Lighthill's Acoustic Analogy
In 1952, Sir James Lighthill revolutionized our understanding of aerodynamic noise by recasting the Navier-Stokes equations into an inhomogeneous wave equation. The source term — Lighthill's stress tensor — acts as a distribution of acoustic quadrupoles throughout the turbulent flow. For an unheated subsonic jet, this analysis yields the celebrated V⁸ scaling law: acoustic power is proportional to the eighth power of jet velocity, explaining why jet engines are so extraordinarily loud.
Spectral Characteristics
Jet mixing noise has a broad spectral shape peaking near Strouhal number 0.2. The peak frequency scales linearly with velocity and inversely with diameter: a 1-meter nozzle at 300 m/s peaks near 60 Hz, while a 0.1-meter nozzle at the same speed peaks near 600 Hz. The spectrum rolls off at roughly 25 dB per decade above the peak, with high-frequency components attenuating rapidly due to atmospheric absorption during propagation to community observers.
Directivity and Mach Waves
Jet noise is not omnidirectional. At low speeds, peak radiation occurs at roughly 30° from the jet axis. As jet Mach number increases, large turbulent eddies convect supersonically, generating intense Mach wave radiation concentrated at shallow downstream angles. This Mach wave emission mechanism dominates the peak noise of military afterburning engines and is the primary target of advanced nozzle shaping and fluid injection noise reduction technologies.
Modern Noise Reduction
Driven by increasingly stringent airport noise regulations (ICAO Chapter 14), engine manufacturers have developed chevron nozzles, variable-geometry exhausts, and ultra-high bypass ratio turbofans. Chevrons break up large-scale turbulent structures into smaller eddies that radiate less efficiently. Ultra-high bypass ratios (12:1 and above) reduce effective jet velocity while maintaining thrust, exploiting Lighthill's V⁸ law to achieve dramatic noise reductions.