Make all three agree
Set the crossflow amplitude to zero. The field becomes steady and all three traces share one horizontal line.
01 / OBSERVE · Aerodynamics
Streamlines, Pathlines & Streaklines
Flow visualisationBrowser calculation
Release a tracer, inject a dye line and freeze the velocity field. In an unsteady flow, their stories separate.
THREE WAYS TO WATCH A FLOWLIVE B
Zoom for detail · drag background to pan
Fixed viewing window: 0–24 m horizontally, approximately −7–7 m vertically; lines are clipped at its edge. Teal: instantaneous streamline; amber: one particle’s path; pink: particles released from one fixed source since t = 0. Marker speeds use the calculated velocities.
Freeze the field
Pause at different phases. A streamline follows the velocity directions at that instant; it is not the future path of a released particle.
Follow the release time
Each point on the pink streakline has a different injection time. The amber tracer always starts at t = 0.
CALCULATED FROM THE SAME MODEL
Follow the response
B · solid turquoise A · dashed amber
Common time cursor
Compare the evidence
| Quantity | A · saved | B · live | Unit |
|---|
A remains fixed until you save again. Export includes settings, selected outputs and curve data.
Equations, assumptions and topic connections
Physical model
Two-dimensional prescribed velocity field u = U, v = A sin(ωt), with ω = 2π/P. It is spatially uniform, divergence-free and inviscid. The cross-stream pressure gradient −ρAω cos(ωt) supplies its material acceleration. No body, viscosity, diffusion or wall is modelled.
x(t;τ) = U(t − τ); y(t;τ) = y₀ + (A/ω)[cos(ωτ) − cos(ωt)]. The streamline at t is y = y₀ + v(t)x/U. A pathline varies t at fixed τ; a streakline varies τ at fixed t.
Topic connections
S02 · Governing Equations: PDF pp. 10–26, 66–75. Candidate source diagrams: pp. 18–20, 25; not reproduced.
Original analytic teaching example
Original schematic diagrams. No manufacturer performance, certification or maintenance-authorisation claim. Numerical verification checks the declared model; it is not experimental validation. Model version: course-foundations-v1.