# Cascade vs Inverse Cascade: Energy flow in 2D and 3D turbulence

We know that vortices tend to coalesce in 2D(inverse cascade) as opposed to 3D where they 'break down' into smaller vortices(cascade) ie. energy flows fro larger to smaller scales in 3D and opposite direction in 2D.

Can this be physically explained?

Can this be, in any way, interpreted from the vorticity equation :

$$\partial_t \vec{\omega} +( \vec{u} \cdot \nabla)\vec{\omega} = ( \vec{\omega} \cdot \nabla)\vec{u}+\nu \nabla^2 \vec{\omega}?$$

• Are you perhaps looking for something like this? – Deep Feb 1 '18 at 6:10