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
Famous quotes containing the word description:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“God damnit, why must all those journalists be such sticklers for detail? Why, they’d hold you to an accurate description of the first time you ever made love, expecting you to remember the color of the room and the shape of the windows.”
—Lyndon Baines Johnson (1908–1973)
“Whose are the truly labored sentences? From the weak and flimsy periods of the politician and literary man, we are glad to turn even to the description of work, the simple record of the month’s labor in the farmer’s almanac, to restore our tone and spirits.”
—Henry David Thoreau (1817–1862)