Eulerian flow field

An Eulerian flow field assigns fluid velocity to each position in space and time. It describes motion from fixed spatial locations rather than by tracking individual fluid particles.

Velocity field: A vector field that assigns a velocity to each point in space and, when time-dependent, each instant. An Eulerian flow field is a velocity field whose vectors represent fluid motion.
Lagrangian description: A description of motion that follows individual material particles through space and time. It tracks fluid parcels, unlike the fixed-location viewpoint of an Eulerian field.
Computational fluid dynamics: The numerical simulation of fluid flow using discretized governing equations. Simulations commonly solve for velocity and pressure on fixed spatial grids.
Pathline: The trajectory traced by a single fluid particle over time. A pathline follows one particle, whereas the field assigns velocity throughout space.
Material derivative: An operator that measures the rate of change of a quantity experienced by a moving fluid particle. It combines local time change with transport through spatial velocity gradients.
Vector field: A function assigning a vector to each point in a region of space. The flow field is a time-dependent vector field with velocity vectors as values.
Particle image velocimetry: An optical method that estimates fluid velocity from the displacement of tracer particles between images. Measurements reconstruct velocities at fixed image locations to estimate the field.
Streakline: The curve formed by all fluid particles that have passed through a specified point. It is an accumulated particle trace, not an instantaneous velocity field.
Streamline: A curve tangent everywhere to the instantaneous velocity field of a flow. Its geometry is obtained from the field at one instant.
Fluid particle: An idealized small parcel of fluid treated as a unit in continuum mechanics. Its changing position through the field defines a particle trajectory.

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Lagrangian flow fieldCompared with: It is the direct fixed-location alternative to this particle-following field.