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A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing.
Baolian Cheng1, J. Glimm, D. H. Sharp
1Applied Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study models bubble mergers in unstable, acceleration-driven mixing layers, revealing a self-similar process. The renormalization group (RNG) model predicts chaotic fluid mixing rates and bubble dynamics, matching experimental data.
Area of Science:
- Fluid Dynamics
- Complex Systems
Background:
- Unstable acceleration-driven (Rayleigh-Taylor) mixing layers exhibit complex bubble merger dynamics.
- Previous models were limited, often to two dimensions, and lacked detailed prediction of experimental parameters.
Purpose of the Study:
- To formulate a three-dimensional model for bubble mergers in Rayleigh-Taylor mixing layers.
- To predict the growth rate and key parameters of chaotic fluid mixing.
- To compare model predictions with experimental results for validation.
Main Methods:
- Developed a model incorporating single bubble velocity, envelope velocity, and a merger process driving an inverse cascade.
- Utilized renormalization group (RNG) evolution to analyze large-time asymptotics and fixed points.
- Incorporated a phenomenological parameter for bubble radii variance and used experimental data for calibration.
Main Results:
- The model predicts the bubble mixing rate (alpha(b)) to be approximately 0.05-0.06.
- It accurately determines mean bubble radius and height separation at merger.
- The model achieves agreement with experimental bubble height-to-width aspect ratios.
Conclusions:
- The developed 3D model successfully captures the self-similar inverse cascade in Rayleigh-Taylor mixing.
- Model predictions align with experimental observations, validating its approach.
- The study provides a framework for understanding chaotic fluid mixing phenomena.