Rayleigh-Ritz optimization of the structure function for a Kolmogorov power density and an approximate analytical...

Area of Science:

• Physics
• Astronomy
• Wave Propagation

Background:

• Wave propagation through extended random media, like interstellar space, is often modeled using simplified structure functions.
• The exact Kolmogorov power spectrum provides a more accurate description of turbulence in such media.

Purpose of the Study:

• To derive an analytical solution for the two-point electric field correlation function based on the Kolmogorov power spectrum.
• To compare the coherence properties of this new model with traditional Gaussian structure function models.

Main Methods:

• Expressing the structure function as an inverse Fourier-Bessel transform.
• Optimizing an approximate series representation using a two-term Gaussian expansion and the Rayleigh-Ritz technique.
• Analyzing the domains of validity and coherence profile of the derived solution.

Main Results:

• An analytical solution for the electric field correlation function was obtained.
• The derived model shows significantly extended correlation distances compared to Gaussian models.
• The domains of validity and coherence profiles were thoroughly examined.

Conclusions:

• The analytical solution based on the Kolmogorov spectrum offers improved accuracy for wave propagation in random media.
• This model predicts persistent correlations over much larger distances than previously assumed.
• The findings have implications for understanding signal coherence in astrophysical and other turbulent environments.