Modelling nonlinear systemsby scale considerations

The macroscopic scale equations which generate locally averaged or filtered variables for nonlinear applications are examined. Conditions of consistency are derived that describe how well the filtered variables satisfy the exact macroscopic scale equations given any model for the residual. An approximate model for the residual is constructed for general nonlinear systems. The theory is demonstrated for the Euler equations for compressible fluid flow and an assessment of the residual model based on global energy balance is made by a numerical experiment.