Numerical simulations of a thermocline in a pressure-driven flow between two infinite horizontal plates

Direct numerical simulations of pressure-driven flow between two infinite horizontal plates with a stabilizing temperature difference imposed on the plates are presented, for different Grashof numbers. A thermocline-like solution is obtained. The thermocline decorrelates velocity fluctuations which results in a high mean flow velocity. Temperature fluctuations decorrelate from the vertical velocity fluctuations and it is found that although ⟨ T ′ 2 ⟩ and ⟨ υ ′ 2 ⟩ increase with Grashof number, ⟨ υ ′ T ′ ⟩ decreases. It is argued from the simulations that this behavior is due to internal gravity waves. It is also found that the demands on the size of the computational box increase with Grashof number.