Numerical Evidence of the k⁻³ Energy Spectrum in Two-Dimensional Turbulence

Abstract

Two-dimensional Navier-Stokes turbulence at very high Reynolds numbers is numerically investigated by the use of spectral method. The energy spectrum obtained here reveals almost the theoretically predicted k⁻³ law in the inertial subrange at Reynolds numbers 5000 and 10000, while giving the k⁻⁴ law at Reynolds number 1000 in agreement with the results of all the so far known numerical work.