MEchanics GAthering -MEGA- Seminar: Talk1 - How non-normality affects turbulent trajectories; Talk2 - Fully nonlinear invariant solutions underlying patterns of Jupiter’s atmosphere
Event details
| Date | 15.11.2018 |
| Hour | 16:15 › 17:30 |
| Speaker | Mirko Farano and Ayse Yesil, ECPS, EPFL |
| Location | |
| Category | Conferences - Seminars |
How non-normality affects turbulent trajectories by Mirko Farano, ECPS, EPFL
Abstract In any dynamical systems, energy growth is usually associated to the presence of unstable modes. However, transient energy growth can also be observed along stable modes. This is due to the non-normality. Non-normality is a property of a dynamical system to exhibit energy amplification for a short time scale, although the starting point is a stable equilibrium. This is due to the non-orthogonality of the eigenmodes of the linearized operator around the starting point. Navier-Stokes equations which are the governing equations of the fluid motion belong to this category, i.e. non self-adjoint systems. We describe the turbulent flow dynamic using a dynamical system approach. For this system transition to turbulence can also be understood by looking at the most amplified modes. Nevertheless the role of the non-normality has not been extensively investigated in the turbulent regime, where trajectories are believed to walk along dynamical connections between equilibria. We investigate the possibility that these connections are thus affected by the non-normality, and diverge from homo/hetero-clinic connections which are currently believed to lead the dynamics.
Fully nonlinear invariant solutions underlying patterns of Jupiter’s atmosphere by Ayse Yesil, ECPS, EPFL
Abstract As far as we know, Jupiter has always had belts on its atmosphere. They have been there since we first looked up in the sky with our telescopes. However, it is still a mystery how these long living structures emerged under the tremendously turbulent atmospheric conditions of the gas giant. With a nonlinear mathematical model, whose main assumption is supported by NASA’s current mission Juno, I am searching for the possible mechanisms that underly the formation of these coherent structures. Particularly, I will discuss the time-invariant solutions of the Busse’s annulus equations in the parameter regime where the system is capable of supporting multiple belt structures.
Abstract In any dynamical systems, energy growth is usually associated to the presence of unstable modes. However, transient energy growth can also be observed along stable modes. This is due to the non-normality. Non-normality is a property of a dynamical system to exhibit energy amplification for a short time scale, although the starting point is a stable equilibrium. This is due to the non-orthogonality of the eigenmodes of the linearized operator around the starting point. Navier-Stokes equations which are the governing equations of the fluid motion belong to this category, i.e. non self-adjoint systems. We describe the turbulent flow dynamic using a dynamical system approach. For this system transition to turbulence can also be understood by looking at the most amplified modes. Nevertheless the role of the non-normality has not been extensively investigated in the turbulent regime, where trajectories are believed to walk along dynamical connections between equilibria. We investigate the possibility that these connections are thus affected by the non-normality, and diverge from homo/hetero-clinic connections which are currently believed to lead the dynamics.
Fully nonlinear invariant solutions underlying patterns of Jupiter’s atmosphere by Ayse Yesil, ECPS, EPFL
Abstract As far as we know, Jupiter has always had belts on its atmosphere. They have been there since we first looked up in the sky with our telescopes. However, it is still a mystery how these long living structures emerged under the tremendously turbulent atmospheric conditions of the gas giant. With a nonlinear mathematical model, whose main assumption is supported by NASA’s current mission Juno, I am searching for the possible mechanisms that underly the formation of these coherent structures. Particularly, I will discuss the time-invariant solutions of the Busse’s annulus equations in the parameter regime where the system is capable of supporting multiple belt structures.
Practical information
- General public
- Free
Organizer
- MEGA.Seminar Organizing Committee