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Time-modulated convection with zero mean temperature gradient
1Department of Mechanical and Aerospace Engineering, University of California at Los Angeles, Los Angeles, California 90095-1597, USA.
Summary
This study numerically investigates temporally modulated Rayleigh-Bénard convection. Results show frequency-dependent synchronous and subharmonic responses, with critical parameters scaling with frequency at high values.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Heat Transfer
Background:
- Rayleigh-Bénard convection is a fundamental model for heat transport.
- Temporal modulation introduces complex dynamics not present in steady-state convection.
- Understanding the onset of convection under time-varying conditions is crucial for various applications.
Purpose of the Study:
- To numerically investigate the onset of temporally modulated Rayleigh-Bénard convection.
- To analyze the effects of antisymmetric and asymmetric boundary temperature conditions.
- To explore the behavior across a wide range of non-dimensional frequencies (omega).
Main Methods:
- Numerical simulations were employed to study the system.
- The study covered a continuous range of non-dimensional frequencies.
- Analysis focused on neutral curves, critical wave number (k(c)), and critical Rayleigh number (R(c)).
Main Results:
- For frequencies below 1, responses alternate between synchronous and subharmonic.
- At high frequencies, critical wave number scales as omega(1/2) and critical Rayleigh number as omega(3/2).
- Subharmonic responses dominate at high frequencies for both boundary conditions.
Conclusions:
- The study reveals complex frequency-dependent dynamics in modulated convection.
- Asymptotic behaviors at high frequencies are identified and characterized.
- Numerical findings show reasonable agreement with existing experimental data.