Speed of sound in vortical flows

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Discussion Overview

The discussion centers around the speed of sound in vortical flows, particularly in the context of ideal gases. Participants explore theoretical frameworks and seek resources for understanding sound propagation in such flows, contrasting it with linear gaseous flows.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for books or papers on the speed of sound in vortical flows, indicating a gap in available resources.
  • Another participant states that in an ideal gas, the speed of sound is given by the formula a = √(γRT), asserting that this holds regardless of whether the flow is vortical or not, as long as the gas is ideal.
  • A third participant references a paper that derives equations for sound in fluids with vorticity, suggesting a more complex approach to understanding sound propagation in such flows.
  • One participant questions the necessity of using advanced formulations like Clebsch potentials for determining the speed of sound in a gas, expressing curiosity about the conditions that warrant such complexity.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of standard sound speed equations in vortical flows versus the need for more complex models. There is no consensus on the necessity or relevance of advanced theoretical frameworks for the original question posed.

Contextual Notes

Some assumptions about the ideal gas behavior and the applicability of certain mathematical models remain unresolved. The discussion reflects varying levels of familiarity with the theoretical concepts involved.

Who May Find This Useful

Researchers or students interested in fluid dynamics, particularly those exploring sound propagation in complex flow regimes, may find this discussion relevant.

zak8000
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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
 
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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.
 
“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
 
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.
 

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