In three-dimensional turbulence, vortex stretching is the central mechanism enabling the transfer of kinetic energy toward smaller scales. If vortex stretching is absent in three-dimensional turbulence, energy is no longer conserved and enstrophy cascades to smaller scales. In this paper we propose a system that interpolates between these two cases by reducing the strength of vortex stretching in the Navier-Stokes equations. The resulting dynamics yield a cascade that is neither a pure energy cascade nor a pure enstrophy cascade. We refer to this process as a mesostrophy cascade. We formulate a consistent picture describing this cascade and the characteristic scales involved in the mesostrophy balance. We illustrate this picture via numerical integrations of the eddy-damped quasinormal Markovian model with reduced vortex stretching.

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• Energy cascade
• Enstrophy
• Isotropic turbulence
• Three-dimensional turbulence