This is a 2D-native view of the same eN method used to predict hypersonic boundary-layer transition, built from two plots instead of a 3D body: a wavepacket amplitude-vs-station trace showing the Mack second-mode signal itself, and the N(x) growth chart engineers actually read off during design.
N(x) = ∫ σ(x') dx' transition when N(x) = N_tr
N(x) ≈ K(M, T_w) · √(Re_x / 10⁶), Re_x = (unit Re) · x
K grows with (M − 3.5) and with wall cooling (1 − T_w/T_aw).
Local wavelength ≈ 2δ(x), boundary-layer thickness
δ(x) ≈ 5x/√Re_x · √(1 + 0.15M²) (same scaling as the 3D model)
- Top plot — the instability wave's actual amplitude vs. distance along the body: it grows smoothly (envelope ∝ N(x)/Ntr clamped to 1) while amplifying, then erupts into broadband turbulent noise once N(x) crosses Ntr at xtr. The local zig-zag spacing shrinks or stretches with the local boundary-layer thickness δ(x), exactly like a real Mack-mode wavepacket whose wavelength tracks 2δ.
- Bottom plot — the same eN chart used to design real hypersonic vehicles (HIFiRE, X-51): N(x) climbing against the dashed Ntr threshold, with a marker at the predicted transition station.
- Mach / wall-cooling / unit Re / N-factor threshold sliders — identical physics to the 3D lab: higher Mach or a colder wall raises K and moves transition toward the nose; higher unit Re builds local Rex faster; a noisier environment lowers Ntr and trips transition earlier ("bypass" transition).
Blue = laminar, amber = amplifying second-mode wave, red = broken-down turbulent flow — same convention as the 3D lab, since it's the same underlying scaling law rendered as a stability diagram instead of a rendered vehicle surface. Simplified, illustrative scaling — not a substitute for full linear-stability-theory (LST) computations.