Why don't the particles bump into each other or change the flow?

The particles are modeled as massless, non-interacting passive tracers. This means they have no inertia and exert no force on the fluid or each other. They simply move with the local velocity defined by the synthetic field, v(x,y,t). This simplification is common in flow visualization to study the structure of the flow itself without the complexity of two-way interactions.

What does the 'wrap' (periodic boundary) condition represent?

The wrap condition creates a simulation domain that repeats infinitely in all directions. When a particle exits one edge, it reappears at the opposite edge with the same velocity. This is a computational technique to model a large, homogeneous flow region without hard walls or boundaries. It's useful for studying patterns and long-term behavior without edge effects, similar to a flow on a toroidal (donut-shaped) surface.

How is this related to real-world fluid flows?

This simulator models the kinematics—the geometry of motion—of a fluid. Real flows like ocean currents, atmospheric winds, or even airflow around a wing can be analyzed by studying the motion of passive elements like smoke, dye, or floating buoys. While real fluids have viscosity and turbulence, the core idea of tracing particles within a velocity field is fundamental to experimental flow visualization and numerical weather prediction.

What do the arrows in the optional grid represent?

The arrows provide a snapshot of the underlying velocity field, v(x,y,t). Each arrow's direction shows the local flow direction at that grid point, and its length is proportional to the local flow speed. This 'vector field' representation is the rule that dictates how every particle moves. Observing how particle paths relate to these instantaneous arrows helps distinguish between streamlines (tangent to the velocity field) and actual particle trajectories, which can differ in an unsteady flow.

Flow Field Particles

Synthetic v(x,y,t); advection with wrap; optional arrow grid.

About this model

Flow Field Particles visualizes the motion of massless tracer particles within a two-dimensional, time-varying velocity field. The core concept is advection, the transport of particles by the bulk motion of a fluid. The simulator defines a synthetic velocity field, v(x, y, t), which is a mathematical function that assigns a velocity vector to every point (x, y) in space and at every moment in time. Particles are introduced into this field and their paths are computed by integrating their velocity over time, following the equation of motion: dr/dt = v(r(t), t), where r(t) is the particle's position vector. This is a direct application of the kinematic description of fluid flow. A key simplification is that particles do not influence the flow field itself; they are passive tracers, ignoring inertia, pressure, and viscosity. This allows the focus to remain on the geometry and evolution of the flow. The simulation uses periodic boundary conditions (wrap), meaning a particle exiting one side of the domain instantly re-enters from the opposite side, simulating an infinite, repeating flow pattern. By interacting, students learn to connect abstract vector field equations to tangible particle trajectories, observe phenomena like streamlines, stagnation points, and chaotic advection, and build intuition for fundamental concepts in fluid kinematics and dynamical systems.

Who it's for: High school and undergraduate students in physics, mathematics, or engineering courses introducing vector fields, fluid dynamics, or computational modeling.

Key terms

Advection
Velocity Field
Vector Field
Particle Tracing
Streamline
Dynamical Systems
Kinematics
Periodic Boundary Conditions

How it works

When you want Perlin curls without a noise dependency: sines and cosines already give vortices and shear on a torus.

Frequently asked questions

Why don't the particles bump into each other or change the flow?: The particles are modeled as massless, non-interacting passive tracers. This means they have no inertia and exert no force on the fluid or each other. They simply move with the local velocity defined by the synthetic field, v(x,y,t). This simplification is common in flow visualization to study the structure of the flow itself without the complexity of two-way interactions.
What does the 'wrap' (periodic boundary) condition represent?: The wrap condition creates a simulation domain that repeats infinitely in all directions. When a particle exits one edge, it reappears at the opposite edge with the same velocity. This is a computational technique to model a large, homogeneous flow region without hard walls or boundaries. It's useful for studying patterns and long-term behavior without edge effects, similar to a flow on a toroidal (donut-shaped) surface.
How is this related to real-world fluid flows?: This simulator models the kinematics—the geometry of motion—of a fluid. Real flows like ocean currents, atmospheric winds, or even airflow around a wing can be analyzed by studying the motion of passive elements like smoke, dye, or floating buoys. While real fluids have viscosity and turbulence, the core idea of tracing particles within a velocity field is fundamental to experimental flow visualization and numerical weather prediction.
What do the arrows in the optional grid represent?: The arrows provide a snapshot of the underlying velocity field, v(x,y,t). Each arrow's direction shows the local flow direction at that grid point, and its length is proportional to the local flow speed. This 'vector field' representation is the rule that dictates how every particle moves. Observing how particle paths relate to these instantaneous arrows helps distinguish between streamlines (tangent to the velocity field) and actual particle trajectories, which can differ in an unsteady flow.

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About this model

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Frequently asked questions

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Frequently asked questions