Frequency power spectrum of the vertical velocity component υ extracted in the middle of the stable layer at (x, y, z) = (−0.2, 2.5, −0.2) over the time series t ∈ (10τ_conv, 32τ_conv) in the problem of turbulent convection and wave excitation described in Sec. 3.2. These results are obtained on a grid with 128³ cells, using the LHLLC Riemann solver and the CTO-WENO scheme of Kolb (2014) for different values of the parameter ε _WENO occurring in the smoothness indicators of the scheme (see Sect. C), ranging from 10⁻¹² to 10². As a reference, power spectra obtained with the numerical options LHLLC + PPM84 and LHLLC + LIN + VL are also shown. The convective turnover frequency (ω_conv = 2π/τ_conv), the Brunt-Väisälä frequency at the location of the point probe (N_BV), and the frequency of the fundamental oscillation mode of the cavity (ω₀ = 1.1) are represented by the black dashed-dotted, dashed, and dotted lines, respectively.