Lagrangian and Eulerian coordinates
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In fluid dynamics the Lagrangian reference frame is a way of looking at fluid motion where the observer follows individual fluid particles as they move through space and time. Plotting the position of an individual particle through time gives the pathline of the particle. This can be visualized by sitting in a boat drifting down a river.
The Eulerian reference frame is a way of looking at fluid motion that focuses on specific points in the space through which the fluid moves. This can be visualized by sitting on the bank of a river and watching the water pass your location. Values about the fluid flow are determined as vectors at discrete locations.
They are related by the Convective derivative or Lagrangian derivative (sometimes called the material derivative):
This tell us the rate of change of F whilst moving with the fluid at velocity u.
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