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Updated: Jun 14, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Stability of rotating stratified shear flow: an analytical study
Summary
This study analyzes the stability of rotating, stratified shear flows. We found that stability depends on rotation number (R) and Richardson number (Ri), with complex behaviors like power-law growth or decay observed even in stable cases.
Area of Science:
- Fluid Dynamics
- Geophysics
- Astrophysics
Background:
- Unbounded shear flows are fundamental in fluid dynamics, with stability influenced by stratification and rotation.
- Understanding these flows is crucial for geophysical and astrophysical phenomena.
Purpose of the Study:
- To investigate the linear stability of unbounded shear flow under uniform vertical density stratification and system rotation.
- To analytically determine the conditions for stability and instability based on rotation and Richardson numbers.
Main Methods:
- Governing equation for plane-wave disturbances derived, involving time-dependent coefficients.
- Analytical solution obtained using Legendre functions.
- Long-time behavior analyzed via asymptotic representations of Legendre functions.
Main Results:
- Stability criteria established in terms of rotation number (R) and Richardson number (Ri).
- Identified conditions for linear stability and instability, including specific ranges for R and Ri.
- Observed coexistence of power-law growth/decay and damped oscillations in 'exponentially stable' cases.
Conclusions:
- The study provides comprehensive stability diagrams for rotating stratified shear flows.
- Highlights the significance of the k(1)=0 mode for spectral energy contributions.
- Offers analytical calculations for 2D kinetic and potential energy contributions in the streamwise direction.
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