Abstract
A simplified closure model for turbulent spectral dynamics is proposed. Beginning with an analytical closure similar to the test field model, energy transfer is modeled by replacing general triad interactions by degenerate triad interactions, resulting in a pair interaction description similar to the classical Heisenberg model. This energy transfer model is coupled to a similarly simplified time scale evolution equation. These simplifications make it possible to preserve many features of much more complex analytical closures like the direct interaction approximation and the Lagrangian renormalized approximation in a computationally tractable model. The model is tested in decaying isotropic turbulence and in forced isotropic turbulence. It is found to exhibit refined properties, including energy backscatter to large scales and the bottleneck phenomenon.
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