theory. Here, the philosophy is rather different: no parametrization of the turbulence cascade is sought, $\rho$ is chosen arbitrarily large, and the similarity with real turbulence is expected to be only kinematic. (Also, the separation of a Kolmogorov constant out of the energy flux $\bar\epsilon$ is arbitrary).

Things can be made a little bit more quantitative, introducing scale by scale the sweep time: $$T_k=k^{-1}\langle u^2\rangle^{-\frac{1}{2}}
\sim \Ckol^{-\frac{1}{2}}\flux^{-\frac{2}{3}}k_0^\frac{1}{3}k^{-1}.
\eqno(2.8)$$ i.e. the time needed to a vortex of size $k^{-1}$ to pass in front of a fixed probe. We see that sweep is important for all scales for which $\gamma_kT_k<1$, i.e., from Eqns. (2.4) and (2.6), for $k>k_0\rho^3$. The Kraichnan model is recovered when sweep can be neglected in all of the inertial range, i.e. for $\rho>(\eta k_0)^{-\frac{1}{3}}$. This means basically that the zero correlation time limit is taken before the infinite Reynolds number limit $\eta k_0\to 0$. In this regime we have: $$\U_\k(t)
\simeq \frac{\k_\perp\k_\perp}{k^2}\frac{2\pi}{\rho}\Ckol^\frac{1}{2}\flux^\frac{1}{3} 
k^{-\frac{10}{3}} \delta(t)
\eqno(2.9)$$ To understand what happens in the regime of dominant sweep, it is convenient to shift to Lagrangian coordinates. Introduce then the coordinate $\z(t|\x,t_0)$ of a fluid parcel which at time $t_0$ is at $\x$, and define the Lagrangian velocity: $$\u^\smalL(\x,t)=\u(\z(t|\x,0),t)
\eqno(2.10)$$ and analogous 