Velocity field

A function that assigns a velocity vector to each position and time in a moving medium, describing how the medium moves throughout space.

Streamline: A curve tangent everywhere to a steady vector field, tracing the instantaneous direction of flow. Streamlines follow the velocity direction at each point in a steady flow.
Vector field: A function assigning a vector to each point in a space or region. A velocity field is a vector field whose values represent motion.
Navier–Stokes equations: Differential equations governing the motion of viscous fluids under forces. Their solutions include velocity fields that satisfy momentum and mass-balance constraints.
Velocity: The rate of change of position with time, expressed as a vector. A velocity field extends the single-object quantity across a medium’s positions.
Pathline: The trajectory traced over time by an individual fluid particle. Pathlines show the motion produced by sampling velocity along a particle’s changing position.
Eulerian description: A description of motion that records physical quantities at fixed positions in space. Velocity fields are commonly specified at spatial locations rather than attached particles.
Computational fluid dynamics: The numerical simulation of fluid flow using discretized governing equations. Simulations calculate approximate velocity values across space and time.
Acceleration field: A function assigning an acceleration vector to each position and time in a medium. It describes changes in velocity rather than the velocity itself.
Material derivative: The rate of change of a quantity experienced while moving with a continuum element. It combines local time variation with change caused by motion through spatial gradients.
Lagrangian description: A description of motion that follows individual material particles through time. It tracks particle trajectories instead of specifying velocity at fixed positions.

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