Abstract
The mean pressure distribution plays an important role in the dynamics of Rayleigh-Bénard convection (RBC). In this work, the mean momentum balance equation is analyzed to reveal the properties of the mean modified pressure. The main findings of the present work include the following. (i) In a turbulent RBC, the mean modified pressure peaks in the near-wall region, and the peak location is found to scale with the Townsend inner length scale. (ii) In the outer layer of a turbulent RBC, the shape of the mean modified pressure is similar to that of the Reynolds normal stress in the vertical direction. (iii) In a turbulent RBC, the modified pressure has a negative trough in the core of the RBC cell. The negative modified pressure at the RBC mid-height dictates an inequality among key parameters for a turbulent RBC including the Prandtl number, Rayleigh number, rms Péclet number, and thermal displacement thickness. The inequality is confirmed by experimental and direct numerical simulation data.
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