## Conservation laws of turbulence models.(English)Zbl 1110.76028

Summary: The conservation of mass, momentum, energy, helicity, and enstrophy in fluid flow are important because these quantities organize a flow, and characterize change in the flow structure over time. In turbulent flow, conservation laws remain important in the inertial range of wave numbers, where viscous effects are negligible. It is in the inertial range where energy, helicity (3d), and enstrophy (2d) must be accurately cascaded for a turbulence model to be qualitatively correct. A first and necessary step for an accurate cascade is conservation; however, many turbulent flow simulations are based on turbulence models whose conservation properties are little explored and might be very different from those of Navier-Stokes equations. We explore conservation laws and approximate conservation laws satisfied by LES turbulence models. For the Leray, Leray deconvolution, Bardina, and $$N$$th order deconvolution models, we give exact or approximate laws for a model mass, momentum, energy, enstrophy and helicity. The possibility of cascades for model quantities is also discussed.

### MSC:

 76F99 Turbulence 76F65 Direct numerical and large eddy simulation of turbulence

### Keywords:

deconvolution; helicity; Leray model; Bardina model
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### References:

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