**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]

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 sheddingfrequency;[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 dissipationlaw in which the parameter

${displaystyle C_{epsilon }}$in

is not constant, as required by the Richardson–Kolmogorovenergy cascade. This new law[15] can be expressed as

${displaystyle C_{epsilon }propto {frac {Re_{I}^{m}}{Re_{L}^{n}}}}$, with

${displaystyle mapprox 1approx n}$, 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]

## . . . Multiscale turbulence . . .

- Laizet, S.; Vassilicos, J. C. (January 2009). “Multiscale Generation of Turbulence”.
*Journal of Multiscale Modelling*.**01**(1): 177–196. doi:10.1142/S1756973709000098. - Mazzi, B.; Vassilicos, J. C. (10 March 2004). “Fractal-generated turbulence”.
*Journal of Fluid Mechanics*.**502**: 65–87. Bibcode:2004JFM…502…65M. CiteSeerX 10.1.1.475.2171. doi:10.1017/S0022112003007249. - Hurst, D.; Vassilicos, J. C. (2007). “Scalings and decay of fractal-generated turbulence”.
*Physics of Fluids*.**19**(3): 035103–035103–31. Bibcode:2007PhFl…19c5103H. doi:10.1063/1.2676448. - Nagata, K.; Sakai, Y.; Inaba, T.; Suzuki, H.; Terashima, O.; Suzuki, H. (2013). “Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence”.
*Physics of Fluids*.**25**(6): 065102–065102–26. Bibcode:2013PhFl…25f5102N. doi:10.1063/1.4811402. - Thormann, A.; Meneveau, C. (February 2014). “Decay of homogeneous, nearly isotropic turbulence behind active fractal grids”.
*Physics of Fluids*.**26**(2): 025112. Bibcode:2014PhFl…26b5112T. doi:10.1063/1.4865232. - Laizet, Sylvain; Sakai, Yasuhiko; Christos Vassilicos, J. (1 December 2013). “Special issue of selected papers from the second UK–Japan bilateral Workshop and First ERCOFTAC Workshop on Turbulent Flows Generated/Designed in Multiscale/Fractal Ways, London, March 2012”.
*Fluid Dynamics Research*.**45**(6): 061001. Bibcode:2013FlDyR..45f1001L. doi:10.1088/0169-5983/45/6/061001. - Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. “Aeroacoustic performance of fractal spoilers”.
*AIAA journal*2012. - Cafiero, G.; Discetti, S.; Astarita, T. (August 2014). “Heat transfer enhancement of impinging jets with fractal-generated turbulence”.
*International Journal of Heat and Mass Transfer*.**75**: 173–183. doi:10.1016/j.ijheatmasstransfer.2014.03.049. - Nedić, J.; Ganapathisubramani, B.; Vassilicos, J. C. (1 December 2013). “Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries”.
*Fluid Dynamics Research*.**45**(6): 061406. Bibcode:2013FlDyR..45f1406N. doi:10.1088/0169-5983/45/6/061406. - Laizet, S.; Vassilicos, J. C. (23 December 2014). “Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient”.
*Journal of Fluid Mechanics*.**764**: 52–75. Bibcode:2015JFM…764…52L. doi:10.1017/jfm.2014.695. hdl:10044/1/21530. - Suzuki, H.; Nagata, K.; Sakai, Y.; Hayase, T. (1 December 2010). “Direct numerical simulation of turbulent mixing in regular and fractal grid turbulence”.
*Physica Scripta*.**T142**: 014065. Bibcode:2010PhST..142a4065S. doi:10.1088/0031-8949/2010/T142/014065. - Manshoor, B.; Nicolleau, F. C. G. A.; Beck, S. B. M. (June 2011). “The fractal flow conditioner for orifice plate flow meters”.
*Flow Measurement and Instrumentation*.**22**(3): 208–214. doi:10.1016/j.flowmeasinst.2011.02.003. - Verbeek, A. A.; Bouten, T. W. F. M.; Stoffels, G. G. M.; Geurts, B. J.; van der Meer, T. H. (January 2015). “Fractal turbulence enhancing low-swirl combustion”.
*Combustion and Flame*.**162**(1): 129–143. doi:10.1016/j.combustflame.2014.07.003. - Goh, K. H. H.; Geipel, P.; Lindstedt, R. P. (September 2014). “Lean premixed opposed jet flames in fractal grid generated multiscale turbulence”.
*Combustion and Flame*.**161**(9): 2419–2434. doi:10.1016/j.combustflame.2014.03.010. hdl:10044/1/26010. - Vassilicos, J. C. (2015). “Dissipation in Turbulent Flows”.
*Annual Review of Fluid Mechanics*.**47**(1): 95–114. Bibcode:2015AnRFM..47…95V. doi:10.1146/annurev-fluid-010814-014637. - Castro, Ian P. (2016). “Dissipative distinctions”.
*Journal of Fluid Mechanics*.**788**: 1–4. Bibcode:2016JFM…788….1C. doi:10.1017/jfm.2015.630. ISSN 0022-1120.

## . . . Multiscale turbulence . . .

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