Abstract
This study examines the dual transfer and spectral scaling laws in forced two-dimensional Navier–Stokes turbulence. The k−5∕3 energy inertial range emerges from this analysis as a minimally steep range that is barely able to support an inverse energy cascade. In other words, an energy inertial range shallower than k−5∕3 is incapable of sustaining a persistent transfer of energy to the large scales, and steeper inertial ranges are possible. The vorticity is found to diverge in the limit of large Reynolds numbers or small viscosity, allowing the classical k−3 enstrophy inertial range to be the only one that may remain bounded in this limit. Steeper (unbounded) enstrophy inertial ranges cannot be ruled out.
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