Steady vortices in plasmas and geophysical flows

Area of Science:

• Geophysical Fluid Dynamics
• Plasma Physics
• Nonlinear Dynamics

Background:

• Two-dimensional fluid models are crucial for understanding complex phenomena in geophysical fluid dynamics and plasma physics.
• The existence of steady, localized vortex solutions is a fundamental question with implications for energy transport and stability.
• Previous studies have explored vortex solutions in specific models, but a general method for diverse systems is needed.

Purpose of the Study:

• To develop and apply a general method for determining the existence of steady, localized monopole vortex solutions in various 2D fluid models.
• To investigate vortex dynamics in geophysical fluid dynamics and plasma physics, including shallow-water equations, drift wave models, and two-field models.
• To analyze the influence of external flows on vortex stability and existence.

Main Methods:

• A two-step method was employed: first, calculating the dispersion relation to find linear wave phase velocities.
• Second, deriving an integral relation for the vortex's center-of-mass velocity and comparing it to the phase velocity spectrum.
• The existence condition is met if the center-of-mass velocity falls outside the range of linear phase velocities.

Main Results:

• Steady localized vortices exist in plasma drift wave models and shallow-water equations when their amplitude is sufficiently large.
• For coupled ion acoustic-drift modes, steady vortices are possible if the ratio of parallel ion velocity to electrostatic potential is large enough.
• In quasigeostrophic two-layer equations, steady vortices can form by combining baroclinic and barotropic components, exceeding Rossby wave speeds.

Conclusions:

• The developed method provides a general framework for identifying steady vortex solutions across different 2D fluid models.
• The existence of steady vortices is contingent on the vortex's center-of-mass velocity surpassing the maximum phase velocity of linear waves.
• External zonal flows can modify vortex dynamics, with anticyclonic shear zones potentially enhancing westward propagation and easterly jets offering shielding.