Doesn't anybody writing military stories have military experience anymore? A subsonic jet flying low makes a crackling roar when very close, though some, like the FA-18 are less noisy, but still very loud. The F-35 here at Pax makes my head hurt. The faster the subsonic jet goes, the more lag there is between when you see it until you hear it, so the buildup of the noise much more sudden. Not a sonic boom, but goes from a distant rumble to crackling thunder very quickly. If the aircraft is supersonic, you won't hear it at all until it passes you and the boom, which is very bomblike, arrives. On the Connie, I had the wife and small kids aboard for a dependents cruise, and we had an F-14 flyby with the wings in full supersonic fold. There is a mist coming off the wing and nose at nearly right angles to the fuselage, the shockwave condensing the air. It was approaching in total silence, as it was going faster than the sound it made. It passed about a thousand feet abeam and maybe 200 ft altitude, I told Karen to cover the kid's ears. The boom made the 85000 ton carrier's deck jump, and knocked pictures of the wall below decks. That was followed by conventional jet noise arriving from behind and receding into the distance, simultaneously, which is impossible to describe. And you are correct, ejecting ordnance into a supersonic slipstream is not in the NATOPS manual for most jets. The supersonic A5C Vigilante tried ejecting nukes out the tail like a turd, because the engineers thought that would work. However, the weapon had a habit of following the jet's slipstream, so that mission never materialized. I've never noted a Doppler shift as described above from a jet because the noise is too white, all frequencies, each shifting proportionally differently. Doppler shifted white noise is still white noise. A prop aircraft will definitely show one. Though if the aircraft pulls up abruptly after a low pass, that is another sound entirely, as the prop takes a bigger bite of air. Watch WWII movies for them. Go watch Top Gun for jets. Better yet, go down to your local recruiting office and live the life for a while, and learn to love it, before you try to write about it.
I was on tanks. I know tanks. Ive been around everything. I live next to an AFB. When the jets take off and land, everyone hears it.
As someone who has worked with jets, its a whooshing sound mixed with thunder. Its a sound with a lot bass, you can really feel it in the depths of chest. Imagine a cannon being fired, yet that sound never stopped and was continuously that loud.
Why not 'thunder?' It doesn't matter, really, what anyone else thinks it sounds like. This is your story and you need to share with your reader what you think it sounds like. I know you're not likely to think that's very helpful, but if you come up with your own word(s) here, you'll feel a lot better about it in the long run. Just remember this: you can't be wrong. The word you pick after agonizing over it until your head hurts will be, in the end, the perfect word.
I spent my entire youth on USAF bases. A fighter jet roars. None of the videos capture the fact that a low altitude fighter jet makes a sound that is as much felt as heard. It vibrates you and makes you cognizant of parts of your inner body that are silent at all other times of one's life.
In 1987, I lost hearing in my left ear due to an RC-135 on ground run up with water injection about 50-100 yards away. What Wreybies said is spot on, it was a crackling roar, the crackling as much inside me as outside, and as I was unable to cover my left ear, a week later it was dead, in the middle of the speech band. Stayed physically qualified for flying duties, though, and retired a few years later.
Zzzzzzzzzzzzzzzeeeeeeeeeeeeeeeaaaaaaaaaaarrrrrrrrrrrrr! That's what my mind thinks it hears. Zear, just pronounced longer.