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Updated: Sep 25, 2025
07:28
Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
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Steady thermal convection representing the ultimate scaling
Shingo Motoki1, Genta Kawahara1, Masaki Shimizu1
1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
Summary
New solutions to the Navier-Stokes equations reveal ultimate scaling in thermal convection. Wall permeability significantly influences heat transfer, showing heat flux scaling independently of thermal diffusivity.
Area of Science:
- Fluid Dynamics
- Heat Transfer
- Nonlinear Dynamics
Background:
- The Navier-Stokes equations govern fluid motion, including thermal convection.
- Understanding heat transfer in confined spaces with permeable boundaries is crucial for various applications.
- Previous studies have explored thermal convection but often with impermeable walls or different boundary conditions.
Purpose of the Study:
- To discover nonlinear simple invariant solutions for thermal convection between permeable walls.
- To investigate the impact of wall permeability on the onset and scaling properties of thermal convection.
- To analyze the ultimate scaling regime and its characteristics.
Main Methods:
- Solving the Navier-Stokes equations for thermal convection with specific boundary conditions (no-slip, permeable walls).
- Utilizing a Newton-Krylov iteration method to obtain two-dimensional steady solutions.
- Analyzing solutions up to high Rayleigh numbers (Ra) and varying parameters like Prandtl number (Pr) and permeability.
Main Results:
- Discovered nonlinear simple invariant solutions representing ultimate scaling.
- Observed ultimate scaling (Nu ~ Ra^(1/3)) for specific conditions (Pr=1, large Ra).
- Demonstrated that wall permeability significantly affects convection onset and scaling, leading to large-scale plumes and strong vertical velocities.
Conclusions:
- Wall permeability plays a critical role in thermal convection dynamics and heat transport.
- The ultimate scaling regime exhibits wall-to-wall heat flux independent of thermal diffusivity.
- The findings provide insights into heat transfer mechanisms in systems with permeable boundaries.
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