MEchanics GAthering -MEGA- Seminar: Talk1 - Instability driven relaxation of an anticyclone; Talk2 - Pattern formation of a thin film flowing under an inclined plane
Event details
Date | 14.11.2019 |
Hour | 16:15 › 17:30 |
Speaker | Eunok Yim & Pier Giuseppe Ledda, LFMI, EPFL |
Location | |
Category | Conferences - Seminars |
Instability driven relaxation of an anticyclone, by Eunok Yim
We study the nonlinear evolution of the centrifugal instability appearing in a columnar anticyclone using a semi-linear approach to model the transient unsteady flow evolution in a self-consistent manner. For anticyclones in a homogeneous viscous flow, the fastest growing instability is without oscillation in time but with a finite axial wavenumber. Hence, the self-consistent model is developed around the spatially averaged time dependent meanflow and the fluctuation, which reduces the problem from 2D nonlinear to 1D semi-linear. The two linear meanflow and fluctuation equations are coupled via the Reynolds stress of the fluctuations.
At a given rotation ratio between the vortex angular velocity and the background rotation, only the most linearly unstable mode is considered for Reynolds numbers Re=800 and 2000 defined with the maximum angular velocity and the radius of the vortex. For both values of Re, the model predicts well the nonlinear evolution of the meanflow and the fluctuation amplitude. Higher harmonics are non-negligible only at the highest value of Re. The results show that the angular momentum of the meanflow is homogenized to a stable state via the action of the Reynolds stresses of the fluctuation.
Pattern formation of a thin film flowing under an inclined plane, by Pier Giuseppe Ledda
We discuss the pattern formation of a thin film flowing under an inclined planar substrate, combining theoretical, experimental and numerical results. The phenomenon is related to the Rayleigh-Taylor instability, in which one heavier fluid is placed above a lighter one. When an upper wall and the substrate inclination are considered, a variety of patterns are observed. The natural and forced dynamics of the flat film to spanwise perturbations and the resulting non-linear structures are studied; in both cases, spanwise-periodic, streamwise-aligned structures, called rivulets, arise. The impulse response of a flat film is numerically and experimentally studied. We analyze the linear response, which does not show any preferential direction; a weakly non-linear model highlights however the selection of the streamwise structures. The fully non-linear evolution leads to a steady pattern characterized by fully saturated rivulets, the profile of which is analyzed in detail. A secondary stability analysis reveals the presence of a range of parameters in which only rivulets are observed, in agreement with the experimental observations. Outside of this range, lenses appear on the rivulets, which may eventually drip.
We study the nonlinear evolution of the centrifugal instability appearing in a columnar anticyclone using a semi-linear approach to model the transient unsteady flow evolution in a self-consistent manner. For anticyclones in a homogeneous viscous flow, the fastest growing instability is without oscillation in time but with a finite axial wavenumber. Hence, the self-consistent model is developed around the spatially averaged time dependent meanflow and the fluctuation, which reduces the problem from 2D nonlinear to 1D semi-linear. The two linear meanflow and fluctuation equations are coupled via the Reynolds stress of the fluctuations.
At a given rotation ratio between the vortex angular velocity and the background rotation, only the most linearly unstable mode is considered for Reynolds numbers Re=800 and 2000 defined with the maximum angular velocity and the radius of the vortex. For both values of Re, the model predicts well the nonlinear evolution of the meanflow and the fluctuation amplitude. Higher harmonics are non-negligible only at the highest value of Re. The results show that the angular momentum of the meanflow is homogenized to a stable state via the action of the Reynolds stresses of the fluctuation.
Pattern formation of a thin film flowing under an inclined plane, by Pier Giuseppe Ledda
We discuss the pattern formation of a thin film flowing under an inclined planar substrate, combining theoretical, experimental and numerical results. The phenomenon is related to the Rayleigh-Taylor instability, in which one heavier fluid is placed above a lighter one. When an upper wall and the substrate inclination are considered, a variety of patterns are observed. The natural and forced dynamics of the flat film to spanwise perturbations and the resulting non-linear structures are studied; in both cases, spanwise-periodic, streamwise-aligned structures, called rivulets, arise. The impulse response of a flat film is numerically and experimentally studied. We analyze the linear response, which does not show any preferential direction; a weakly non-linear model highlights however the selection of the streamwise structures. The fully non-linear evolution leads to a steady pattern characterized by fully saturated rivulets, the profile of which is analyzed in detail. A secondary stability analysis reveals the presence of a range of parameters in which only rivulets are observed, in agreement with the experimental observations. Outside of this range, lenses appear on the rivulets, which may eventually drip.
Practical information
- General public
- Free
Organizer
- MEGA.Seminar Organizing Committee