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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]. 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^[2] or active^[3] (example on YouTube of a non-fractal active grid).

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^[4], such as reducing acoustic noise from wings modifying the geometry of spoilers^[5], enhancing heat transfer from impinging jets passing through grids^[6], increasing the drag of flows past normal plates^[7], enhancing mixing by energy-efficient stirring^[8], improved flow metering and flow conditioning in pipes^[9] and improving combustion^[10]. In 2013 the EU awarded a Marie Curie grant of 3.8M Euros for research and training of 13 young scientists and engineers in multiscale turbulence in order to further explore and apply the properties of these flows^[11]^[12].

Multiscale turbulence has also played an important role into probing the internal structure of turbulence^[13]. 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).

References

^ Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (01): 177–196. doi:10.1142/S1756973709000098.
^ Hurst, D.; Vassilicos, J. C. (2007). "Scalings and decay of fractal-generated turbulence". Physics of Fluids. 19 (3): 035103. doi:10.1063/1.2676448.
^ Thormann, A.; Meneveau, C. (February 2014). "Decay of homogeneous, nearly isotropic turbulence behind active fractal grids". Physics of Fluids. 26 (2): 025112. doi:10.1063/1.4865232.
^ Laizet, S.; Sakai, Y.; Vassilicos, J. C. (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. 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. 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. doi:10.1017/jfm.2014.695. {{cite journal}}: no-break space character in |first2= at position 3 (help)
^ 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.
^ 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.
^ "Multisolve". Retrieved 25 February 2015.
^ "Multisolve Marie Curie grant".
^ Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics: 95-114. doi:10.1146/annurev-fluid-010814-014637.

[1] Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (01): 177–196. doi:10.1142/S1756973709000098.

[2] Hurst, D.; Vassilicos, J. C. (2007). "Scalings and decay of fractal-generated turbulence". Physics of Fluids. 19 (3): 035103. doi:10.1063/1.2676448.

[3] Thormann, A.; Meneveau, C. (February 2014). "Decay of homogeneous, nearly isotropic turbulence behind active fractal grids". Physics of Fluids. 26 (2): 025112. doi:10.1063/1.4865232.

[4] Laizet, S.; Sakai, Y.; Vassilicos, J. C. (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. doi:10.1088/0169-5983/45/6/061001.

[5] Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. "Aeroacoustic performance of fractal spoilers". AIAA journal 2012.

[6] 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.

[7] 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. doi:10.1088/0169-5983/45/6/061406.

[8] 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. doi:10.1017/jfm.2014.695. {{cite journal}}: no-break space character in |first2= at position 3 (help)

[9] 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.

[10] 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.

[11] "Multisolve". Retrieved 25 February 2015.

[12] "Multisolve Marie Curie grant".

[13] Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics: 95-114. doi:10.1146/annurev-fluid-010814-014637.

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@@ Line 7: / Line 7: @@
 [[File:Fractalgrids.pdf|thumb|Three examples of multiscale [[Turbulence | turbulence]] generators. From left to right, a [[Fractal|fractal]] cross [[Grid (spatial index)|grid]], a [[Fractal|fractal]] square [[Grid (spatial index)|grid]] and a [[Fractal|fractal]] I [[Grid (spatial index)|grid]]. {{YouTube| id= FaWCLl_qVR4 | title= See}} the [[Manufacturing|manufacturing]] of a fractal grid.]]
-As [[Turbulence | turbulent]] flows contain [[Eddy (fluid dynamics) | eddies]] with a wide range of scales, exciting the [[Turbulence | 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<ref>{{cite journal|last1=Laizet|first1=S.|last2=Sakai|first2=Y.|last3=Vassilicos|first3=J. C.|title=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|journal=Fluid Dynamics Research|date=1 December 2013|volume=45|issue=6|pages=061001|doi=10.1088/0169-5983/45/6/061001}}</ref>, such as reducing [[Noise (acoustic)|acoustic noise]] from wings modifying the geometry of [[Spoiler (aeronautics)|spoilers]]<ref> Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. [http://arc.aiaa.org/doi/pdf/10.2514/1.J051387 "Aeroacoustic performance of fractal spoilers"]. ''[[AIAA journal]]'' 2012.</ref>, enhancing [[Heat transfer|heat transfer]] from impinging jets passing through grids<ref>{{cite journal|last1=Cafiero|first1=G.|last2=Discetti|first2=S.|last3=Astarita|first3=T.|title=Heat transfer enhancement of impinging jets with fractal-generated turbulence|journal=International Journal of Heat and Mass Transfer|date=August 2014|volume=75|pages=173–183|doi=10.1016/j.ijheatmasstransfer.2014.03.049}}</ref>, increasing the [[Drag (physics)|drag]] of flows past normal plates<ref>{{cite journal|last1=Nedić|first1=J.|last2=Ganapathisubramani|first2=B.|last3=Vassilicos|first3=J. C.|title=Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries|journal=Fluid Dynamics Research|date=1 December 2013|volume=45|issue=6|pages=061406|doi=10.1088/0169-5983/45/6/061406}}</ref>, enhancing mixing by energy-efficient stirring<ref>{{cite journal|last1=Laizet|first1=S.|last2=Vassilicos|first2=J. C.|title=Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient|journal=Journal of Fluid Mechanics|date=23 December 2014|volume=764|pages=52–75|doi=10.1017/jfm.2014.695}}</ref>, improved flow metering and flow conditioning in pipes<ref>{{cite journal|last1=Manshoor|first1=B.|last2=Nicolleau|first2=F. C. G. A.|last3=Beck|first3=S. B. M.|title=The fractal flow conditioner for orifice plate flow meters|journal=Flow Measurement and Instrumentation|date=June 2011|volume=22|issue=3|pages=208–214|doi=10.1016/j.flowmeasinst.2011.02.003}}</ref> and improving combustion<ref>{{cite journal|last1=Goh|first1=K. H. H.|last2=Geipel|first2=P.|last3=Lindstedt|first3=R. P.|title=Lean premixed opposed jet flames in fractal grid generated multiscale turbulence|journal=Combustion and Flame|date=September 2014|volume=161|issue=9|pages=2419–2434|doi=10.1016/j.combustflame.2014.03.010}}</ref>. In 2013 the EU awarded a [[Marie Curie Actions|Marie Curie grant]] of 3.8M Euros for research and training of 13 young scientists and engineers in multiscale turbulence in order to further explore and apply the properties of these flows<ref>{{cite web|url=http://www.multisolve.eu|accessdate=25 February 2015|title=Multisolve}}</ref><ref>{{cite web|url=http://cordis.europa.eu/project/rcn/105080_en.html}}</ref>.
+As [[Turbulence | turbulent]] flows contain [[Eddy (fluid dynamics) | eddies]] with a wide range of scales, exciting the [[Turbulence | 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<ref>{{cite journal|last1=Laizet|first1=S.|last2=Sakai|first2=Y.|last3=Vassilicos|first3=J. C.|title=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|journal=Fluid Dynamics Research|date=1 December 2013|volume=45|issue=6|pages=061001|doi=10.1088/0169-5983/45/6/061001}}</ref>, such as reducing [[Noise (acoustic)|acoustic noise]] from wings modifying the geometry of [[Spoiler (aeronautics)|spoilers]]<ref> Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. [http://arc.aiaa.org/doi/pdf/10.2514/1.J051387 "Aeroacoustic performance of fractal spoilers"]. ''[[AIAA journal]]'' 2012.</ref>, enhancing [[Heat transfer|heat transfer]] from impinging jets passing through grids<ref>{{cite journal|last1=Cafiero|first1=G.|last2=Discetti|first2=S.|last3=Astarita|first3=T.|title=Heat transfer enhancement of impinging jets with fractal-generated turbulence|journal=International Journal of Heat and Mass Transfer|date=August 2014|volume=75|pages=173–183|doi=10.1016/j.ijheatmasstransfer.2014.03.049}}</ref>, increasing the [[Drag (physics)|drag]] of flows past normal plates<ref>{{cite journal|last1=Nedić|first1=J.|last2=Ganapathisubramani|first2=B.|last3=Vassilicos|first3=J. C.|title=Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries|journal=Fluid Dynamics Research|date=1 December 2013|volume=45|issue=6|pages=061406|doi=10.1088/0169-5983/45/6/061406}}</ref>, enhancing mixing by energy-efficient stirring<ref>{{cite journal|last1=Laizet|first1=S.|last2=Vassilicos|first2=J. C.|title=Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient|journal=Journal of Fluid Mechanics|date=23 December 2014|volume=764|pages=52–75|doi=10.1017/jfm.2014.695}}</ref>, improved flow metering and flow conditioning in pipes<ref>{{cite journal|last1=Manshoor|first1=B.|last2=Nicolleau|first2=F. C. G. A.|last3=Beck|first3=S. B. M.|title=The fractal flow conditioner for orifice plate flow meters|journal=Flow Measurement and Instrumentation|date=June 2011|volume=22|issue=3|pages=208–214|doi=10.1016/j.flowmeasinst.2011.02.003}}</ref> and improving combustion<ref>{{cite journal|last1=Goh|first1=K. H. H.|last2=Geipel|first2=P.|last3=Lindstedt|first3=R. P.|title=Lean premixed opposed jet flames in fractal grid generated multiscale turbulence|journal=Combustion and Flame|date=September 2014|volume=161|issue=9|pages=2419–2434|doi=10.1016/j.combustflame.2014.03.010}}</ref>. In 2013 the EU awarded a [[Marie Curie Actions|Marie Curie grant]] of 3.8M Euros for research and training of 13 young scientists and engineers in multiscale turbulence in order to further explore and apply the properties of these flows<ref>{{cite web|url=http://www.multisolve.eu|accessdate=25 February 2015|title=Multisolve}}</ref><ref>{{cite web|url=http://cordis.europa.eu/project/rcn/105080_en.html|title=Multisolve Marie Curie grant}}</ref>.
 Multiscale turbulence has also played an important role into probing the internal structure of [[Turbulence | turbulence]]<ref>{{cite journal|last1=Vassilicos|first1=J. C.|title=Dissipation in Turbulent Flows|journal=Annual Review of Fluid Mechanics|date=2015|page=95-114|doi=10.1146/annurev-fluid-010814-014637|url=http://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-010814-014637}}</ref>. This sort of turbulence allowed researchers to unveil a novel [[Dissipation | dissipation]] law in which the parameter <math>C_\epsilon</math> in