Frequency-averaged dissipation rates as a function of the aspect ratio (left), of the number of steps (middle), and of the ratio (right), using vertically periodic boundary conditions. These results were obtained for one stably stratified interface and E = K = 10⁻⁵. In each panel the orange filled circles correspond to the total dissipation rate, while its viscous and thermal contributions are represented by the empty red triangles and blue squares, respectively. On the y-axis, the frequency-averaged dissipation rates in the layered case, , is normalised by the frequency-averaged dissipation rate of the fully convective case, , which is indicated by the horizontal blue dashed line. We adopted a forcing amplitude that is proportional to ω for these calculations.