SELF-SIMILARITY OF DECAYING 2-DIMENSIONAL TURBULENCE

Simulations of decaying two-dimensional turbulence suggest that the on e-point vorticity density has the self-similar form P omega similar to t f(omega t) implied by Batchelor's (1969) similarity hypothesis, exc ept in the tails. Specifically, similarity holds for \omega\ < omega(m ), while p(omega) falls off rapidly above. The upper bound of the simi larity range, omega(m), is also nearly conserved in high-Reynolds-numb er hyperviscosity simulations and appears to be related to the average amplitude of the most intense vortices (McWilliams 1990), which was a n important ingredient in the vortex scaling theory of Carnevale et al . (1991). The universal function f also appears to be hyperbolic, i.e. f(x) similar to c/2\X\(1+qc), for \x\ > x, where q(c) = 0.4 and x* = 70, which along with the truncated similarity form implies a phase tr ansition in the vorticity moments [GRAPHICS] between the self-similar 'background sea' and the coherent vortices. Here c(q) and c are univer sal. Low-order moments are therefore consistent with Batchelor's simil arity hypothesis whereas high-order moments are similar to those predi cted by Carnevale et al. (1991). A self-similar but less well-founded expression for the energy spectrum is also proposed. It is also argued that omega(s) = x/t represents 'mean sea-level', i.e. the (average) threshold separating the vortices and the sea, and that there is a spe ctrum of vortices with amplitudes in the range (omega(s),omega(m)). Th e total area occupied by vortices is also found to remain constant in time, with losses due to mergers of large-amplitude vortices being bal anced by gains due to production of weak vortices. By contrast, the ar ea occupied by vortices above a fixed threshold decays in time as obse rved by McWilliams (1990).