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?

<P0-S0>  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. <P0-S1>  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. <P0-S2>  His studies identified the boundary layer, thin-airfoils, and lifting-line theories. <P0-S3>  The Prandtl number was named after him. <P0-S4> Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German engineer. <SEP> <P1-S0> 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. <P1-S1>  The model was developed by Ludwig Prandtl in the early 20th century. <P1-S2>  Prandtl himself had reservations about the model, describing it as, "only a rough approximation," <SEP> <P2-S0> 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. <P2-S1>  This period represents the dawn of aviation which was fraught with uncertainties and numerous paths to many possible worlds. <P2-S2>  The book captures two main conclusions from this period. <P2-S3>  The first order conclusion of this book is about "what engineers know." <P2-S4>  Five case studies from the history of aeronautical engineering are used to argue engineering often demands its "own" scientific discoveries. <P2-S5>  Thus, engineering should be understood as a knowledge-generating activity that includes applied science but is not limited to applied science. <P2-S6>  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. <P2-S7>  These patterns form an “epistemology” of engineering that may point the way to an “engineering method” as something distinct from scientific method. <P2-S8>  Walter Vincenti ends the work with a general "variation-selection model" for understanding the direction of technological innovation in human history. <P2-S9>  The book is filled with numerous additional observations and stories told by a practitioner and instructor. <P2-S10>  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. <P2-S11>  Read it carefully. <P2-S12>  Read it one hundred times." <SEP> <P3-S0> Sir Gilbert Thomas Walker, CSI, FRS (14 June 1868 – 4 November 1958) was an English physicist and statistician of the 20th century. <P3-S1>  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. <P3-S2>  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. <P3-S3>  He developed the methods in the analysis of time-series data that are now called the Yule-Walker equations. <P3-S4>  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. <P3-S5>  He was also instrumental in aiding the early career of the Indian mathematical prodigy, Srinivasa Ramanujan.