Bounding temperature dissipation in time-modulated Rayleigh-Bénard convection
Abstract
We use the background method to find an upper bound on the nondimensional temperature dissipation, ‖ ∇ T » 22‖ for Rayleigh-Bénard convection with the temperature of one boundary modulated in time. The resulting bound depends on characteristics of the temperature modulation profile, f (t ) , including the nondimensional parameter ω , which is defined as the supremum of | f'(t ) | . It is found that the resulting bound on ‖ ∇ T » 22 ‖ grows like √{ω } for ω ≫Ra , with Ra fixed, and like √{Ra } for Ra ≫ω , with ω fixed. Asymptotically, the bound for large Ra has the same leading order behavior as the nonmodulated case, with modulation effects appearing only at O (Ra−1 /2) .
- Publication:
-
Physical Review Fluids
- Pub Date:
- May 2021
- DOI:
- 10.1103/PhysRevFluids.6.L051501
- Bibcode:
- 2021PhRvF...6e1501C