Numerical Simulation of Two-Dimensional Turbulence

The two‐dimensional incompressible Navier‐Stokes equations are numerically integrated in order to test the validity of Kraichnan's predictions on the structure of two‐dimensional turbulence. The numerically simulated turbulence is produced by an artificial forcing function, constructed from a randomly varying set of Fourier modes lying within a narrow spectral band near scalar wavenumber $k_e$ . For the case of turbulence maintained by a constant rate of energy injection, Kraichnan predicts the development of two power‐law energy spectra, a $k^{\text{−5/3}}$ range for frequencies less than $k_e$ , and a $k^{\text{−3}}$ range for those greater than $k_e$ . The numerical results are consistent with these predictions, although truncation and aliasing errors restrict the useful spectral range of the calculations to less than that desirable for a fully satisfactory test. The predictions and results are apparently relevant to several areas of geophysical fluid dynamics and to the correct interpretation of other numerical simulation experiments.