Séminaires à venir

Séminaires du LadHyX
(10h45-Bât. 67-Bibliothèque)
Séminaires Mécanique et Systèmes Vivants
(Bât. Turing)

Lieu : Bibliothèque LadHyX, 10h45

Résumé :

Without instabilities, gas around a forming protostar remains in orbit, and the final star cannot form; dust grains cannot accumulate to form planets; and the compositions of meteorites cannot be explained. Unfortunately, the Keplerian motion within a disk is assumed by most astrophysicists to be stable by Rayleigh’s theorem because the angular momentum of the disk increases with increasing radius. We show that there is a new purely hydrodynamic instability that is violent and destabilizes the protoplanetary disk, filling it with turbulence. The essential ingredients of the new instability are rotation, shear, and vertical density stratification, so the instability can occur in stratified Boussinesq (or fully compressible) Couette flows. Our new instability, called the zombie vortex instability, occurs at critical layers where neutrally-stable eigenmodes are singular in the inviscid limit (but finite, with a width that scales as the Reynolds number Re to the -1/3 power when viscosity is present) and requires an initial finite-amplitude perturbation. In a flow initialized with weak Kolmogorov noise with initial Mach number Ma, when Ma > Re-1/2 (~10-7 in a protoplanetary disk) the instability will be triggered and create turbulence and large-volume and large-amplitude vortices that fill the disk. When the initial perturbation is an isolated vortex, the vortex triggers a new generation of vortices at the nearby critical layers. After this second generation of vortices grows large, it triggers a third generation. The triggering of subsequent generations continues ad infinitum in a self-similar manner creating a 3D lattice of turbulent 3D vortices. Viscous dissipation, although unimportant in protoplanetary disks, is important in lab flow, so we consider how dissipation might affect the search for a zombie instability in laboratory Couette flows.

Lieu : Bibliothèque LadHyX, 10h45

Résumé :

The current Juno spacecraft mission to Jupiter provides us with a wealth of new data to which we can apply geophysical fluid dynamics to better understand the Jovian atmosphere’s global circulation and dynamics. First, we discuss the Thermal Wind Equation (TWE), which provides the relationship between horizontal gradients of the temperature and vertical wind shear. This textbook equation is not valid at or near the equator, but here we derive an extension of it that is valid and which allows us to deduce wind shears, vertical plumes, and global circulations in the Jovian tropics. We also show how this new TWE can be used for the atmospheres of earth and Neptune. We also examine the unexpected longevity of Jupiter’s Great Red Spot and other geophysical vortices. Vortices in the ocean and atmosphere dissipate energy via various mechanisms, including wave emission, turbulence, viscous loss, and thermal radiation. However, many astrophysical and geophysical these vortices are observed to live much longer than the time scales of these dissipation processes. Here we model these processes as either Rayleigh drag or Newtonian cooling with time scale and use simulations of the 3D Boussinesq equations to model observations. Our results show that vortices in fact do NOT decay at the imposed Rayleigh or Newton time scales; they decay much slower, sometimes by factors of 100. The slow decay is due to secondary meridional circulation crated by the primary vortices, which converts potential energy to the kinetic energy and vice versa and slows down the decay. In the presence of horizontal shear, the circulation can extract the shear energy and further energize the vortex. We explain the existence of the meridional circulation, the slow decay, and the resulting cyclone-anticyclone asymmetry using the numerical results, a physical model, and simplified equations. Our results suggest that the observed longevity of some vortices can be explained without a forcing mechanism. For very long-lived vortices, such as the Great Red Spot, our results imply that much weak forcing, compared to what originally thought, is needed to maintain the vortices indefinitely.