Lighthill's eighth power law¶
An aeroacoustic scaling law stating that far-field sound power from compact low-Mach turbulent flow scales with the eighth power of characteristic velocity.
Core Idea¶
Lighthill's law estimates jet-noise acoustic power as proportional to density, squared source length, and U⁸ divided by the fifth power of sound speed, under compact-source and low-Mach assumptions. The acoustic analogy treats turbulence as an effective quadrupole source; dimensional scaling and retarded propagation make radiated efficiency rise approximately as Mach number to the eighth power. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Lighthill's eighth power law belongs to aeroacoustics and is useful where the analyst can specify the typed aeroacoustics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the turbulent source is compact and low-Mach in a uniform medium, characteristic velocity and length are defined, far-field total acoustic power is measured, and the U-to-the-eighth scaling regime is respected. The scope is broad within that domain but bounded by the need for the turbulent source is compact and low-Mach in a uniform medium, characteristic velocity and length are defined, far-field total acoustic power is measured, and the U-to-the-eighth scaling regime is respected. Conceptual acoustic scaling identity only; no aircraft, propulsion, industrial-noise, or hazardous-flow operating procedure is provided.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the turbulent source is compact and low-Mach in a uniform medium, characteristic velocity and length are defined, far-field total acoustic power is measured, and the U-to-the-eighth scaling regime is respected the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Lighthill's eighth power law. Lighthill's eighth power law compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed aeroacoustics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the turbulent source is compact and low-Mach in a uniform medium, characteristic velocity and length are defined, far-field total acoustic power is measured, and the U-to-the-eighth scaling regime is respected independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of aeroacoustics because they reuse the typed aeroacoustics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, The acoustic analogy treats turbulence as an effective quadrupole source; dimensional scaling and retarded propagation make radiated efficiency rise approximately as Mach number to the eighth power., and type the carrier, state every parameter and convention in the definition, test that the turbulent source is compact and low-Mach in a uniform medium, characteristic velocity and length are defined, far-field total acoustic power is measured, and the U-to-the-eighth scaling regime is respected, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Lighthill's eighth power law Domain-specific
Parents (1) — more general patterns this builds on
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Lighthill's eighth power law is a kind of Allometry and Scaling Law Prime
The proposed strict upward parent is
prime:allometry_and_scaling_law.
Hierarchy path (1) — routes to 1 parentless root
- Lighthill's eighth power law → Allometry and Scaling Law → Scaling and Scale Dependence → Scale
Neighborhood in Abstraction Space¶
Lighthill's eighth power law sits in a sparse region of the domain-specific corpus (62nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Acoustics, Recording & Sound Control (17 abstractions)
Nearest neighbors
- Sonic boom — 0.87
- Statistical energy analysis — 0.87
- Acoustic streaming — 0.86
- Infrasound — 0.86
- Reverberation — 0.86
Computed from structural-signature embeddings · 2026-09-08