Multiscale turbulence

Multiscale turbulence is a class of turbulent flows in which the chaotic motion of the fluid is forced at different length and/or time scales. This is usually achieved by immersing a body in a moving fluid; the obstacle may have a specific arrangement of length scales or have it's geometry actively changed by some control system (as illustrated on YouTube).

Three examples of multiscale turbulence generators. From left to right, a fractal cross grid, a fractal square grid and a fractal I grid.

As turbulent flows contain eddies with a wide range of scales, exciting the turbulence at particular scales (or range of scales) allows one to fine-tune the properties of that flow. Multiscale turbulent flows have been successfully applied in different fields, such as reducing acoustic noise from wings modifying the geometry of spoilers, enhancing heat transfer from impinging jets passing through grids, increasing the drag of flows past normal plates or enhancing mixing . Further research of multiscale turbulence is currently in place in order to further explore the properties of these flows.

Multiscale turbulence has also played an important role into probing the internal structure of turbulence. This sort of turbulence allowed researchers to unveil a novel dissipation law in which the parameter $C_{\epsilon }$ in

$\epsilon =C_{\epsilon }{\frac {{\mathcal {U}}^{3}}{\mathcal {L}}}$

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law can be expressed as $C_{\epsilon }\propto {\frac {Re_{I}^{m}}{Re_{L}^{n}}}$, with $m\approx n$, where $Re_{I}$ and $Re_{L}$ are respectively Reynolds numbers based on initial (such as free-stream velocity and the object's length scale) and local conditions (such as the rms velocity and integral length scale). The region of the flow where this new law holds is termed non-equilibrium turbulence as it implies an imbalance between the energy fed down the cascade by the large (energy containing) scales and that which is dissipated (at the smallest scales).