Background

• Aircraft auralization at both NASA and Empa
• Auralizations seem too perfect
• Atmospheric turbulence gives random fluctuations

Goal

Implement NAF plugin for atmospheric turbulence fluctuations

Overview

• Atmospheric turbulence
• Generating sequence of scintillations
• NAF implementation
• Results

Atmospheric turbulence and wave propagation

Dynamic refractive-index field

Spatial autocorrelation

Turbulence wavenumber spectrum

Scattering due to turbulence

Scintillations

• Transfer function not constant, but time-variant
• Fluctuations of log-amplitude χ(t) and phase S(t) of signal due to atmospheric turbulence
• Audible χ(t) fluctuations, and additional decorrelation from S(t)

Generating sequence of scintillations

Concept

• Line-of-sight wave propagation
• Gaussian-distributed fluctuations
• A power spectral density function
  • Fourier pair with autocorrelation function

Line-of-sight propagation

• Distance d between source and receivers
• Spatial separation ρ between receivers

Gaussian model

• Variances
  • $\sigma_{\chi}^2 = \sigma_{S}^2 = \frac{\sqrt{\pi}}{2} \sigma_{\mu}^2 k^2 d L_0$
• Correlation function spherical wave
  • $B(\rho) = \frac{\mathrm{erf}\left(\rho/L_0\right)}{\rho/L_0}$
• Covariance
  • C(ρ)=B(ρ)σ

Space-to-time conversion

• Refractive-index field transported with velocity v_⊥
• Correlation time τ₀ = L₀/v_⊥
• Correlation lag τ = ρ/v_⊥
• Correlation B(τ)

Transverse speed aircraft

• Field not transported but sampled by aircraft
• $v_{\bot} = \left\| \mathbf{v_s} - (\mathbf{v_s} \cdot \mathbf{\hat{o}} ) \cdot \mathbf{\hat{o}} \right\|$
• Faster source samples field fluctuations faster

NAF implementation

Block diagram

NAF implementation

• Currently:
  • Pre-compute fluctuations with separate Python script
  • NAF plugin applies fluctuations
• Future:
  • NAF plugin that computes fluctuations on-the-fly

Results

Auralization - Without

Auralization - With

Observations

• Clear amplitude modulations
• Few decorrelation
• Phase fluctuations strong enough
• Paths seem too correlated

Challenges

• Obtain good input values

Conclusions

• Method to generate scintillations
• Applied to aircraft auralization
• NAF plugin demo