I am interested in capturing LFO type sounds in nature. Something that starts at a high oscillating rate and drops to a lower one... Does anything come to mind? Animals, natural phenomena (weather, springs, rivers, etc)
A couple of years ago I had the pleasure of watching Encounters at the end of the world at the cinema. The recordings of seals and other marine life in that film are really amazing, and an amazing experience in the cinema
Most of the sounds are like sawtooth LFOs - from high to low.
In a sense though, many natural phenomena create LFO style patterns when graphed on a larger scale. If you think about an environment which contains birds and insects for example, they all fall into a natural rhythm as they try to be heard. This on-off pattern is like a complex interdependent pattern of square waves.
And of course, if you graph the rise and fall of the sea you get the original sine wave:
This is quite a nice clip. As a cicada gets going it's 'chirp' starts of of at a low oscillating rate then progressively increases.
Check out this blog about the dispersion of sound waves in ice sheets:
If you listen to the recording at 35s in particular they captured an awesome sound which may be the kind of thing you're after.
They also share their recording technique which is nice.
The opposite happens with Hornbills. That "ooh-ooh-ooh-AH AH AH" screech one often hears in jungle scenes isn't a monkey, but rather a bird, and it's just the crescendo of a pretty long (multi-minute) song that starts with a low "whoo," not unlike an owl, and raises in frequency of utterance as well as pitch. Still, an interesting (if inversed) morph over time. Recorded this myself in Thailand many years back.
Breaking waves are good, too, as are thunder claps.