Fluid Dynamics

Fluid dynamics is the branch of physics that describes how liquids and gases move — how water flows through a pipe, how air flows over a wing, and why both can switch, seemingly without warning, from smooth and predictable to swirling and chaotic. Almost everything in this hub traces back to one idea: a fluid parcel obeys Newton's second law just like any other object, but because it deforms continuously and interacts with its neighbours through pressure and viscosity, the resulting equations of motion — the Navier-Stokes equations — are dramatically harder to solve than anything in rigid-body mechanics. This hub gathers every interactive fluid and aerodynamics simulation on mysimulator.uk into one guided starting point, so instead of staring at a partial differential equation you can drag a slider and watch the physics unfold pixel by pixel in your browser.

The simplest entry point is Bernoulli's principle: along a streamline, faster-moving fluid has lower pressure, and slower-moving fluid has higher pressure. That one trade-off explains why an aircraft wing's curved upper surface generates lift, why a shower curtain billows inward, and why a carburettor can meter fuel using nothing but airspeed. Push a little further into confined flow — water forced through a pipe — and the picture splits into two regimes named after Osborne Reynolds: laminar flow, where fluid moves in smooth, orderly layers with a parabolic velocity profile, and turbulent flow, where the same fluid mixes chaotically across the pipe with a flatter, blunter profile. Which regime you get is set entirely by the Reynolds number, a dimensionless ratio of inertial to viscous forces — cross roughly 2,300 in a pipe and the flow tips from one regime into the other.

Turbulence itself is one of the last great unsolved problems in classical physics — the Navier-Stokes existence and smoothness problem is a Clay Millennium Prize question precisely because nobody has proven that solutions always stay well-behaved in three dimensions. The Kármán vortex street simulation shows one of the most visually striking consequences: past a certain Reynolds number, flow past a cylinder doesn't just become chaotic, it self-organises into a beautifully regular alternating pattern of shed vortices. The same shedding mechanism makes power lines sing in the wind, sets the pitch of a car aerial's whistle, and was implicated in the 1940 collapse of the Tacoma Narrows Bridge, whose deck oscillated in resonance with the vortex-shedding frequency.

The instability simulations dig deeper into how order breaks down. Rayleigh-Bénard convection heats a fluid layer from below and shows that, past a critical Rayleigh number, random thermal noise self-organises into regular convection rolls that move heat far more efficiently than plain conduction — the same mechanism that drives cells in a heated pan of oil, in Earth's mantle, and in the Sun's outer layers. Rayleigh-Taylor instability puts a dense fluid on top of a lighter one and watches the interface between them tear into the mushroom-shaped plumes familiar from mushroom clouds and supernova remnants. Both simulations are genuine numerical solvers, not pre-baked animations, so changing the driving parameter changes the pattern that emerges, not just its speed.

The aerospace end of the hub applies the same fluid mechanics to wings and bodies moving through air. The NACA airfoil simulation lets you generate a real 4-digit NACA profile and read off its lift and drag coefficients from thin-airfoil theory, while the wind tunnel and flight simulator let you push a wing past its stall angle and watch lift collapse as the boundary layer separates from the surface. At the far end of the speed range, the supersonic flow simulation shows what happens once a body moves faster than the local speed of sound: a Mach cone forms, oblique and bow shocks appear, and pressure and density jump discontinuously across them according to the Rankine-Hugoniot relations — the same physics that produces a sonic boom.

Together these simulations cover the full arc of the topic: the algebraic simplicity of Bernoulli's equation, the statistical mystery of turbulence, the pattern-forming instabilities that appear whenever fluids are pushed out of equilibrium, and the applied aerodynamics that keeps aircraft in the air. Every solver here — the lattice-Boltzmann method, smoothed particle hydrodynamics, and the stable-fluids Navier-Stokes integrator — genuinely computes the flow frame by frame rather than replaying a fixed animation, so changing the Reynolds number, viscosity or angle of attack changes the physics you see, not just the visuals. Follow the learning path below for a suggested order, or jump straight into the categories for the full simulation lists.