Extended Data Fig. 1: Anisotropic growth rate spectrum of the KH instability, along with the spectra of energies.

The mean flow is directed along x and varies along z. The spectrum of the linear growth rate γ_KH of the KH instability is anisotropic. The growth rate is the largest around k = (±0.5, 0), which represents the 2D KH instability. The growth rate is zero for k_x = 0 and k_y ≠ 0. The square boxes in the upper half of the figure show time-averaged spectra of energies in horizontal field E(b_x) and horizontal flow E(u_x) (the contribution of the initial mean flow is removed). These spectra share the upper right-hand logarithmic colour bar, extending from yellow to black. The square boxes in the lower half of the figure show time-averaged spectra of energies in vertical field E(b_z) and vertical flow E(u_z). These share the lower right-hand linear colour bar, extending from white to blue. The center of each square box represents the wavenumber resolved in the nonlinear simulation (only a small part of the wavenumber range is shown, as the KH instability exists at large scales |ka| ≱ 1). The special square box centred at k = (0,0) is shared by four quadrants. All quantities are measured using a and U₀.