A family of new, high order NS-α models arising from helicity correction in Leray turbulence models

This report gives a reinterpretation of the NS-α model which leads to a family of high order NS-α-deconvolution models with NS-α as the zeroth order case. First, we show that the Navier–Stokes-α model arises by adding helicity correction to Leray-α model. Higher order Leray models have recently been proposed in [W. Layton, R. Lewandowski, A high accuracy Leray-deconvolution model of turbulence and its limiting behavior, Anal. Appl. 6 (1) (2008); W. Layton, C. Manica, M. Neda, L. Rebholz, Numerical analysis and computational testing of a high-accuracy Leray-deconvolution model of turbulence, Numer. Methods Partial Differential Equations, in press]: the so-called Leray-deconvolution models, that employ van Cittert approximate deconvolution to decrease consistency error. We use an analogous helicity correction idea to develop a family of higher order accurate NS-α type models, the NS-α-deconvolution models. We prove several mathematical and physical properties for this new family of models and discuss the design of efficient algorithms for them.