The onset of instability for zonal stratospheric flows
数学专题报告
报告题目(Title)：The onset of instability for zonal stratospheric flows
报告人(Speaker)：林治武
地点(Place)：后主楼1124
时间(Time)：2025年7月10下午2:00-3:00
邀请人(Inviter)：许孝精
报告摘要
We investigate some qualitative aspects of the dynamics of the Euler equation on
a rotating sphere that are relevant for stratospheric flows. Zonal flow dominates the dynamics
of the stratosphere and for most known planetary stratospheres the observed flow pattern is
a small perturbation of an n-jet, which corresponds to choosing the Legendre polynomial of
degree n as the stream function. Since the 1-jet and the 2-jet are stable, the main interest
is the onset of instability for the 3-jet. We confirm conjectures based on numerical simulations by proving that there exist positive and negative critical rotation rates
for the linear instability of 3-jet. Turning to the nonlinear problem, we prove that linear instability implies nonlinear instability and that, as the rotating rate goes to infinity, nearby traveling waves gradually change from a cats’s eyes streamline pattern to a profile with no stagnation points. This is a joint work with Adrian Constantin, Pierre Germain and Hao Zhu.
