Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation
Iwayama, T., Watanabe, T. and Shepherd, T. G. (2001) Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation. Journal of the Physical Society of Japan, 70 (2). pp. 376-386. ISSN 1347-4073
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To link to this article DOI: 10.1143/JPSJ.70.376
The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number kE corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime (k →0) is theoretically derived to be E(k) ∼k5, using a quasinormal 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 Π(k) for k< kE can be entirely expressed by Π(-)(k), which is the total net input of energy to wave numbers <k arising from interactions with wave numbers p, q > k. Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log (k/kE)<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four. ©2001 The Physical Society of Japan