Description
In the Eulerian specification of the flow field, the flow quantities are depicted as a function of position x and time t. Specifically, the flow is described by a function
giving the flow velocity at position x at time t.
On the other hand, in the Lagrangian specification, individual fluid parcels are followed through time. The fluid parcels are labelled by some (time-independent) vector field a. (Often, a is chosen to be the center of mass of the parcels at some initial time t0. It is chosen in this particular manner to account for the possible changes of the shape over time. Therefore the center of mass is a good parametrization of the velocity v of the parcel.) In the Lagrangian description, the flow is described by a function
giving the position of the parcel labeled a at time t.
The two specification are related as follows:
because both sides describe the velocity of the parcel labeled a at time t.
Within a chosen coordinate system, a and x are referred to as the Lagrangian coordinates and Eulerian coordinates of the flow.
Read more about this topic: Lagrangian And Eulerian Specification Of The Flow Field
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