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Analysis and Modelling of the Commutation Error

A multiscale dynamic analysis of the commutation error, based on the filtering approach is performed. The similarity multiscale hypothesis proposed by Bardina (1983) and extended by Geurts and Holm (2006) to the commutation error is examined in detail and an extension of the Germano identity to the analysis and the modelling of the commutation error is proposed. For a detailed analysis under controlled condition the method is first applied to synthetic turbulence and subsequently to the a-priori analysis of a turbulent channel flow at Reτ=590. The results illustrate the flexibility of the dynamic modelling approach. Combined with a scale similarity assumption for the commutation error very satisfactory results have been obtained for first order derivatives and reasonable results for second order derivatives. In all cases the modelling of the commutation error resulted in smaller errors than the error obtained by neglecting the commutation error.