Speed of sound in vortical flows

[zak8000]

hi there

I am currently working with linear flows and using a ultrasonic setup to determine the speed of sound in a linear gaseous flow. But I would like to know more about the speed of sound in a vortical flow. Unfortunately I haven't been able to find any good book with regard to my topic and was wandering anyone could offer a good book or paper to get me going

thanks

 

[boneh3ad]

In an ideal gas, the speed of sound is always $a = \sqrt{\gamma R T}$ where $\gamma$ is the ratio of specific heats, $R$ is the specific gas constant and $T$ is the static temperature. It doesn't matter if it is vortical or quiescent or anything else as long as it is an ideal gas in this case.

 

[Bobbywhy]

“Wave Equation for Sound in Fluids with Vorticity”

“Abstract
We use Clebsch potentials and an action principle to derive a closed system
of gauge invariant equations for sound superposed on a general background
flow. Our system reduces to the Unruh (1981) and Pierce (1990)
wave equations when the flow is irrotational, or slowly varying. We illustrate
our formalism by applying it to waves propagating in a uniformly rotating
fluid where the sound modes hybridize with inertial waves.”
http://arxiv.org/abs/cond-mat/0106255

 

[boneh3ad]

Assuming you have an ideal gas and can treat it as a continuum, there is no need to set up a wave equation and Clebsch potentials (of which I am only vaguely familiar) in order to determine the speed of sound at a given point in a gas.

Of course me being me, now I am on a quest to figure out why the authors required a more complicated formulation like in the linked paper. They didn't really explain when and why you would need that in the paper and I don't have time to dig any further at the moment, but I am quite curious. The authors seem mostly interested in vorticity in superfluids, and I doubt that applies all that well to the OP's question, though I guess it might.

 

[PJC01]

for your interest in the speed of sound in vortical flows! This is a very interesting and complex topic that has been studied by many scientists and researchers. I would recommend looking into some papers and books by experts in the field such as Prof. William K. George from the University of Illinois at Urbana-Champaign or Prof. Alexander Smits from Princeton University. Some specific papers that may be of interest to you include "Acoustics of vortical flows" by Prof. George and "Sound generation in high-speed turbulent shear flows" by Prof. Smits. These papers can provide a good overview of the current understanding and research in this area. Additionally, looking into journals such as the Journal of Fluid Mechanics or the Journal of Sound and Vibration may also provide valuable information on the subject. I hope this helps and good luck with your research!