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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