Acoustic black and white holes of potential flow in a tube

We propose a new simple model of acoustic black hole in a thin tube, where the difference in the gravitational potential is used to create a transonic flow. The main merit of our transonic flow model is that the Euler equations can be solved analytically. In fact, we can obtain an exact solution to the equation in terms of a height function in the monatomic case gamma 1/4 5/3. For arbitrary gamma, we find that it takes a simple form by the near-sonic approximation. Moreover, we obtain two analytic solutions describing a backward wave and a forward wave, from which we can confirm the existence of sonic horizons.

Automated summary

We propose a new simple model of an acoustic black hole in a thin tube by utilizing the difference in gravitational potential to generate transonic flow. The analytical solution for the Euler equations can be obtained in our transonic flow model, providing an exact solution in terms of a height function for the monatomic case with gamma 1/4 5/3. By the near-sonic approximation, we find a simple form for arbitrary gamma. Additionally, two analytic solutions describing a backward wave and a forward wave are obtained, demonstrating the existence of sonic horizons.