A hierarchical turbulence model

A system of ordinary differential equations obtained by projecting the Navier-Stokes equation onto a special type of functional basis is considered. The basis describes the aggregate of vortices of different scale. The centers of vortices of various sizes move in a composite field of the velocities of all the larger vortices. The dynamic system corresponding to this basis is found to be only weakly connected. Only a limited number of variables appear in each significant component of the system. The variables pertain to the vortices of similar size that are overlapping one another in space. In the representation given here, the equations describing the cascade transfer of energy along the spectrum are obtained without resorting to the suppositions used in deriving phenomenological equations in cascade models of turbulence.