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Updated: Apr 16, 2026
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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Modulational instability of co-propagating internal wavetrains under rotation
1Department of Mathematics, University College London, London WC1E 6BT, United Kingdom.
Chaos (Woodbury, N.Y.)
|March 2, 2015
Summary
Earth's rotation stabilizes long internal waves, unlike in non-rotating systems. This study analyzes the coupled nonlinear Schrödinger equation for the Ostrovsky equation, revealing stabilization conditions for wavetrain pairs.
Area of Science:
- Fluid dynamics
- Oceanography
- Nonlinear wave theory
Background:
- Long internal waves in non-rotating frames are described by the Korteweg-de Vries (KdV) equation.
- KdV theory predicts stability for isolated monochromatic wavetrains.
- Coupled nonlinear Schrödinger equation (CNLS) analysis reveals instability in systems of two co-propagating KdV wavetrains.
Purpose of the Study:
- To investigate the effect of Earth's rotation on the stability of co-propagating internal wavetrains.
- To derive the CNLS equation for the rotation-modified KdV, or Ostrovsky, equation.
- To identify conditions under which rotation stabilizes these wave systems.
Main Methods:
- Derivation of the CNLS equation for the Ostrovsky equation.
- Analysis of the stability of wavetrain pairs within this framework.
- Focus on cases with different wavenumbers but identical linear group speeds.
Main Results:
- Earth's rotation can stabilize pairs of co-propagating internal wavetrains.
- Stabilization occurs when both waves' wavelengths exceed that of the fastest linear wave.
- The derived CNLS for the Ostrovsky equation governs this rotational stabilization.
Conclusions:
- Rotation introduces a stabilizing effect on long internal waves that is absent in non-rotating systems.
- The Ostrovsky equation framework provides a means to study this rotational stabilization.
- Understanding these stability dynamics is crucial for modeling internal wave propagation in oceanic environments.
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