1. Boundary-layer transition: laminar → transitional → turbulent
Air immediately next to a solid surface is slowed by viscosity. The region affected by that slowdown is the boundary layer. Increase velocity, plate length, or disturbance level and watch how the transition location moves upstream.
What the boundary-layer model is doing
At each location x, the page computes Reₓ = ρU∞x/μ using μ = 1.789×10⁻⁵ Pa·s. A clean flat-plate classroom marker of Reₓ ≈ 5×10⁵ is adjusted downward by the disturbance slider solely to make the sensitivity of transition visible.
Before transition, the visual uses the familiar laminar thickness estimate δ ≈ 5x/√Reₓ. Downstream of transition it trends toward δ ≈ 0.37x/Reₓ^0.2. Real transition—especially at high Mach number—depends on roughness, acoustic disturbances, wall temperature, pressure gradients, nose bluntness, instability modes, and other effects.
2. Airflow around an aircraft from subsonic to hypersonic Mach numbers
Move the Mach slider slowly through Mach 1 and then into the hypersonic regime. The animation changes from smooth pressure communication to transonic shocks, supersonic Mach waves, and a thin hypersonic shock layer.
M < 0.8
0.8–1.2
1.2–5
5–10
> 10
Important interpretation notes
For supersonic flow, the page displays the Mach angle μ = sin⁻¹(1/M). This is the angle of an infinitesimal Mach wave. A real aircraft's finite-strength shocks depend on body shape and flow deflection, so the drawn lines are not a geometry-specific CFD solution.
The pressure and temperature ratios shown use the ideal normal-shock equations as a reference. Aircraft shocks are often oblique rather than normal. At hypersonic speeds, high-temperature chemistry, dissociation, vibrational excitation, nonequilibrium effects, viscosity, and shock-layer interactions can make the perfect-gas model inadequate.
3. What changes as Mach number increases?
Pressure information can travel upstream
Disturbances move through the air faster than the aircraft. Streamlines bend smoothly and there is no attached shock system.
Shocks appear
Near Mach 1, local pockets of supersonic flow can terminate in shocks. Above Mach 1, disturbances are confined to Mach-wave regions and finite compression turns generate oblique shocks.
Shock layer and heating dominate
Mach waves become very shallow, strong shocks can sit close to slender surfaces, kinetic energy becomes enormous, and aerothermodynamics becomes central to the problem.
4. Questions for students
These work well as quick in-class prompts. Students can answer them by manipulating the page rather than memorizing definitions first.
- What happens to the transition location when velocity increases but all other quantities stay fixed?
- Why can a turbulent boundary layer be thicker yet have a “fuller” velocity profile?
- Why is a single critical Reynolds number only a classroom approximation?
- What does increasing surface roughness do to transition in the teaching model?
- What happens to Mach angle as Mach number increases?
- Why can a high-Mach aircraft at high altitude have lower dynamic pressure than a slower aircraft near sea level?
- Why is the normal-shock pressure ratio only a reference for the aircraft drawing?
- At what point should you become suspicious of a constant-γ perfect-gas temperature prediction?
5. Key formulas used on this page
| Concept | Formula | What students should notice |
|---|---|---|
| Reynolds number | Reₓ = ρU∞x/μ | Increases with density, velocity, and distance; decreases with viscosity. |
| Laminar boundary-layer thickness | δ ≈ 5x/√Reₓ | The layer grows downstream. |
| Turbulent boundary-layer thickness | δ ≈ 0.37x/Reₓ^0.2 | Turbulent mixing generally produces a thicker layer. |
| Mach number | M = V/a | Mach compares flight speed with the local acoustic speed. |
| Speed of sound | a = √(γRT) | Sound speed depends on local temperature. |
| Mach angle | μ = sin⁻¹(1/M) | For M > 1, μ shrinks as Mach increases. |
| Dynamic pressure | q = ½ρV² | Density and velocity both matter. |
| Normal-shock pressure ratio | p₂/p₁ = 1 + [2γ/(γ+1)](M₁²−1) | Strong compression grows rapidly with upstream Mach number. |
| Perfect-gas stagnation temperature | T₀ = T[1 + (γ−1)M²/2] | A useful reference, but increasingly limited in high-enthalpy hypersonic flow. |