Airflow & vortex wakes

Before you start

Air rushing past a car, a cyclist or a bridge pier leaves a disturbed region behind it, and that region costs energy: it accounts for much of the drag that vehicles must overcome. On the pipes page, we meet viscosity in water flowing smoothly along a pipe. When the flow becomes faster or the obstacle larger, smooth flow can give way to swirling vortices. A single number, the Reynolds number, compares two tendencies: how strongly the moving air tends to keep going, and how strongly viscosity smooths the flow out. It helps us predict which kind of flow we will see.

Tracer smoke makes the otherwise invisible airflow easier to follow. What trail does it leave behind the object? Keep one setting long enough for that trail to develop before changing the flow. A quick glance just after an adjustment can confuse a pattern still developing with a lasting difference. Compare the air ahead of the object with the region behind it: where does it turn, and where do swirls appear? These changes give the Reynolds number something concrete to describe. It compares the relative importance of two influences on the flow; it does not draw every smoke line for us.

The setupThis is a two-dimensional wind tunnel. Air enters from the left and meets an obstacle, which can be a cylinder, an ellipse, a square, a triangle or an airfoil. The smoke is carried along by the calculated airflow; click in the tunnel to release more. You can drag the body, change its angle, and set the Reynolds number, which compares how strongly the moving air tends to keep going with how strongly viscosity smooths the flow.

What to do and noticeStart at a low Reynolds number and wait until the smoke pattern behind the body stops changing. Then raise the Reynolds number and wait again: behind a cylinder, swirls begin to leave alternately from its upper and lower edges. Compare drag and lift only after the wake has settled. Finally, keep the Reynolds number fixed, change the shape, and compare how wide the wake is. The smoke shows where the air goes; it is not a picture of the air molecules themselves.

01 / 03 · Make airflow visible

Predict firstCan a stationary obstacle experience a force?

Preparing the model…

Guided lesson

Build an intuition for velocity fields, drag and wake vortices using smoke.

Prerequisites: Fluids flow and include both liquids and gases. Viscosity describes frictional effects between neighbouring layers.

01 / 03

Make airflow visible

Predict firstCan a stationary obstacle experience a force?

Now let air enter from the left and meet a fixed cylinder. White smoke follows the air and helps us see where it goes; it is not a magnified picture of air molecules. Keep $\mathrm{Re}=20$ , the cylinder and smoke display, then play and let the wake develop. A wake means the flow behind the body that has been changed by its presence.

Why can a stationary body still feel a force? A small air parcel of mass $m$ and velocity $v$ has momentum $mv$ . Changing either the size or direction of velocity changes momentum. The cylinder makes air turn around it, requiring forces; the body receives an opposite reaction. The component along the incoming flow is drag, and the perpendicular component is lift. Since air flows rightward here, drag on the cylinder normally points right.

F_{\rm air}=\frac{\Delta(mv)}{\Delta t},\qquad F_{\rm body}=-F_{\rm air}

This is Newton’s second law in momentum form: at constant mass, $\overline F=\Delta(mv)/\Delta t=m\Delta v/\Delta t=m\overline a$ over the chosen interval. The bars mean average values; instantaneous force uses $F=dp/dt$ instead. The model estimates force by adding momentum changes at the boundary, then smooths the displayed reading slightly. After the smoke pattern develops, switch to Pressure. Warm colours mean higher pressure and cool colours lower pressure. Pressure is perpendicular force per area; these colours are not temperature.

This is a two-dimensional section: the cylinder extends into and out of the screen. Speed and size are set in a numerical grid without assigning physical metres and seconds, so a drag coefficient is not a force in newtons. Next we will explain what $\mathrm{Re}$ controls, then return to the coefficients.

How to observe

At low Re the wake is relatively steady. Increase Re and watch for vortices leaving from alternating sides; allow time for the flow to develop.
Compare a cylinder, ellipse, square, triangle and airfoil. Let the wake develop before comparing drag and lift.
Smoke represents tracers carried by the flow, not visible air molecules.

What this model simplifies

D2Q9 lattice Boltzmann flow includes viscosity and a no-slip solid boundary. This is a two-dimensional, nearly incompressible, low-Mach model; finite resolution and tunnel boundaries affect drag estimates, so it is not an aircraft-design tool. Re uses the original cylinder diameter as a common reference across shapes. Alternating wake vortices are not full three-dimensional turbulence. Gases are compressible; shocks and high-speed flight require a different model.

SourcesD. Schroeder · Lattice Boltzmann PDAS · NACA airfoil thickness