Fourier-Weierstrass mode analysis for thermally driven turbulence

The eddy size and temperature distribution in the inertial subrange of turbulent Rayleigh-Bénard flow at a Rayleigh number Ra≊${10}^{11}$ is calculated from the Boussinesq equations. Velocity and temperature fields are decomposed into Fourier modes with geometrically scaling wave numbers. 1/3 scaling for both velocity u and temperature FTHETA is obtained in agreement with Shraiman and Siggia’s finding, but there is no indication of a new scaling range as claimed recently. We resolve this discrepancy. The isotropization by eddy decay is demonstrated in terms of the ${\mathit{u}}_3$FTHETA scaling, which appreciably differs from 2/3; testing this new quantity experimentally would be of great interest.