Stability of barotropic vortex strip on a rotating sphere

Area of Science:

• Fluid dynamics
• Geophysical fluid dynamics
• Atmospheric science

Background:

• Jet streams are crucial atmospheric phenomena influencing global weather patterns.
• Barotropic vortex strips serve as simplified models for understanding jet stream dynamics.

Purpose of the Study:

• To analyze the linear and nonlinear stability of a barotropic vortex strip on a rotating sphere.
• To model atmospheric jet streams and investigate their stability characteristics.
• To explore the geophysical relevance to planetary jet streams.

Main Methods:

• Linear stability analysis of a piecewise-continuous vorticity distribution.
• Numerical computation of nonlinear vortex strip evolution.
• Comparison of linear and nonlinear results.

Main Results:

• Vortex strip stability increases with width and rotation speed.
• The inner flow region is most unstable when polar vorticities are positive and equal.
• Complex instabilities and remote instability regions emerge with opposing polar vorticities.
• Nonlinear simulations show good agreement with linear analysis for small widths, leading to rolling-up vortex cores.

Conclusions:

• The barotropic vortex strip model provides insights into jet stream stability.
• Planetary rotation and vorticity distribution significantly impact jet stream behavior.
• The model's findings have relevance for understanding jet streams on Jupiter, Saturn, and Earth.