Many students, when first learning fluid dynamics, are intrigued by the dichotomy between Eulerian and Lagrangian approaches. Most master the Eulerian frame that is so much the foundation of dynamics that concepts like “advection,” “enstrophy production,” and “vortex tipping” are immediately associated with particular terms in the Eulerian equations of motion. Other students, intrigued by how the Lagrangian formulation seems more directly related to the way properties are distributed and fluids accelerate, strive to master the mathematics of the Lagrangian frame, including the complex, and to my mind less than intuitive, nonlinearity of the spatial gradient in Lagrangian coordinates. The challenge is great enough, and the examples of successful analytical work in Lagrangian coordinates are rare enough, that most abandon the Lagrangian approach before mastering it.

Davis, R. 2007. Review of Lagrangian Fluid Dynamics, by A. Bennett. Oceanography 20(1):205–206, https://doi.org/10.5670/oceanog.2007.98.

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