Turbulence Rough and Smooth

Fluid turbulence exhibits strong and seemingly random fluctuations. Despite the highly turbulent nature of the weather and climate systems, we can forecast both quite well. Large Eddy Simulations (LES) and Reynolds Averaged Navier-Stokes Simulations (RANS) do not resolve small scales but are effective in predicting specific turbulent flows. Can we better understand why this is so? Can we quantify this using experimental observations? Here, we present experimental results from the Max Planck Variable Density Turbulence Tunnel, in which we generated turbulence using an active grid and repeated the process with similar initial conditions up to 30,000 times. Regardless of the turbulence strength and the distance downstream from the grid, we found that the energy carrying large-scales of the turbulence were smooth and reproducible. Smaller-scale turbulence, however, was rough, i.e., completely random. The rough turbulence carried only a small amount of the flow's energy. We observed the transition from smooth to rough turbulence at a length scale slightly smaller than the turbulence's energy injection scale. These findings can be related to modeling carried out in LES and RANS. In LES, velocity decomposes into a filtered or resolved component and a residual component, the latter of which is the sub-grid scale. Conversely, RANS follows a similar principle, modeling turbulent fluctuations through time averaging, similar to what we report in these experiments. As another analogy to LES, the ensemble average in our experiments acts as a filter, and the remaining signal can be interpreted as the resolved component typically used in LES. Conversely, the rough part of our experimental signal corresponds to the sub-grid scale of LES that requires modeling. This means that the cutoff length scale (or, conversely, wavelength) of LES corresponds to the transition from smooth to rough in our measurements, where the velocity field turns from reporducible to random. Our findings suggest that turbulence with similar forcing conditions is reproducible and thus predictable. For example, if the inflow conditions are known, the gusts acting on wind turbines or buildings should be predictable. Specifically, our findings imply that large-eddy and climate simulations do not require full resolution of smaller scales because smooth and rough turbulence are separable.  

This work was conducted with Florencia Falkinhoff and Noe Clavier.