Abstract
Understanding the behavior of the kinetic energy spectrum and flux in two-dimensional (2D) turbulent thermal convection remains a challenge. In this paper, using high-resolution direct numerical simulation of Rayleigh-Bénard convection for Rayleigh numbers – and unit Prandtl number, we show that 2D turbulent convection exhibits Bolgiano-Obukhov scaling. At small wave numbers, where buoyancy feeds energy to the velocity field, kinetic energy exhibits inverse cascade. Consequently, the kinetic energy spectrum scales as and the kinetic energy flux shows scaling at small wave numbers. Buoyancy is weakened at large wave numbers, and this leads to a constant enstrophy cascade and kinetic energy spectrum, similar to 2D hydrodynamic turbulence. However, the entropy spectrum exhibits a bispectrum with the upper branch varying as . We also observe constant entropy flux in the inertial range. Finally, we also draw a connection between the entropy flux in the dissipation range and the entropy dissipation rate in the bulk.
4 More- Received 1 March 2023
- Accepted 5 January 2024
DOI:https://doi.org/10.1103/PhysRevFluids.9.023502
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