Early stages of the reference solution. Mid-layer temperature distributions (at z_m) at times tu_rmsk_f = 3.4 (top) and tu_rmsk_f = 362.0 (middle), plotted as functions of x and y. In each plot, the mid-layer temperature is normalised by its mean value (horizontally averaged), with the contours showing the deviations from the mean. Bottom: mid-layer kinetic energy spectra at the same times, normalised by the average kinetic energy at z_m at each time. Here k is the horizontal wavenumber (in the x direction), whilst k₁ = 2π∕λ is the fundamental mode. The inset highlights the low wavenumber behaviour, using a non-logarithmic abscissa to include k∕k₁ = 0.