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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Convective instability and boundary driven oscillations in a reaction-diffusion-advection model
Estefania Vidal-Henriquez1, Vladimir Zykov1, Eberhard Bodenschatz1
1Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
Chaos (Woodbury, N.Y.)
|November 3, 2017
Summary
A fixed upstream boundary in reaction-diffusion-advection systems can create a new local instability, generating continuous waves. This boundary-induced wave source is suppressed at high advection speeds.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Mathematical biology
Background:
- Reaction-diffusion-advection systems exhibit complex spatiotemporal dynamics.
- Convective instability leads to downstream advection of perturbations.
- Understanding wave generation and propagation is crucial in various scientific fields.
Purpose of the Study:
- To investigate the emergence of a novel instability in reaction-diffusion-advection systems with a fixed upstream boundary.
- To characterize the properties of the boundary-induced wave source.
- To explore the influence of advection speed on this instability.
Main Methods:
- Analytical analysis of a modified Martiel-Goldbeter reaction-diffusion model.
- Numerical simulations incorporating an advection term.
- Quantitative description and characterization of wave packets.
Main Results:
- A fixed upstream boundary condition can induce a local absolute instability alongside convective instability.
- This boundary-induced instability acts as a continuous wave source, generating waves propagating both upstream and downstream.
- The newly identified instability is suppressed in the limit of high advection speeds.
Conclusions:
- Boundary conditions can fundamentally alter the stability properties of reaction-diffusion-advection systems.
- The discovered instability provides a mechanism for continuous wave generation in convectively unstable regimes.
- This finding has potential implications for understanding biological signaling, such as in Dictyostelium discoideum.
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