Spectral dynamics of turbulent heat flux in plane Rayleigh–Bénard convection

The spectral budget of the vertical heat flux left angle bracket w theta right angle bracket ⟨ w θ ⟩ $\langle w\theta \rangle$ is investigated in turbulent Rayleigh–Bénard convection by direct numerical simulation. Eight cases spanning three Rayleigh numbers ( italic Ra equals 1 times 10 Superscript 5 Ra = 1 × 10 5 $\textit{Ra} = 1\times 10^5$ , 6 times 10 Superscript 6 6 × 10 6 $6\times 10^6$ and 4 times 10 Superscript 8 4 × 10 8 $4\times 10^8$ ) and up to three geometric aspect ratios each are computed at italic probability equals 1 Pr = 1 $\textit{Pr} = 1$ . The premultiplied spectra of left angle bracket w theta right angle bracket ⟨ w θ ⟩ $\langle w\theta \rangle$ reveal a two-peak structure when both italic Ra Ra $\textit{Ra}$ and upper Gamma <mm