Key points are not available for this paper at this time.
The dynamical equations which describe the behavior of isotropic turbulence in two dimensions are derived on the basis of the hypothesis that fourth-order cumulants of the velocity field are zero. The equations are then integrated numerically as an initial-value problem for an inviscid fluid. The result shows that the calculated rate of energy transfer is greater toward the larger scales than the smaller scales. The most remarkable feature revealed by the computation is that the energy-spectrum function assumes negative values during the course of time for medium-sized eddies. Truncation errors which arise from finite difference approximations in numerical integration are examined. From this result, it is concluded that the hypothesis of zero fourth-order cumulants does not always guarantee positive energy, at least, for a turbulent flow in two dimensions.
Yoshimitsu Ogura (Sun,) studied this question.