Jun 08 2007

The Difference between the Lagrangian and Eulerian Viewpoints

Published under Weather

When describing a moving fluid, there are two primary ways of viewing it.The first is to pick a particle, or parcel, and follow its movement throughout the fluid. This is seen in the first figure below. The black curly line represents the motion of some fictitious particle as it moves through the background fluid, which in this case is white. This is called a Lagrangian frame of reference. An example of a Lagrangian frame of reference is a camera on top of a race car.

lagrangian description of motion

eulerian description of motion

The second viewpoint is to remain fixed, and the fluid moves around you. In the bottom image above, we can see the blue lines of the fluid moving from left to right across the image, and the black dot in the center is where we take our measurements. An example of an Eulerian frame of reference is a webcam that doesn’t move, such as the University of Arizona webcam. It will show the same background of the mountains and buildings, but foreground objects such as people and clouds will move through the frame. Another example of an Eulerian point of reference, continuing the racing example, is as a spectator from the grandstands.

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