FLOW FIELD SPECIFICATION Eulerian and Lagrangian descriptions: Eulerian Lagrangian

Velocity field and trajectories StreamlinesParallel (tangent) to the velocity vector → boundaries are streamlines. Represent velocity trajectories. slope of streamlines

What can we say about these streamlines?

PathlinesTrajectory of an identified water parcel – represent one particle at different times. (e.g. progressive vector diagrams)

StreaklinesPathlines that move more than a single point through the flow. Represent multiple particles at one time. Effective way to identify flow discontinuities through large separation of the points in the Streakline. Streamlines = Pathlines = Streaklines if the flow is steady, i.e.,

Stream function In two dimensional flow we can define a stream function Ψ, such that: x y A B What is the mass flux ρQ across the line AB? If AB II to y, then Q = u dy But in general AB can be defined by (dy,-dx), so that

If A and B are on the same streamline, then Q = 0, so Ψ must be a constant along a streamline. Another way to look at it: slope of streamlines Ψ must be a constant along a streamline.

Differentiating following a fluid parcel Adopting the Eulerian description, the rate of change of properties following a parcel: local advective