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FLOW FIELD SPECIFICATION Eulerian and Lagrangian descriptions: Eulerian Lagrangian

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

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www.me.bme.hu/~karolyi/results/advect/advection.html What can we say about these streamlines?

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PathlinesTrajectory of an identified water parcel – represent one particle at different times. http://projects.ict.usc.edu/animation/fluidsim.htm (e.g. progressive vector diagrams)

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StreaklinesPathlines that move more than a single point through the flow. Represent multiple particles at one time. https://visualization.hpc.mil/wiki/Streaklines 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.,

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Stream function In two dimensional flow we can define a stream function Ψ, such that: http://www.atmos.albany.edu/student/gareth/diagnostics.html 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

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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.

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

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Eulerian Description • A finite volume called a flow domain or control volume is defined through which fluid flows in and out. • There is no need to keep.

Eulerian Description • A finite volume called a flow domain or control volume is defined through which fluid flows in and out. • There is no need to keep.

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