Effect of Mean Flow Shear on Cross Phase and Transport Reconsidered

We reconsider the important question of the effect of a strong mean shear flow on the transport of a passive scalar field. By incorporating the effect of resonance, we show that the flux scales with the mean shear $\Omega$ as ${\Omega }^{-1}$. The results also indicate that the scaling of the flux and cross phase with shear is rather weak and that the cross phase is not always more heavily suppressed than the amplitude of the turbulence. Furthermore, we show that the scalings of flux and cross phase with $\Omega$ depend on the statistics of the turbulent flow.

Figure 1

Spectral intensity is localized within width $W_k$ around rational surface $x=0$. The maximum of the intensity is slightly shifted from $x=0$ by $\Delta$ due to the shear. This shift $\Delta$ is exaggerated for clarity.