated with the colon (e.g. a:, t:).  While this alphabet was in use, various changes were implemented, including the addition of capital letters.  After 1929, Novgorodov's alphabet was replaced by a form of Latin script based on the Uniform Turkic Alphabet.  This was in turn replaced in 1939 by an alphabet using the Cyrillic script.  Prior to the Novgorodov alphabet, various "ad hoc" phonetic Latin and Cyrillic-based systems had been developed.

Metamathematics: Metamathematics is the study of mathematics itself using mathematical methods.  This study produces metatheories, which are mathematical theories about other mathematical theories.  Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century.  Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59).  An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system.  An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.

Aristide Cavaillé-Coll: Aristide Cavaillé-Coll (] ; 4 February 1811 – 13 October 1899), was a French organ builder.  He has the reputation of being the most distinguished organ builder of the 19th century.  He pioneered innovations in the art and science of organ building that permeated throughout the profession and influenced the course of organ building and organ composing through the early 20th century.  The organ reform movement sought to return organ building to a more Baroque style; but since the 1980s, Cavaillé-Coll's designs have come back into fashion.  After Cavaillé-Coll's death, Charles Mutin maintained the business into the 20th century.  Cavaillé-Coll was the author of many scientific journal articles and books on the organ in which he published the results of his researches and experiments.  He was the inventor of several organ sounds/ranks/stops such as the "flûte harmonique".

Gilbert Walker: Sir Gilbert Thomas Walker, CSI, FRS (14 June 1868 – 4 November 1958) was an English physicist and statistician of the 20th century.  Walker studied mathematics and applied it to a variety of fields including aerodynamics, electromagnetism and the analysis of time-series data before taking up a teaching position at Cambridge University.  Although he had no experience in meteorology, he was recruited for a post in the Indian Meteorological Department where he worked on statistical approaches to predict the monsoons.  He developed the methods in the analysis of time-series data that are now called the Yule-Walker equations.  He is known for his groundbreaking description of the Southern Oscillation, a major phenomenon of global climate, and for discovering what is named after him as the Walker circulation, and for greatly advancing the study of climate in general.  He was also instrumental in aiding the early career of the Indian mathematical prodigy, Srinivasa Ramanujan.

Rockdale (Fallston, Maryland): Rockdale, also known as The Robinson/Stirling Place, is a historic home and farm complex located at Fallston, Harford County, Maryland, United States.  It is a farm developed from the late 18th century through the early 20th century.  The dwelling is in three parts.  The east room of the east wing is the earliest section dating from the 18th century.  The largest or main portion of the dwelling dates from between 1815 and 1830.  The north wing, a bay centered in the south façade of the second story, and a small conservatory, date from the very early 20th century.  The main house is five bays in length, two and a half stories, of stone construction, stuccoed and scored.  The home is surrounded by several outbuildings, trees, and other plantings, and the remains of formal gardens and garden structures developed in the early 20th century.  It was the residence of William E. Robinson (1860-1935), an entrepreneur in the local canning industry.

Ludwig Prandtl: Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German engineer.  He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of aerodynamics, which have come to form the basis of the applied science of aeronautical engineering.  In the 1920s he developed the mathematical basis for the fundamental principles of subsonic aerodynamics in particular; and in general up to and including transonic velocities.  His studies identified the boundary layer, thin-airfoils, and lifting-line theories.  The Prandtl number was named after him.

Supporting paragraphs: Mixing length model Ludwig Prandtl
Answer: Ludwig Prandtl