Instability in stratified accretion flows under primary and secondary perturbations

Area of Science:

• Fluid Dynamics
• Astrophysics
• Plasma Physics

Background:

• Understanding the stability of rotating and stratified shear flows is essential in astrophysical contexts.
• Accretion disks are complex systems where shear, rotation, and stratification play critical roles.

Purpose of the Study:

• To investigate the conditions under which parametric instability can develop in a horizontal linear shear flow with vertical rotation and stratification.
• To analyze the implications of this instability for astrophysical accretion flows.

Main Methods:

• The study considers a horizontal linear shear flow with vertical uniform rotation and stratification in an unbounded domain.
• A primary vertical velocity perturbation and a radial density perturbation are introduced to analyze parametric instability.
• The analysis is extended to the shearing sheet approximation relevant for astrophysical accretion flows.

Main Results:

• A parametric instability can develop if N(2) > 8Ω(0)(2Ω(0)-Λ), where N is the buoyancy frequency, Ω(0) is the ambient rotation rate, and Λ is the shear rate.
• For astrophysical accretion flows, this condition translates to N(2) > 8Ω(0)(2)(2-q), where q is the local shear gradient.
• In a stratified constant angular momentum disk (q=2), instability occurs for any N>0 with a maximal growth rate of (3√[3]/16)ɛ.
• For a stratified Keplerian disk (q=1.5), instability requires N > 2Ω(0), with a maximal growth rate dependent on Ω(0)/N.

Conclusions:

• Parametric instability is a viable mechanism in stratified shear flows with rotation.
• The findings provide insights into the stability of astrophysical accretion disks, particularly concerning the influence of stratification and shear.
• The specific conditions for instability and growth rates vary between different disk models (e.g., constant angular momentum vs. Keplerian).