2013/03/13 by Solomon Endlich, Alberto Nicolis, Endlich, Solomon +1
Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #High Energy Physics - Theory (hep-th) #Quantum, superfluid, helium dynamics #Solar and Space Plasma Dynamics #hep-th #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1303.3289
29 pages + 10 page appendix
arxiv created 2013/03/13 · openalex publication_date 2013/03/13 · arxiv updated 2013/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. Our analysis is fully relativistic, but, if desired, the non-relativistic limit can be taken at any stage. We demonstrate the potential of our method by some sample calculations: the relativistic corrections to the emission and to the scattering of sound by vorticose (possibly turbulent) motions, and, more interestingly, the vortex-vortex long range interaction mediated by sound. These results are, to our knowledge, new. For the last one, we find a 1/r3 potential between localized vortex configurations (e.g., vortex rings), whose strength and detailed structure depend on a certain multipole moment of the vortices under consideration. We also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory.