Discrete Conservation of Helicity in Numerical Simulations of Incompressible Turbulent Flows

  • D. Vallefuoco
  • F. CapuanoEmail author
  • G. Coppola
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an inviscid invariant of the 3D incompressible Navier–Stokes equations,
$$\frac{\partial {u}_{i}}{\partial t} + \mathscr {N}_{i}({u}) = -\frac{\partial {p}}{\partial x_{i}} + \frac{1}{\text {Re}}\frac{\partial ^2 {u}_{i}}{\partial x_{j}\partial x_{j}}, \quad \quad \frac{\partial {u}_{i}}{\partial x_{i}}=0 \;,$$
where \(\mathscr {N}_{i}(u)\) is the non-linear convective term and Re is the Reynolds number.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LMFA, École Centrale de LyonÉcullyFrance
  2. 2.University of Naples Federico IINaplesItaly

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