can anybody give me an explanation about what is the acoustic source for a plunging jet, like tap flow enter into a basin? is there any exiting theory like Lighthill theory in aero-acoustic to explain that?
My understanding is that, in general, sound in fluid flows is generated by aspects of the flow that cause transient pressure fluctuations with a particular frequency (or range of frequencies). So, in fluids, turbulence is a major source. If a flow is completely steady and laminar, then there won't be any transient pressure fluctuations to cause sound to be produced.
In a flow with a free surface, such as that you describe, I would think it also possible that surface waves caused by the plunging jet could be a source of sound waves.
Acoustics is a whole field of Engineering/Physics, which contains a lot of theory (such as the Lighthill theory you mention). However, I'm not an acoustics expert and I don't know what theory exists about that specific case you mention.
This question might also be relevant.