Hyperbolic lines and the stratospheric polar vortex

Area of Science:

• Geophysical Fluid Dynamics
• Atmospheric Science
• Dynamical Systems

Background:

• Lagrangian hyperbolicity conditions are crucial for understanding fluid flow dynamics.
• Previous studies focused on rigorous mathematical conditions for identifying hyperbolic and elliptic structures.

Purpose of the Study:

• To review and apply recent mathematical conditions for Lagrangian hyperbolicity to stratospheric circulation.
• To compare rigorous conditions with phenomenological and nonrigorous methods for detecting coherent structures.

Main Methods:

• Review of necessary and sufficient conditions for Lagrangian hyperbolicity.
• Application of these conditions to southern hemisphere winter stratospheric wind data (ECMWF).
• Comparison with phenomenological criteria and finite-size Lyapunov exponents (FSLE).

Main Results:

• Rigorous conditions for hyperbolicity were found to be too restrictive (sufficient) or too permissive (necessary) for stratospheric data.
• Phenomenological criteria and FSLE successfully identified hyperbolic structures and elliptic coherent structures (ECS) barriers.
• The sufficient condition for Lagrangian ellipticity was too weak to detect ECS like the polar vortex.

Conclusions:

• Rigorous mathematical conditions for Lagrangian hyperbolicity and ellipticity are insufficient for analyzing stratospheric dynamics.
• Nonrigorous methods, particularly FSLE, show potential for identifying chaotic mixing and coherent structures in geophysical flows.
• Further theoretical work is needed to reconcile rigorous and nonrigorous approaches for a complete kinematic understanding.