Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation

The low wave number range of decaying turbulence governed by the Charney-Ha segawa-Mima (CHM) equation is examined theoretically and by direct numerica l simulation. Here, the low wave number range is defined as values of the w ave number k below the wave number k(E) corresponding to the peak of the en ergy spectrum, or alternatively the centroid wave number of the energy spec trum. The energy spectrum in the low wave number range in the infrared regi me (k -> 0) is theoretically derived to be E(k) similar to k(5), using a qu asinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads (k, p, q) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux II(k) for k < k(E) can be entirely expressed by II(-)(k), which is the total net input of energy to w ave numbers < k arising from interactions with wave numbers p, q > k. Furth ermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log(k/k(E)) < -0.5, where the nonlo cal interactions are defined to be those triad interactions for which the r atio of the largest leg of the triad to the smallest leg is larger than fou r.