Click and drag to stir a fluid and generate vortex structures. Rankine vortex model velocity field with particle tracer visualization. Karman vortex street and vortex-pair presets included.
What exactly is a vortex? I see them in water and smoke, but what's the physics behind the swirling motion?
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Basically, a vortex is a region in a fluid where the flow revolves around an axis line. The key is that it has circulation, meaning the fluid particles have angular momentum. In this simulator, when you click and drag, you're injecting that rotational motion into the fluid. Try it now—you'll see the particle tracers start to swirl.
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Wait, really? So the "Core radius ε" slider must be important. What does it control in the vortex I just made?
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Exactly! The core radius, often called $\epsilon$, defines the size of the vortex's solid, rotating heart. Inside this core, the fluid spins like a rigid disk. Outside, the swirl speed dies off. Slide it smaller and you get a tighter, more intense core. Make it larger, and the rotation is spread out over a bigger area. It's a key parameter in the Rankine vortex model this simulator uses.
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That makes sense. And the "Viscosity" slider? It says it's the decay rate—does that mean my vortex will eventually fade away?
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In practice, yes! Real fluids have viscosity, which is internal friction that dissipates kinetic energy as heat. A high viscosity (move the slider right) causes your vortex to decay quickly, smoothing out the motion. A low viscosity (move it left) lets the vortex persist much longer, creating those beautiful, sustained swirls. This is why smoke rings in air last longer than similar swirls in honey.
Physical Model & Key Equations
The simulator uses the Rankine vortex model, which combines two flow regimes. Inside the core, the flow rotates with constant vorticity (like a solid). Outside, it behaves as an irrotational (potential) flow.
Here, $v_{\theta}$ is the tangential (swirling) velocity at a distance $r$ from the vortex center. $\Gamma$ is the circulation strength (set by your click-and-drag force), and $\epsilon$ is the core radius you control with the slider. This model avoids the infinite velocity at $r=0$ that a simple potential vortex would have.
The motion of the tracer particles is calculated by integrating their velocity over time. The simulator also models viscous decay, which gradually reduces the circulation $\Gamma$.
$$\frac{d\Gamma}{dt} = -\nu \, \nabla^2 \omega$$
In simpler terms, the change in vortex strength over time ($d\Gamma/dt$) is proportional to the fluid viscosity $\nu$ (your "Viscosity" slider) and the Laplacian of vorticity $\omega$. A higher $\nu$ leads to faster decay ($\Gamma$ drops quickly), causing the vortex to fade.
Real-World Applications
Aerospace & Automotive Design: Engineers simulate vortex formation around wingtips (wingtip vortices) and car side mirrors to understand and reduce drag. Using CAE tools, they can optimize shapes to minimize these energy-shedding structures, directly improving fuel efficiency.
Structural Engineering: Tall buildings and bridges must be analyzed for vortex shedding, which can cause dangerous oscillations. The alternating pattern seen in a Kármán vortex street (which you can create by dragging multiple times in a row) is a key phenomenon studied to prevent failures like the infamous Tacoma Narrows Bridge collapse.
Meteorology & Oceanography: Large-scale vortices are the engines of weather systems. Hurricanes and typhoons are massive atmospheric vortices with a distinct calm eye (the core) and high-speed rotating winds. Oceanic eddies similarly transport heat and nutrients across vast distances.
Industrial Mixing & Process Engineering: In chemical reactors or water treatment plants, controlled vortices are used to mix fluids efficiently. The core radius and decay rate are critical parameters for ensuring reactants are blended thoroughly without creating dead zones or excessive energy loss.
Common Misconceptions and Points to Note
There are a few key points you should be aware of when starting to play with this tool. First, you might think "moving the mouse quickly creates a stronger vortex," but it's not that simple. This simulator assigns vortex strength, called "circulation Γ," along the mouse's trajectory. This means the 'area enclosed by the trajectory' you move has a greater impact than the 'speed' of the movement. Drawing a large circle slowly can sometimes create a stronger vortex than moving quickly in small, jittery motions. This connects to a practical caution: not to confuse "velocity" and "vorticity" when setting boundary conditions.
Next is the relationship between the parameters "Viscosity" and "Vortex Core Radius ε." Both relate to how a vortex spreads, so they might seem to have similar effects, but their physical meanings are completely different. "Viscosity" is a property of the fluid itself, representing the process where vortex energy dissipates into heat (decays). On the other hand, "Vortex Core Radius ε" is a parameter in the computational model, determining at what scale the structure of the vortex core is smoothed out. For example, setting ε extremely small (like 0.01) and viscosity to zero makes the vortex very sharp and barely decaying, which can easily lead to numerical instability (the vortex strength exploding). In practical CFD as well, it's crucial to distinguish between parameters for modeling and physical property values.
Finally, don't forget the fundamental limitation that this is a "2D" simulation. The screen is flat, right? Real flows are 3D, so the beautiful vortex filaments you see here would actually stretch and tangle complexly as vortex tubes. Even if you recreate a Kármán vortex street with this tool, 3D disturbances (spanwise fluctuations) quickly arise in the actual wake behind a cylinder. While 2D calculations are excellent for grasping the essence of a phenomenon, a major pitfall in practical analysis seeking quantitative values is the constant need to consider 3D effects.
Set viscosity (0.001–0.1 Pa·s) using the slider to control energy dissipation in the vortex core.
Adjust particle count (500–5000) to increase tracer density for clearer streamline visualization.
Configure epsilon (0.01–1.0) to modify vortex strength and circulation intensity.
Click and drag within the simulation domain to initiate vortex formation and observe Rankine or Karman structures.
Monitor particle trajectories in real-time as they spiral around the vortex axis.
Worked Example
Simulating a tornado-like vortex: Set viscosity to 0.015 Pa·s (air-like), particle count to 2000, epsilon to 0.45 m²/s. Drag across the domain to generate a Rankine vortex with solid-body rotation in the core (r < 0.3 m) and irrotational flow in the outer region. Observe peak tangential velocity of ~8 m/s at r=0.25 m, then velocity decay proportional to 1/r beyond the core radius.
Practical Notes
Higher viscosity (0.05+ Pa·s) damps vortex persistence; use low values (0.002 Pa·s) for long-duration oceanic gyres or low-pressure systems.
Particle count above 3500 reveals Karman vortex street formation in cylinder wake scenarios; balance with computational load.