A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence

Energy transfer in turbulence is a result of nonlinear interactions among different scales of motion. For the purposes of quantitative analyses, various definitions of scales of motion can be used. This nonuniqueness leads to the possibility, raised in the literature on the subject, that properties of the energy transfer deduced from such analyses can be qualitatively affected by the scale definitions employed. We address this question by computing detailed energy exchanges between different scales of motion in direct numerical simulations databases of isotropic turbulence and employing different scale definitions. The scales of motion are defined by decomposing velocity fields using three specific filters: sharp spectral, Gaussian, and tangent hyperbolic. The traditional analysis of the energy transfer in terms of sharp spectral filters is generalized to smooth filters with broad support in the spectral space. The computed detailed energy transfer functions show only a minor quantitative dependence on the filter type. The qualitative conclusions obtained using sharp spectral filters are the same as for smooth filters, unless the latter has a very broad spectral support. (C) 2007 American Institute of Physics.