Extended Data Fig. 2: Rossby/drift wave turbulence.
Simulations of Eq. (27) describing Rossby/drift wave turbulence demonstrates one-dimensionalization of the 2D flow and the appearance of a pattern with characteristic scale given by the Rhines scale 1/kR13,14,15,16,17,18,19,127. Each column shows, from top to bottom: (i) the vorticity averaged along the y direction at final time, (ii) the vorticity field at final time, (iii) the power spectrum of the vorticity averaged over the last 1/6 of the simulation and (iv) the ky average of this quantity. The equation is integrated using the pseudospectral solver Dedalus128 on a L × L square domain with size L = 2π discretized with N = 256 Fourier harmonics per dimension using a 3rd-order 4-stage Diagonally Implicit/Explicit Runge-Kutta scheme (RK433 in Dedalus)166 with an adaptive timestep for 1500 simulation time units. The forcing is taken to be a Gaussian random field concentrated on a ring of radius kf = 28 (red line) and bandwidth kfw = 1.5 (light red rectangle) in Fourier space, scaled by the forcing rate ϵ = 0.001. We take a linear drag α = 0.01, a viscosity ν = 0.00001. The β parameter is (a) β = 0, (b) β = 20, (c) β = 40, (d) β = 80, leading to the measured values of the Rhines wavenumber \({k}_{{\rm{R}}}=1/2\sqrt{\beta /{U}_{{\rm{rms}}}}\) given in the figure (blue line in the bottom plots) in which Urms is obtained from the measured energy spectrum.
