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.^[1][2] This is usually achieved by immersing in a moving fluid a body with a multiscale, often fractal-like, arrangement of length scales. This arrangement of scales can be either passive^[3][4] or active^[5]

Three examples of multiscale turbulence generators. From left to right, a fractal cross grid, a fractal square grid and a fractal I grid. See on YouTube the manufacturing of a fractal 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.,^[6] such as:

• Reducing acoustic noise from wings by modifying the geometry of spoilers;^[7]
• Enhancing heat transfer from impinging jets passing through grids;^[8]
• Reducing the vortex shedding intensity of flows past normal plates without changing the shedding frequency;^[9]
• Enhancing mixing by energy-efficient stirring;^[10][11]
• Improving flow metering and flow conditioning in pipes;^[12]
• Improving combustion.^[13][14]

Multiscale turbulence has also played an important role into probing the internal structure of turbulence.^[15] This sort of turbulence allowed researchers to unveil a novel dissipation law in which the parameter ${\displaystyle C_{\epsilon }}$ in

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

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law^[15] can be expressed as ${\displaystyle C_{\epsilon }\propto {\frac {Re_{I}^{m}}{Re_{L}^{n}}}}$, with ${\displaystyle m\approx 1\approx n}$, where ${\displaystyle Re_{I}}$ and ${\displaystyle Re_{L}}$ are Reynolds numbers based, respectively, on initial/global conditions (such as free-stream velocity and the object's length scale) and local conditions (such as the rms velocity and integral length scale). This new dissipation law characterises non-equilibrium turbulence apparently universally in various flows (not just multiscale turbulence) and results from non-equilibrium unsteady energy cascade. This imbalance implies that new mean flow scalings exist for free shear turbulent flows, as already observed in axisymmetric wakes^[15][16]