Isotropic turbulence and periodicity: An alternative comprehensive study
Evangelos Akylas and Elias Gravanis
CFE-ERCIM 2012, 1-4 December 2012 in Oviedo, Spain, abstract E1033
Turbulence theory predicts specific laws for the evolution of the turbulence statistics during the period of decay. Under isotropic conditions, statistical arguments allow for the extraction of the well–known Karman–Howarth (KH) equation, which connects the double and triple velocity correlations, averaged over space. Direct Numerical Simulations (DNS) of isotropic turbulence solve massively the velocity field in a bounded periodic box. Although the most common and convenient tool for studying accurately turbulence characteristics, through solving directly the Navier-Stokes equations, the presence of the periodic boundary breaks the isotropy and affects in general the turbulence statistics in a, more or less, unknown way. Periodical boundary conditions are introduced for the first time to KH equation in order to mimic the DNS logic, but keeping, by construction, the isotropy conditions always true. Furthermore, the Oberlack and Peter’s model is analyzed and used in order to close the system of the equations and produce the evolution of the statistics of isotropic decaying turbulence. The results are compared with highly resolved DNS of isotropic turbulence which have been performed in CUT using a parallelized code. The comparison reveals excellent qualitative agreement enlightening the basic mechanism through which the boundary affects the turbulence.
Evangelos Akylas and Elias Gravanis
CFE-ERCIM 2012, 1-4 December 2012 in Oviedo, Spain, abstract E1033
Turbulence theory predicts specific laws for the evolution of the turbulence statistics during the period of decay. Under isotropic conditions, statistical arguments allow for the extraction of the well–known Karman–Howarth (KH) equation, which connects the double and triple velocity correlations, averaged over space. Direct Numerical Simulations (DNS) of isotropic turbulence solve massively the velocity field in a bounded periodic box. Although the most common and convenient tool for studying accurately turbulence characteristics, through solving directly the Navier-Stokes equations, the presence of the periodic boundary breaks the isotropy and affects in general the turbulence statistics in a, more or less, unknown way. Periodical boundary conditions are introduced for the first time to KH equation in order to mimic the DNS logic, but keeping, by construction, the isotropy conditions always true. Furthermore, the Oberlack and Peter’s model is analyzed and used in order to close the system of the equations and produce the evolution of the statistics of isotropic decaying turbulence. The results are compared with highly resolved DNS of isotropic turbulence which have been performed in CUT using a parallelized code. The comparison reveals excellent qualitative agreement enlightening the basic mechanism through which the boundary affects the turbulence.