Peter Nielsen 教授 特別講演会

The fluid mechanics literature abounds with strange eddy viscosities v_t and other turbulent diffusion coefficients, K: For suspended sediment K increases with sediment settling velocity in a given flow and is different from v_t. Bubbles and momentum display different K_s around plunging jets, K_heat is usually greater than K_salt in the ocean thermocline, while experiments from Kyoto University give the opposite for a different scenario. Some truly strange eddy viscosities are found in oscillatory boundary layer flow. There, the local shear stresses are typically ahead of the local velocity gradients. Hence complex-valued v_t are required with an argument to match the phase shift. Recently considerable progress has been made with respect to rationalising these odd observations. The clue is to use the classical mixing length idea but then not immediately assume that the mixing length l_m is infinitesimal compared to the overall scale L. In other words, we keep more than the Fickian, (or gradient diffusion term) in the mixing flux q_m:

It then turns out that the differential diffusion of suspended sediment can be explained by the term. Each species has its own L, and smaller L gives larger K. Similarly, the phase lead of the shear stress (the momentum flux) in oscillatory flow is explained by the fact that leads . Hence, the total of the [ ] in the middle expression above (with c replaced by u) leads .

The new theory has potential in all turbulent mixing scenarios where l_m/L is finite. Mathematical challenges arise because the untruncated expression for q_m leads to difference equations rather than differential equations.