Thu June 16th 2011
Journal Club Static structure function of turbulent flow from the Navier-Stokes equations
Detlef Lohse


The velocity field of a fully developed isotropic turbulent flow is decomposed into a smoothed field ui(r) and a strongly fluctuating part ûi(r) depending on a length r which is varied through all scales. The eddies described by ui(r) loose their energy either by direct dissipation or by energy transfer to the ûi(r)-eddies. Both contributions can be traced back to the second order static structure function D(r) and the Lagrangian time correlation function. The latter can also be evaluated in terms of D(r). The energy balance then gives an integro-differential equation for D(r) which determines D(r) uniquely. The solution is not only in agreement with the scaling behaviour in the viscous and inertial subranges as predicted by dimensional arguments, but it also gives the correct transition between the two regimes. A comparison with experimental data is offered.

“Static structure function of turbulent flow from the Navier-Stokes equations”, H. Effinger and S. Grossmann. Zeitschrift für Physik B Condensed Matter. Vol. 66, 3 (1987).
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing