Abstract
Rigorous estimates to support the Batchelor–Kraichnan–Leith theory of 2-D turbulence are made for time-dependent forcing at all length scales. The main estimate, derived under several different assumptions on the smoothness of the force in space and time, bounds the dissipation wavenumber κ η from above and below in terms of a generalized Grashof number. That estimate is shown to be connected to the energy power law, the dissipation law, and the enstrophy cascade. These results impose certain restrictions on the shape of the force, which in several cases is allowed to be discontinuous in time.
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