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Eulerian mean flow from an instability of convective plumes
1Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study models plumes in thermal convection to understand large-scale flow origins. It identifies an instability in vertical flow that leads to steady Eulerian mean flow, linking it to plume profiles.
Area of Science:
- Fluid Dynamics
- Thermodynamics
- Instability Theory
Background:
- Large-scale flows are crucial in systems driven by Archimedean forces.
- Thermal convection at high Rayleigh and Prandtl numbers exhibits complex plume dynamics.
Purpose of the Study:
- To investigate the dynamical origin of large-scale flows in systems driven by concentrated Archimedean forces.
- To model plume behavior in thermal convection and deduce the onset of mean flow.
Main Methods:
- Development of a two-dimensional model of plumes.
- Analysis of convective states with parallel vertical flow driven by buoyancy.
- Derivation of the linear instability equation and identification of instability modes.
Main Results:
- An instability of the convective state leads to the onset of mean flow.
- One instability mode results in steady Eulerian mean flow.
- The origin of mean flow is directly linked to the profiles of unperturbed plumes.
Conclusions:
- The study provides a precise link between plume profiles and the emergence of large-scale Eulerian mean flow.
- A nonlinear partial differential equation for Eulerian mean flow was derived for a special case.
- The findings lay the groundwork for extending the analysis to three-dimensional systems.