Modulation of turbulent Rayleigh-Bénard convection under spatially harmonic heating.

We numerically study turbulent Rayleigh-Bénard (RB) convection under spatial temperature modulation, where the bottom temperature varies sinusoidally around a mean value in space. Both two- and three-dimensional simulations are performed over the Rayleigh number range 10^{7}≤Ra≤10^{10} and the wave number range 1≤k≤120 at fixed Prandtl number Pr=0.7.