Numerical simulation of developing and decaying two-dimensional turbulence

Abstract

Two-dimensional isotropic turbulence is investigated in its development from an arbitrarily specified initial flow through its transformation into a statistically self-preserving decaying flow. Numerical simulation is the principal method of investigation. The early development is characterized by rapid growth of the mean squared vorticity gradient, and this growth is found to be predicted satisfactorily by the quasi-normal hypothesis. During the later states of decay the numerical results are found to be generally consistent with the predictions by Kraichnan, Leith and Batchelor of a k−3 inertial range spectrum. The dimensionless constant of the spectrum is found to be near 2, about half the value found earlier for turbulence maintained by a constant forcing amplitude. The results are also consistent with Batchelor's predictions of the time-dependent behaviour of certain quadratic moments: An inconsistency in those predictions is pointed out, however, which can be resolved by altering the inertial range spectrum by a logarithmic term, as suggested by Kraichnan. The most important two-point Eulerian correlation functions are exhibited. An investigation is made of the Gaussianity of the flow with results indicating a strong tendency toward intermittency in the enstrophy dissipation.