Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions
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Summary
This summary is machine-generated.We developed a 2D model for slow-fast quasilinear systems, enabling efficient computation by slaving fast fluctuations to mean fields. This approach reveals marginal stability manifolds organizing complex multiscale flows.
Area Of Science
- Fluid dynamics
- Dynamical systems theory
- Computational physics
Background
- Quasilinear (QL) systems with fast instabilities exhibit complex dynamics.
- Scale separation between slow mean fields and fast fluctuations is key.
- Existing formalisms are limited, particularly in higher dimensions.
Purpose Of The Study
- Extend a formalism for slow-fast QL systems to two dimensions (2D).
- Develop an efficient hybrid solution algorithm exploiting scale separation.
- Investigate the role of marginal stability in organizing flow dynamics.
Main Methods
- Derivation of a 2D extension of the slow-fast QL formalism.
- Development of a hybrid fast-eigenvalue/slow-initial-value algorithm.
- Derivation of an ODE for the evolution of the fastest-growing mode's wave number.
Main Results
- The 2D formalism successfully slaved fast fluctuations to mean fields, maintaining marginal stability.
- An ODE governing the slow evolution of the fastest-growing mode's wave number was derived.
- The model demonstrated the concept of marginal stability manifolds in geophysical turbulence.
Conclusions
- Marginal stability manifolds are crucial organizing structures in multiscale flows.
- The developed formalism and algorithm offer efficient analysis of 2D QL systems.
- This approach provides insights into quasicoherent structures in constrained geophysical turbulence.
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