For a long time I've been curious about predicting the acoustic power spectrum of river sound from hydrodynamic measurements.
It's apparent that most of the energy of this river is contained between the 200 Hz and 2000 Hz bands. Removing the time axis (by taking a median) makes it easier to see that the energy is actually distributed around a few central bands (500 or 630 Hz):
A similar pattern (with varied bandwidth) has appeared at dozens of measurement locations near alpine rivers.
Of course there are possible environmental factors - such as terrain attenuation or atmospheric effects - that could be producing such a peaked spectrum. For the sake of a simpler answer, let's assume the receiver position is above the river pointed at the flow and that the receiver is in the far field.
Is there a theory that predicts such a peaked acoustic power spectrum in terms of measurable hydrodynamic properties?
I'm assuming that most of this energy is either coming from resistance in the form of rocks (on the bed or sticking up in the flow) or from the sound of turbulence, itself.
In the former case I thought Johnson-Nyquist noise might be helpful (by analogy), and in the latter perhaps Kolmogorov's length microscales? I've also considered explanations derived from Sir James Lighthill's aeroacoustic analogy.
I'm especially interested in theory that could be coupled to practical hydrology measurements such as slope, discharge, or grain size.