Flow, Turbulence and Combustion

, Volume 101, Issue 2, pp 343–364 | Cite as

Effects of Discrete Energy and Helicity Conservation in Numerical Simulations of Helical Turbulence

  • Francesco CapuanoEmail author
  • Donato Vallefuoco


Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an inviscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space- and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations.


Helicity Discrete conservation properties Turbulence 


Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Industriale (DII)Università di Napoli “Federico II”NapoliItaly
  2. 2.Fluid Mechanics and Acoustics LaboratoryÉcole Centrale de Lyon, UMR 5509 CNRSLyonFrance

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