Scaling law for coherent vortices in decaying drift Rossby wave turbulence

We numerically study the time evolution of coherent vortices in decaying turbulence described by the Charney-Hasegawa-Mima equation with the weak dissipation. Self-organized coherent vortices develop through the mutual advection and the vortex merging. The dimensional analysis provides the dynamical scaling law of structure function of the potential vorticity field S(k,t) = E(5/4)lambda(1/2)t(1/2)G(k/(k) over bar(t)) [(k) over bar(t) similar to E(-1/8)lambda(3/4)t(-1/4)] with a scaling function G(x), which turns out to be in good agreement with numerical experiments. In physical space, quantities related to coherent vortices develop algebraically with time. The dimensional analysis predicts that the total number N of vortices decreases as N similar to t(-chi) with exponent chi = 1/2. Moreover, it is found that the remarkable feature of this system is the approximate conservation of the area of the coherent region in the potential vorticity field.