Scaling in hard turbulent Rayleigh-Bénard flow

Abstract

Rayleigh-Bénard flow for Rayleigh numbers Ra=108¿1011 (hard turbulence regime) is studied solving the Boussinesq equations with the Fourier-Weierstrass ansatz introduced recently [Eggers and Grossmann, Phys. Fluids A 3, 1958 (1991)]. The plumes and swirls detaching from the boundary layers are mimicked by volume stirring on all scales down to the Rayleigh-number-dependent scale of these thermals. Wave-number spectra, frequency spectra, and structure functions are presented both for velocity and temperature fluctuations. As the scale decreases the velocity-temperature cross correlation decreases much faster than both velocity and temperature autocorrelations. In the viscous subrange all wave-number spectra decay exponentially. Based on the experimental Ra dependence of the mean temperature fluctuations we can calculate the Ra dependence of the mean velocity fluctuations as well as of the mean temperature and velocity time derivatives. The inner length scale eta is found to scale [is proportional to] Ra-0.32±0.01