报告题目: Dynamic transitions in axisymmetric nonlinear systems and applications
Dynamic transitions of dissipative systems can be classified into three categories:continuous type,
catastrophic type, and mixed type. In fluid dynamics, it is essential to know the specific transition type
involved in many unstable phenomena. In this talk, we aim to completely classify the dynamic transitions
arising in the axisymmetric systems modeled by the equations with a fourth-second order structure, thus
covering a broad class of problems in geophysical fluid dynamics. A transition theorem is established by
reducing the governing equations to a system of ODEs, derived by employing approximate invariant
manifolds. We also provide an algorithm by which one can numerically determine the transition type for
any problem whose governing equations are equipped with the required fourth--second order structure.
Finally, we apply our results to examine the transition types associated with the baroclinic instability in a
quasi-geostrophic system in an annular channel.
王泉，美国印第安纳大学博士后，四川大学特聘研究员，主要从事相变动力学、流体动力学稳定性与大气科学方向的研究工作，在SCI检索刊物Physics of Fluids、Journal of Differential Equations、Physica D、Journal of the Atmospheric Sciences等一流期刊上发表学术论文20余篇。