2009/05/31 by Freddy Bouchet, Hidetoshi Morita · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Asymptotic analysis #Backward Euler method #Classical mechanics #Dissipative system #Euler equations #Euler's formula #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Instability #Mathematical analysis #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Navier-Stokes equation solutions #Physics #Quantum mechanics #Streamlines, streaklines, and pathlines #Vortex #Vorticity #cond-mat.stat-mech #math-ph #math.MP #physics.class-ph
paper · pdf · doi:10.1016/j.physd.2010.01.020
To be published in Physica D, nonlinear phenomena (accepted January 2010)
arxiv created 2010/02/08 · openalex publication_date 2010/02/11 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the asymptotic behavior and the asymptotic stability of the two-dimensional Euler equations and of the two-dimensional linearized Euler equations close to parallel flows. We focus on spectrally stable jet profiles U(y) with stationary streamlines y0 such that U'(y0)=0, a case that has not been studied previously. We describe a new dynamical phenomenon: the depletion of the vorticity at the stationary streamlines. An unexpected consequence, is that the velocity decays for large times with power laws, similarly to what happens in the case of the Orr mechanism for base flows without stationary streamlines. The asymptotic behaviors of velocity and the asymptotic profiles of vorticity are theoretically predicted and compared with direct numerical simulations. We argue on the asymptotic stability of these flow velocities even in the absence of any dissipative mechanisms.