Physics of Fluids -- January 1997 -- Volume 9, Issue 1, pp. 171-180

### On the decay of two-dimensional homogeneous turbulence

- J. R. Chasnov
*The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong*

(Received 19 June 1996; accepted 3 September 1996)

Direct^{ }numerical simulations of decaying two-dimensional turbulence in a fluid of^{ }large extent are performed primarily to ascertain the asymptotic decay^{ }laws of the energy and enstrophy. It is determined that^{ }a critical Reynolds number *R*_{c} exists such that for initial^{ }Reynolds numbers with *R*(0) < *R*_{c} final period of decay solutions result,^{ }whereas for *R*(0) > *R*_{c} the flow field evolves with increasing Reynolds^{ }number. Exactly at *R*(0)=*R*_{c}, the turbulence evolves with constant Reynolds^{ }number and the energy decays as *t*^{ – 1} and the enstrophy^{ }as *t*^{ – 2}. A *t*^{ – 2} decay law for the enstrophy was^{ }originally predicted by Batchelor for large Reynolds numbers [Phys. Fluids^{ }Suppl. II, **12**, 233 (1969)]. Numerical simulations are then performed^{ }for a wide range of initial Reynolds numbers with *R*(0) > *R*_{c}^{ }to study whether a universal power-law decay for the energy^{ }and enstrophy exist as *t*. Different scaling laws are observed^{ }for *R*(0) moderately larger than *R*_{c}. When *R*(0) becomes sufficiently^{ }large so that the energy remains essentially constant, the enstrophy^{ }decays at large times as approximately *t*^{ – 0.8}. ©*1997 American Institute*^{ }of Physics. ^{ }

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