GRAVITATIONAL-WAVE INSTRUMENTATION · AN INTERACTIVE SIMULATION
Atmospheric Newtonian noiseWhen the air above an observatory pulls directly on its mirrors.
No acoustic barrier can block gravity. Explore how passing infrasound wave packets and turbulent daytime air parcels couple gravitationally to suspended interferometer mirrors—and why thermal eddies force third-generation detectors deep underground.
Based on Wenhui Wang's UT Arlington Ph.D. dissertation (2025) and the companion paper by Wenhui Wang & Teviet Creighton (2025). The direct MavMatrix PDF download returned HTTP 403 to automated retrieval, so all equations, environmental baselines, detector curves and 1D numerical validation steps implemented here come directly from Wang's dissertation record and the published companion paper (arXiv:2505.05690).
DUAL-STAGE ATMOSPHERIC FIELD SIMULATION · SYNCED MODEL
What moves around the test mass, and how the geometry maps to strain
Every temperature fluctuation or pressure wave in the open air pulls gravitationally on a detector's suspended mirrors through Newton's inverse-square law. Below, the rendered 3D scene (bedrock or shelter, vacuum tube, laser arm, moving air parcels) is paired side-by-side with the synced geometric model and camera frustum from Wang & Creighton (2025).
Why geometry bridges to strain: each cold/warm parcel pulls along δg_x ∝ x / r³. Smooth wind only fluctuates on the crossing timescale D / v (exponentially damped above it); cycloidal circulation of radius R modulates acceleration at f = v / (2πR), turning exponential shielding into a power-law tail.
COHERENT VS INCOHERENT ACOUSTIC FIELDS · EQS. (5) & (10)
Infrasonic Newtonian noise and underground wave-packet floors
A perfectly coherent horizontal sound wave at speed v_s = 340 m/s is exponentially suppressed underground as e^(−ωD/v_s). Real atmospheric wave trains, however, stay spatially coherent only over a finite packet length l = Qλ, replacing pure exponential decay below e^(−πQ) with a weaker power-law tail.
Explore acoustic shielding
Notice how small Q weakens surface pressure coherence below e^(−πQ) yet raises noise deep underground whenever D/λ > Q/2, because wave packets fail to cancel smoothly over the long crossing window D/v_s.
ADVECTED KOLMOGOROV TURBULENCE & 1D MONTE CARLO
Why turbulent wind turns an exponential cliff into a power law
Smooth uniform wind glides past a mirror over timescale D/v, dying off exponentially above f ~ v/(2πD). Once surface roughness or eddies roll air parcels along cycloidal loops of radius R = v/Ω, frozen temperature pockets re-accelerate near f = v/(2πR), lifting a steep f^(−29/6) locus into the gravitational-wave band.
Appendix A.1 · Live 1D Kolmogorov Monte Carlo
Generates a 1,024 m Gaussian parcel ribbon filtered in Fourier space to D_T(Δr) = 0.2 (Δr)^(2/3) K², orbits parcels on a cycloid of radius R at height D, sums G δm_i x_i/r_i³, and FFTs δg_x(t) in real time.
Predicted peak f = v/(2πR) = 1.99 Hz · Simulated normalized peak at 2.50 Hz (2.34e-21 vs Eq. A.2 1.98e-21 Hz⁻¹/², L = 4 km, θ = 40°, δA = 1 m²).
Before computing gravitational pull, the generated 1D airmass is checked across lag scales Δr to verify the inertial-range Kolmogorov power law holds without artificial fine-tuning of spectral amplitude:
Agreement in the inertial range (Δr ≥ 0.5 m) confirms both the spatial correlation slope and absolute temperature variance match Eq. (A.2) assumptions.
SECTION 4 BENCHMARKS · ALIGO, EINSTEIN TELESCOPE, COSMIC EXPLORER, GRADIOMETERS
Where atmospheric Newtonian noise bites into 2G, 3G and torsion detectors
Select an observatory from Section 4 of Wang & Creighton (2025) to overlay its digitized design sensitivity against the canonical 95th-percentile infrasound and daytime peak thermal bands at any siting depth D.
Siting depth & band budget
L = 10 km underground third-generation detector targeting ~2-10 Hz sensitivity (Punturo / ET sensitivities).
SURFACE ENCLOSURES D_EFF & VOLUMETRIC TOMOGRAPHY · §§2.3 & 5
Building a bigger hall versus mapping every cubic metre of wind
Because surface structures surround the test mass on three sides rather than only from above, the inverse-distance solid-angle integral compresses effective depth:
For a hemisphere of radius R = 6 m, D_eff = 3.0 m matches the roll-off of Fiorucci et al. (2018). For a half-cube, Wang & Creighton quote 0.5480 h whereas uniform upper-hemisphere numerical quadrature evaluates to 0.6015 h; either way, achieving D_eff = 100 m via an above-ground hangar would require a ~180 m structure, making underground siting far more practical (while simultaneously cutting seismic NN).
Coherent seismic and acoustic fields can be predicted from a sparse perimeter array. Incoherent thermal eddies have correlation length l_corr ~ v / ω and demand real-time 3D tomography throughout a hemisphere of radius D:
Eddy correlation scale l = v/(2πf) = 1.59 m at v = 10 m/s. Achieving 100 m underground performance on the surface at 1 Hz requires ~10⁵–10⁶ independent sub-second temperature measurements to millikelvin precision—likely achievable only via remote atmospheric lidar or absorption-line tomography, placing solar-orbit missions in view for <1 Hz bands.
WHAT THIS CHANGES FOR OBSERVATORIES
Why thermal advection sets the low-frequency frontier
Coherent seismic and acoustic fluctuations can in principle be monitored with sparse seismometers or infrasound arrays and subtracted in feed-forward pipelines. Wind-advected temperature perturbations, however, carry correlation scales of only a couple of metres at 1 Hz—meaning atmospheric Newtonian noise acts as an irreducible siting constraint unless detectors bury test masses at least ~100 m underground (for 2–10 Hz sensitivity) or leave Earth's atmosphere behind in solar orbit below 1 Hz.